Mechanical Systems and Signal Processing 182 (2023) 109496
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Mechanical Systems and Signal Processing
journal homepage: www.elsevier.com/locate/ymssp
Invited Review Paper
Towards novel energy shunt inspired vibration suppression
techniques: Principles, designs and applications
Xingbao Huang, Bintang Yang *
State Key Laboratory of Mechanical Systems and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240,
China
A R T I C L E I N F O
A B S T R A C T
Communicated by Miguel Matos Neves
Vibration control is an overwhelmingly concerned issue that exists in many industrial fields such
as machinery, aerospace and civil engineering. Indeed, in terms of energy perspective, the nature
of vibration control is scientifically disposing the vibration energy migration issues and enhancing
the energy transfer, conversion and dissipation. It should be noted that high-efficiency vibration
suppression is conducive to improving the working capability of mechanical devices, prolonging
the service life of sensitive components, and promoting the security and stability of flexible ar­
chitectures. Due to the attractive merits such as easy design, friendly installation, low attached
mass and wideband vibration attenuation, the dynamic vibration absorbers (DVAs) are exten­
sively developed and employed. This review paper is committed to investigate the current
multifarious vibration suppression technologies and establish the collaboration between various
vibration control methods from the perspective of energy shunt. Moreover, several attempts are
conducted to provide feasible guidance for the development direction of state-of-the-art nonlinear
DVAs in the future. In terms of energy shunt concept, general vibration control methods can be
innovatively divided into regression energy strategy, syntonic elastic energy strategy, heat energy
dissipation strategy and regenerative energy strategy. The regression energy strategy refers to
energy sinks in which the trapped energy is mainly exploited to overcome intra-well or inter-well
barrier. Syntonic elastic energy strategy is employed to describe the local resonance deformation
energy generation and dissipation, such as distortion of substructures in metamaterials. Dampers
mainly consider the use of damping force to dissipate kinetic energy, impact, without considering
the restoring force, in this regard, magnetorheological dampers, eddy current dampers and
switched-coupling dampers are semblable in counteracting or dissipating the kinetic energy of the
primary system; due to the significant heat generation during transformation operation, heat
energy strategy is opted for describing their energy evolution. According to the law of energy
conservation, the larger the proportion of energy converted, the smaller the other forms of en­
ergy; thereby energy conservation efficiency can be used to measure the decrease of vibration
energy. The regenerative energy strategy is referring to vibration control method based on
available energy conversion and utilization. Finally, a concise summary on energy shunt strategy
based DVAs and some intractable ongoing issues are presented. Additionally, the challenges and
development trends of neoteric nonlinear vibration absorbers in the future are prospected.
Keywords:
Dynamic vibration absorbers (DVAs)
Energy dissipation
Energy conversion
Energy sinks
Metameterials
* Corresponding author.
E-mail addresses: huang_xingbao@163.com (X. Huang), btyang@sjtu.edu.cn (B. Yang).
https://doi.org/10.1016/j.ymssp.2022.109496
Received 30 November 2021; Received in revised form 24 April 2022; Accepted 22 June 2022
Available online 28 July 2022
0888-3270/© 2022 Elsevier Ltd. All rights reserved.
Mechanical Systems and Signal Processing 182 (2023) 109496
X. Huang and B. Yang
1. Introduction
The fundamental philosophy of vibration control is uncomplicatedly and efficiently regulating and reallocating vibration energy of
target protected system (primary structure). The controllable management of undesired energy flow and storage is a crucial schedule
for most mechanical applications. Vibration isolation is a typical technique that interdicts the input energy from vibration source to the
primary structure by means of employing flexible support, damping element or active control force. The vibration isolation technology
has not been extensively exploited mainly due to the inconvenience of installation, the large occupancy space and the unmeant damage
to the main structure. Nevertheless, vibration absorption technology has been extensively developed and labeled as superior char­
acteristics such as easy design, friendly installation, small attached mass and wideband vibration attenuation. Vibration absorption can
distribute ambient energy to the attached resonators in which the unwanted energy is dissipated or converted by using multiple small
mass attachments. The traditional dynamic vibration absorption method mainly uses the frequency tuning principle to weaken the
resonance peak of the main system, and the vibration energy is only temporarily transferred to the vibration absorption structure
without real dissipation or transformation. When the parameters of the vibration absorption unit or the excitation frequency change,
the vibration energy will return to the primary system (PS). Therefore, the traditional dynamic vibration absorption method is difficult
to be applied to structure vibration suppression in complex vibration environment. Nonlinear vibration absorption methods have been
gradually developed to achieve broadband vibration suppression; however, it is difficult to accurately and actively control the
nonlinear characteristics. Mass ratio is also a main factor restricting the application of nonlinear vibration suppression method. The
development of nonlinear vibration suppression technology with small mass ratio is expected to solve the complex vibration control
issues.
Efficient vibration energy redistribution and energy conversion are the feasible guarantees for stable vibration control. The
traditional dynamic vibration absorber mainly relies on frequency tuning to transfer the kinetic energy of the main system to itself, and
the resonance energy is dissipated gradually through structural damping. In this regard, the damping dissipation efficiency influences
transfer efficiency of vibration energy from the PS to attached dynamic vibration dampers. Energy sinks refer to those who has obvious
energy transfer characteristics. Because of the reaction force, the additional architecture will return a proportion of the kinetic energy
back to the PS, however, the kinetic energy of the PS gradually decreases as the locking-in energy of the attached architecture in­
creases. Hence, regression energy strategy is used to describe the energy redistribution behavior of the whole system and the energy
decrease of the PS. Local resonance mechanism and Bragg scattering are the main fundamentals of vibration and noise reduction of
metamaterials. The vibration or sound energy is trapped in multiple local resonators and consumed by the deformation work of the
locally resonant structures. Therefore, destination of the energy flow caused by metamaterials is the local substructures’ deformation
energy whose ultimate transformation form is heat energy. Hereby syntonic elastic energy strategy is employed to describe the local
resonance deformation energy generation and dissipation. The damping device makes it produce friction, bending, torsion, shear,
viscous hysteretic deformation, elastic–plastic hysteretic deformation, viscoelastic hysteretic deformation to absorb the energy
generated in the vibration structure. Dampers and vibration absorbers are similar to a great extent, such as damping force and damping
ratio, but there are essential differences between them. Dampers mainly consider the use of damping force to dissipate kinetic energy,
impact, without considering the restoring force, of course, part of the damper itself has the restoring force, which itself is also a kind of
recoverable damping or vibration absorber, such as springs, rubber pads, etc. In this regard, magnetorheological dampers, eddy
current dampers and switched-coupling dampers are semblable in counteracting or dissipating the kinetic energy of the PS, and finally
all work done by passive/active damped force is converted to heat energy. Herein, Heat energy dissipation strategy is suitable to cover
these three vibration control modes. Electromagnetic, piezoelectric, electrostatic and triboelectric energy conversion technologies are
mainly based on electromechanical coupling conversion mechanism, where electric energy is generated from charge-oriented
movement or surface electrostatic charge redistribution. Theoretically, the higher the energy conversion efficiency, the faster the
vibration energy decreases. Thereby, the hybrid energy conversion technology including smart materials and electromagnetic coupling
is a potential alternative for efficient vibration energy management. Accordingly, regenerative energy strategy is adopted to represent
vibration control methods based on advanced energy conversion.
In engineering applications, vibration inhibition issues are often regarded as minimizing the transient response of protected object.
During recent decades, a large number of researchers have made continuous efforts to improve the vibration-proof performance [1–3].
In the perspective of energy flow passive vibration isolation is regarded as a block that cuts down the energy flow form vibration source
to the protected system, and force or displacement offset mechanism is adopted in active vibration isolation applications. High static
stiffness and low dynamic stiffness are expected for many mechanical components, some efforts on the quasi-zero stiffness configu­
rations are explored for excellent vibration isolation [4,5]. Gatti et al. [6] proposed a quasi-zero-stiffness (QZS) suspension by using a
combination of linear springs and rigid links arranged with specific geometry into a compact device. Chai et al. [7] presented a novel Xshaped mechanism based 3 degrees of freedom (3-DOF) anti-vibration unit with enhanced QZS effect in a large stroke to achieve lowfrequency vibration isolation in three directions simultaneously. Vibration energy absorption and transfer technology can achieve
efficient energy dissipation while protecting the original structure. Nonlinear energy transfer systems have attracted much attention
for their lightweight, high robustness and wideband damping properties. Nonlinear energy sink (NES) and metamaterials are typical
representatives of broadband suppression. NES is widely applied to broadband vibration suppression of structures subjected to sto­
chastic excitations [8], wind-induced vibration [9,10] and whirling vibration [11,12]. Thereinto, metamaterials have multiple
adjustable bandgaps due to their neoteric unnatural fabrication. Metamaterials with high porosity, low relative density and high
energy absorption and dissipation have been gradually applied in vibration and noise reduction engineering. Aerospace, rail trans­
portation, automobile, ship equipment and other fields urgently need metamaterial [13–15] structures with lightweight and special
functions. Metamaterial with negative modulus [16–18], negative stiffness [19,20] and negative Poisson’s ratio [21,22] are the
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preferred candidates to vibration elimination due to their pleasurable special mechanical properties. Acoustic metamaterials bring a
new approach to the problem of low frequency sound absorption and insulation, and scientists have found some relatively light
resonance structures. Acoustic Membrane structure can be used in the structural design of acoustic metamaterials to achieve low
frequency sound absorption and insulation. Yang et al. [23] first proposed the membrane type of acoustic absorber, and found that only
0.28 mm thick film can obtain a 146 Hz resonance. Mei et al. [24] first proposed an elastic membrane to clamp the periodic structure of
a semi-cylindrical mass block to obtain deep subwavelength acoustic blackbodies experimentally. Notwithstanding significant ultrathin size and good acoustic performance, the prestress of membrane material itself is difficult to control. With the help of advanced 3D
printing technology, the sound insulation structure of metamaterial based on Helmholtz resonator can achieve better low-frequency
sound absorption [25–27]. Additionally, low-frequency locally resonant band gap excellent characteristics can be achieved by
fabricating QZS metamaterials [28–30].
In some special circumstances, such as space impulse energy or vibration energy is difficult to dissipate due to ultra-flexible and
low-damping structures. Some occasional perturbations such as satellite attitude adjustment, cosmic wind and thermal alternating
load may cause continuous flutter response of the satellite payload platform. Therefore, the stable one-way energy transfer strategy is
the key to space micro-vibration control. The term micro-vibration usually refers to the vibration issues that related to low-level
mechanical vibration or disturbance from 10-6g0 to 10-4g0 (g0 denotes the gravity acceleration of the earth) [31], usually occur at
frequencies ranging from less than 0.1 Hz to 1 kHz [32]. In the aerospace field, micro-vibration may exist for a long time due to the
extremely small environmental damping. This will worsen the working environment for airborne instruments, such as reducing the
accuracy of sensitive optical telescopes or reducing the positioning accuracy of space cameras. The main interference source of
spacecraft in orbit is usually the mechanical rotation device, such as reaction wheel and momentum wheel assembly [33–35].
Advanced equipment and facilities in semiconductors, nanotechnology, lasers, quantum communication satellites and optical in­
struments are ultra-precise and vibration-sensitive. The state-of-the-art star-to-earth laser docking technology enables the quantum
communication. However, due to the unavoidable environmental vibration and self-triggered micro-vibration, the performance of
advanced equipment and instruments is affected. The ultra-precise micro-vibration control of vibration sensitive precision equipment
is of great significance. Therefore, the lightweight multi-cells with various stiffness, high energy decomposition and transfer perfor­
mance are embraced in space equipment. Energy sinks provide a satisfactory and feasible alternative to the classical vibration ab­
sorbers due to their significant energy capture and dissipation under low frequency and impulsive excitations. A linear energy sink
composed of a series of small linear oscillators has a reversible absorption limit and an unsavory return time [36,53]. Irreversible
transient energy pumping from protected system to small attachments is a popular strategy for vibration control. Targeted energy
transfer (TET) usually occurs through 1:1 resonance capture, which is due to the nonlinearity of the intrinsic stiffness of the NES
blocking the preferred resonant frequencies of the PS [37–39]. However, the TET performance of NES is unsatisfactory when ambient
excitation frequency is too low to reach threshold of nonlinear energy transfer. Therefore, the active control of energy transfer and
redistribution under broadband excitation is the key to achieve fast energy transfer and vibration attenuation.
Energy harvesting technology is now extensively exploited in mechanical vibration devices for electrical energy conversion without
regard to base vibration control. Mass-spring-damping system is the core of vibration absorber and vibration energy converter. If such a
device is connected to a structure with high impedance, it has little effect on structural vibration reduction, but it can be used to
convert mechanical vibration into electrical energy. However, by connecting it to a structure with a relatively low impedance, the
device can attenuate vibration because it can act as a vibration absorber and energy converter. Vibration suppression is essentially the
effective neutralization, transfer, conversion or dissipation of vibration energy. For a deterministic vibration excitation scenario, the
transient input of vibration energy to the system can be considered to be approximately constant. Therefore, the overall energy
conversion efficiency can be employed to evaluate the residual energy of the main system, that is, improving energy conversion ef­
ficiency is a theoretically feasible means to achieve excellent vibration suppression performance under deterministic input energy. In
the case of transient impulse excitation, the input energy can be expressed as the kinetic energy of impact which can be obtained by the
momentum theorem. Accordingly, the vibration control efficiency of the PS subjected to impulsive scenarios can be indicated as energy
conversion efficiency which is defined as the ratio of output electric energy and impact kinetic energy. Indeed, there are many factors
affecting energy conversion efficiency, such as impact intensity, vibration amplitude, excitation frequency, external impedance,
electromechanical coupling coefficient and so on. In order to achieve the maximum output power and power efficiency, impedance
optimization strategy for the harvesting circuit is always adopted to determine the optimal external impedance [40,41]. The linear
energy harvester means that the energy harvesting efficiency is significant only when ambient excitation is around the fundamental
frequency of the PS. The vibration migration from the PS to linear oscillators depends on the ability to adaptively match the external
forced resonance [42,43]. In order to overcome the defects of linear energy harvesting system, a nonlinear energy harvesting system is
designed to adapt to frequency fluctuation and frequency detuning [44–46]. For the sake of inhibiting the vibration of weakly damped
structures, the combination of TET and energy conversion can effectively dispose the vibration energy, especially for low-frequency
disturbances such as cosmic winds, thermally induced vibrations of solar panels and space debris impacts in space. Energy conver­
sion efficiency can be used as an evaluation index to measure the vibration suppression performance of the system. Nonlinear energy
conversion technology has the potential to be developed as a regenerative vibration control method because of its high conversion
efficiency and wideband characteristics. Many researchers have conducted numerous efforts to enhance the capability of vibrationbased energy harvesters [47–49]. The broadband nonlinear energy transfer characteristics of the passive cubic nonlinearity and
multi-stable nonlinearity are studied [50–52]. The vibration control method based on multi-stable nonlinear energy transformation
and dissipation is expected to provide a new feasibility to solve the intractable impact and vibration problems. Efforts of exploring the
reciprocity between vibration suppression and energy conversion have been done by means of the incorporation of NES and energy
harvesting [53–55] during recent decades.
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In this review, we aim to present an overview concerning recent advances of DVAs and their applications in terms of energy transfer
modes. The general schematic diagram of energy shunt and conversion is described in Fig. 1. In Fig. 1, the fundamental components of
DVAs are presented in the view of energy. The mass of DVAs involves kinetic energy which can be transferred to small attachments by
means of energy sinks; the elastic component contains elastic potential energy and strain energy where undamped spring represents
absolute potential energy and metamaterials denote local strain energy; the damping elements such as structural dampers, magne­
torheological dampers and eddy current dampers dissipate a large proportion of system energy into heat energy. With the development
of smart materials and microelectronic technology, energy conversion techniques are exploited to convert the vibration energy into
electric energy. Therefore, improving the energy conversion efficiency is a potential measure to decompose the kinetic energy of the
main system. The challenging ambient working conditions require more adaptive and efficient vibration absorbers attached to the
mechanical components without altering their own critical structures. Fig. 2 describes the schematic description of energy decom­
position and redistribution in a neoteric DVA, where it can be found that there is a trade-off of energy redistribution between the main
system and the attached structures. Assuming the ambient vibration energy is gradient-free, the distribution of lock-in energy
(including kinetic energy and deformation energy), converted available energy and heat energy is an indirect measurement for vi­
bration control performance. In section 2, the concept of energy sinks and their extensive engineering applications are illustrated. The
syntonic elastic energy mechanism is described in section 3, where local resonance and Bragg scattering induced exotic artificial
materials such as acoustic metamaterials and elastic metamaterials are presented to demonstrate their excellent sound absorption,
sound insulation, vibration and noise reduction performance. In section 4 the heat energy dissipation strategy is introduced in terms of
magnetorheological dampers, eddy current dampers (ECDs) and switched-coupling dampers. The idea of energy reuse can be realized
through using advanced energy conversion and storage technologies, and then the alternative evaluation criterion of vibration sup­
pression can be expressed as energy conversion efficiency. Section 5 introduces numerous nonlinear energy conversion technologies
including smart materials and electromagnetic conversion mechanisms and their corresponding vibration suppression properties.
Finally, this paper summarizes several proposed vibration control strategies in terms of their applicability and relative merits.
Moreover, some contemporary ongoing problems, underlying challenges and prospects in the future are comprehensively discussed.
2. Regression energy strategy (Energy sinks)
2.1. Linear energy sinks
The concept of energy sinks provides a new and feasible alternative to replace conventional vibration suppression techniques
[56,57] where their applicability is limited, especially under low-frequency or transient excitation. For linear energy sink (LES), the
Fig. 1. The general schematic diagram of energy shunt and conversion in terms of vibration control.
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X. Huang and B. Yang
Fig. 2. The schematic description of energy decomposition and redistribution in a neoteric DVA.
input energy transfers to multiple linear oscillators and returns back to the main structure after a certain time. In general, the input
energy is just trapped as temporary storage in small attached oscillators. A portion of mechanical energy from the small oscillators
becomes the input energy after a period of time, the exotic phenomenon can be easily understood and explained in the literatures
[72,74,75], afterwards, the silent primary structure will animate remarkably. In terms of the energy pathway, the concept of LES is
different from the conventional vibration absorption pattern observed in an elaborate system using multiple tuned absorbers. Previous
works of art on the absorption of energy from the PS by small oscillators have shown that there is a tradeoff between number of
pendulums and the demand to have a damping loss in the suspended pendulums. As long as the quantity of pendulums is sufficiently
enormous or infinite, there is no essential energy dissipation in each oscillator [53–62,64]. Therefore, the energy transfer efficiency of
the LES depends seriously on the number and distribution of small oscillators. Due to the narrow band effect and undamped condition,
the system’s entire energy is unaltered and the energy transfer is limited to the approximately repeated exchange among different
forms of mechanical energy. Indeed, the kinetic energy of the primary structure does not drop monotonously, but rises sharply after a
recovery [65]. The theoretical and experimental observations on LES performance have been covered in recent years [63,65].
Akay et al. [36] demonstrated the concept of energy sink through experiments and found that this energy sink can absorb most of
kinetic energy from the PS. Besides, they also demonstrated the importance of frequency distribution and energy sink on enhancing the
vibration suppression capacity. A primary mass comprised of a steel block and many pendulums is shown in Fig. 3, where a
Fig. 3. (a) A primary mass composed of a steel block and many pendulums; (b) A pendulum snapshot after a period of time [36].
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Mechanical Systems and Signal Processing 182 (2023) 109496
X. Huang and B. Yang
reciprocating energy exchange between the primary system and pendulums is observed. It is found that a consistent wave-like mode
shape forms at the beginning of reciprocating energy exchange in Fig. 3(a). Nevertheless, the energy is mainly captured by the
pendulums after a period of time (return time), as shown in Fig. 3(b). Koc et al. [63] described a new concept of absorbing vibration
using a set of optimal undamped oscillators appended to the PS, as shown in Fig. 4. Regardless of the loss mechanism, vibrational
energy can be efficiently and irreversibly captured through limited quantities of linear additional oscillators. The optimal distribution
of fundamental frequency of the oscillators prohibits a conspicuously attenuated (almost 90% reduction) energy regress to the PS, as
given in Fig. 5.
The energy absorption efficiency of a series of linear oscillators is related to their frequency distribution and the loss factor over the
selected time period. Of note, if the number of undamped oscillators is not optimized, the efficiency of the LES may be discounted.
Additionally, the applicability of LES system to vibration abatement of the host structures subjected to broadband or random excitation
is unsatisfactory.
2.2. Nonlinear energy sinks (NESs)
2.2.1. Mathematical description of the NESs
NESs with strong nonlinearity are widely exploited in the absorption and control of wideband frequency vibration. The NESs, which
consists of apparent cubic stiffness and varying low damping, shows a significant energy transfer efficiency from the main structure to
the secondary mass [66–68]. Ding and Chen [70] provided a comprehensive review of the latest research progress of NESs. They firstly
introduced the important vibration control characteristics of the vibration control system, and emphasized the complex dynamics that
may lead to the coupling between NES and the host structure, then summarized the realization method of optimal damping effect and
the design method of NES defect compensation. When the main structure is disturbed by a transient impulse whose energy is over the
certain threshold, NES almost irreversibly absorbs whole energy of the system, and meanwhile acts as a wideband passive adaptive
controller also called passive TET [71–73]. However, an effective NES threshold cannot be triggered if both the frequency and
amplitude of the ambient vibration are too low. TET is a paramount characteristic of NESs, and its implicit fundamental principle is
shielded transient resonance capture (TRC) or TRC cascade [69]. Savadkoohi et al. [75] proposed a general multi-DOF system with a
parallel NES device tree. The detailed prototype four-tier structure has two parallel NESs at the top level, as shown in Fig. 6. The use of
parallel NES allows to disseminate the mass along the structure and significantly reduces the threshold nonlinear stiffness. Moreover,
the equivalent damping of two NES in parallel is twice that of a single NES, which means that the energy dissipation effect of this
configuration will be more efficient than that of the corresponding single NES system. Under the excitation of the chirped signal with a
scanning bandwidth of 3–5 Hz, the nonlinear energy pumping of TET is obviously observed in the amplitude of frequency response
function (FRF) of the concerned host structure, as described in Fig. 6. The NES energy pumping efficiency is up to 66.67% which means
the vibration amplitude of the main system decreased by 9.54 dB compared with the counterpart without NES coupling, as shown in
Fig. 6(b). Additionally, the parallel NES configuration can also be exploited to establish NES with several levels of activation that could
be able to control several modes of a linear master structure via tuning each NES or groups on a chosen linear mode. Parallel NES helps
to reduce energy in proportion to their damping factor times their own mass. It is also important to declare that these different and
independent NES dissipation factors act additionally. The two principles of linear additivity and separated activity of NES in parallel
underline that the efficiency of each NES.
Carcaterra et al. [76] proposed a new theory of energy redistribution and dissipation in dynamic constructions by introducing
clustered beams to a continuous main architecture and applied it to the aerospace industry, as shown in Fig. 7. They made comparison
of the FRFs of the controlled object at “point P” with and without the vibration suppression device and found a significant reduction in
the FRF amplitude (nearly 93% decrease comparing with the case without NES structure). With the implementation of the clustered
beams, the vibration migration of satellite components is remarkably improved. Therefore, this configuration can be used as an energy
absorption device to protect sensitive components in space.
Dai et al. [77] introduced a NES to improve the vibration suppression performance of an elastically mounted square prism when it
galloped along cross-flow orientation, as shown in Fig. 8. In Fig. 8, the galloping vibration caused by the aerodynamical effect can be
reduced by means of adding a NES to the galloping square prism, and they found that the NES system with appropriate mass ratio,
Fig. 4. Schematic diagram of a main system attached with multiple small mass-spring units [63].
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Fig. 5. Numerical results of multiple linear energy sinks:(a) Fundamental frequency variation with respect to number of mass-spring units; (b)
Displacement response of the PS; (c) Entire energy evolution of the PS [63].
Fig. 6. (a) Two parallel network elements at the top; (b) Frequency response function at the top of the test structure under chirp excitation [75].
Fig. 7. (a) Schematic diagram of primary cluster coupling; (b) Fabricated primary cluster devices [76].
stiffness ratio and damping ratio can obtain almost 68% reduction in vibration amplitude of the main system.
The governing equations of an elastically-mounted rigid square prism coupled with a NES subjected to external fluid forces are
given by [77].
⎧
⎪
⎪
⎨
(m − mnes )ÿ1 + cẏ1 + ky1 + cnes (ẏ1 − ẏ2 ) + knes (y1 − y2 )3 = fL (y1 )
(1)
⎪
mnes ÿ2 + cnes (ẏ2 − ẏ1 ) + knes (y2 − y1 )3
⎪
⎩
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Mechanical Systems and Signal Processing 182 (2023) 109496
X. Huang and B. Yang
Fig. 8. Schematic of a fluid induced NES employed in galloping architectures [77].
where m and mnes are the mass of the cylinder and NES per unit length, respectively; c and k denote the structural damping and stiffness,
respectively; cnes and knes represent the damping and stiffness of the NES. Based on the assumption that the quasi-steady hypothesis is
utilized to describe the aerodynamic force [78], the galloping force per unit length of a symmetric cross-section fL can be expressed as:
⎛ ⎞n
∑
ẏ
1
2
fL (y1 ) = ρa DU
an ⎝ 1 ⎠
(2)
2
U
n=1,2,...
where ρa is the density of the fluid, D is the effective diameter of square prism, and U denotes the inflow velocity. an (n = 1, 2, 3) is the
empirical parameter.
Geng et al. [79] investigated vibration abatement performance of the constrained NESs via applying a piecewise sprung compo­
nent. The mathematical model and architectonics of proposed piecewise spring is presented in Fig. 9. For transient impulsive exci­
tations, the vibration responses of the linear oscillator (LO) and nonlinear energy sink (NES) are capable of being estimated by
simultaneously calculating the retained energy. The transient mechanical energy of the linear system and NES with respect to different
k2 and L is shown in Fig. 10, where it is obviously seen that the energy trapping ratio of NES is significant when the impact velocity is
1.3 m/s, additionally, the transient vibration suppression performance is excellent. From Fig. 10(a) it can be seen that the vibration
amplitude of LO can be reduced to over 90% within 2 s duration. Nonlinear forces in NES are always achieved via springs, magnets,
buckling beams, etc. Zou et al. [80] presented a device capable of customizing nonlinear forces by using a pre-compressed spring, a
bearing and a raceway, as shown in Fig. 11. Based on smooth track design in Ref. [80] a hardening nonlinear system, a softening
nonlinear system, a bi-stable system, a tri-stable system, and a piecewise nonlinear system can be easily obtained.
2.2.2. Engineering applications of the NESs
Wang et al. [81] proposed a track NES that contains an auxiliary mass that can move freely along a peculiarly fabricated track
functioning as a vibration absorber capable of suppressing vibration of primary system under broadband vibration. The design and
modelling of the track NES is shown in Fig. 12(a) and (b). The governing motion equations can be written by.
Fig. 9. The prototype of a piecewise NES: (a) mathematical model; (b) physical design [79].
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Mechanical Systems and Signal Processing 182 (2023) 109496
X. Huang and B. Yang
Fig. 10. Dynamic characteristics of the LO and the NES: (a) The displacement time history of the LO;(b) The energy capture ratio of the NES with
respect to impact time [79].
Fig. 11. Schematic diagram of the device and its application to vibration energy harvesting, vibration isolation, and NES [80].
⎧
⎪
⎪
⎪
⎪
⎨
( ′
′
′ )
m1 x1′′ + c1 x1 + c2 x1 − x2 + k1 x1 + k2 (x1 − x2 ) = − m1 x′′g
( ′
(
)
′ )
′
′
m2 x′′2 + c2 x2 − x1 + k2 (x2 − x1 ) − cN uN − FN uN , uN , u′′N = − m2 x′′g
(
)
⎪
(
)
⎪
′
′
⎪
⎪
mN u′′N + cN uN + FN uN , uN , u′′N = − mN x′′2 + xg′′
⎩
(3)
The track NES system [81] achieves almost 85% reduction in vibration amplitude of the primary system under impulse-like ex­
citations, as shown in Fig. 12(c).
Grounded NES (GNES) refers to those that are linked the main architecture with linear springs and nonlinearly coupled to the
ground [82,83]. Yao et al. [84] designed a GNES system for lateral vibration muffle of a rotor system. The prototypical design of the
GNES and its application are shown in Fig. 13(a) and (b). There is an obvious energy tradeoff between the rotor system and the GNES
system, as presented in Fig. 13(c) and (d). In Fig. 13(c) and (d), vibration suppression efficiency is up to 90% within 0.2 s impact
duration. Fig. 13(e) and (f) are wavelet transforms for the rotor-GNES system. From Fig. 13(e) and (f) it can be easily seen that the TET
phenomenon occurs in the coupled system, and the transient trapped energy in GNES is more considerable (nearly five times) than that
of rotor system.
Considering the gyroscopic moment of the rotor, the kinematic equations of the rotor-GNES system are established as follows [84].
⎧
⎪
⎪
⎪
m1 ẍ + krr x + c1x ẋ + krf θy + kc (x − xn ) = m1 rω2 cos(ωt)
⎪
⎪
⎪
⎪
⎨ m1 ÿ + krr y + c1y ẏ − krf θx + kc (y − yn ) = m1 rω2 sin(ωt)
(4)
Jd θ̈x + ΩJp θ̇y − kfr y + kff θx = 0
⎪
⎪
⎪
mn ẍn + c2x ẋn − kc (x − xn ) + kn0 xn + fnx (x) = 0
⎪
⎪
⎪
⎪
mn ÿn + c2y ẏn − kc (y − yn ) + kn0 yn + fny (y) = 0
⎩
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Fig. 12. (a) Design of track NES; (b) Mathematical model; (c) Acceleration and displacement responses of the 2nd floor under impulse-like exci­
tations[81].
where ×, y and xn, yn are displacements of the disc and the NES mass in x and y direction, respectively. m1 is the mass of the rotor. r is
the disc eccentricity. θx and θy denote rotation angle in x and y direction. Jd and Jp are radial moment and polar moment of inertia of
the disc. c1x, c1y are the damping of the rotor system in x and y direction, respectively. krr, krf, kfr, kff are bending and torsional
stiffnesses of the rotor, respectively.
The incorporation of NES and smart materials such as piezoelectric and magnetostrictive materials is a good attempt to dispose the
dual issues that involves vibration absorption and energy reuse. The studies on piezoelectric-based NES have been reported recently
[85–87]. The magneto-mechanical coupling behavior of giant magnetostrictive material (GMM) transducers has been widely studied
[88–90]. Due to the positive and negative effects of the GMM, based on the Villari effect, the GMM adaptively adjusts the stiffness and
damping of the NES through the induced current generated by the coil around the GMM rod. Fang et al. [91] studied the integration of
NESs and GMM energy collectors for vibration control and energy conversion, providing an effective vibration control method, and the
structure illustration of the NES-GMM prototype is described in Fig. 14.
The biased magnetic effect and the prestress should be taken into account in GMM applications [92–94]. The application of
magnetic bias is to obtain large magnetization gradient of the GMM rod in the axial orientation, and configuration of the applying
prestress is capable of improving magnetostrictive sensitivity and hence obtaining maximum amplitude output under a certain driving
magnetic field intensity. From the concept of state of stress, FNES can be obtained by.
FNES = FGMM − F0 = (σ − σ0 )
2
πdGMM
(5)
4
where F0 is the preload, σ is the stress, σ0 is the prestress, and dGMM is the diameter of GMM rod.
The entire energy of the system is primarily divided into several terms, namely the remaining energy in the PS, reserved energy in
NES system, the energy absorbed in GMM system that are expressed as the following equations [108]:
Win (t) = TPS (t) + VPS (t) + WPS (t) + TNES (t) + VNES (t) + WNES (t) + Wh (t) + Wm (t) + Ws (t)
(6)
The transient energy trapping efficiency of PS, NES and GMM are calculated by.
ηPS (t) =
TPS (t) + VPS (t) + WPS (t)
× 100%
Win (t)
(7)
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Fig. 13. GNES structure and application. (a) GNES structure; (b) Applied to a rotor system; Time domain response: (c) Rotor system; (d) Rotor-GNES
system; Wavelet energy transforms for the rotor-GNES system: (e) Rotor system; (f) GNES [84].
Fig. 14. Dynamic model of NES-GMM system: (a) mathematical model; (b) cross-view of GMM bar [91].
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ηNES (t) =
TNES (t) + VNES (t) + WNES (t)
× 100%
Win (t)
ηGMM (t) =
(8)
Wh (t) + Wm (t) + Ws (t)
× 100%
Win (t)
(9)
A nonlinear beat phenomenon occurs, and the input energy firstly applied to the PS is passively dredged to the NES-GMM system in
the time domain, as described in Fig. 15. From Fig. 15(a) and (b) it can be seen that the energy capture ratio quickly increases to 90%
after 0.3 s duration; with increase in NES mass ratio the lock-in energy in NES-GMM and the converted electric energy are over 90% of
the input energy, meanwhile the resident energy of the PS is decreased to a very low level (less than 10%), as shown in Fig. 15(b), (c)
and (d).
Generally, in this section state-of-the-art techniques of energy sinks and their applications are presented. For fixed frequency vi­
bration excitation, linear energy sink can achieve satisfactory vibration suppression performance, however, for broadband or random
excitations, its efficiency is greatly reduced. Compared with linear energy sinks, NES applications are more efficient in nonlinear
vibration and impulse suppression without evident return. By means of introducing the appropriate mass ratio, stiffness ratio and
damping ratio the energy harvesting efficiency and the energy trapping capacity of a NES system can be improved to over 90%. The
energy trapped in NES system is finally converted into available energy or dissipated into heat.
2.3. Vibro-impact NESs
2.3.1. The concept of vibro-impact NES (VI-NES) model
Repeated contact-separation energy transfer method has emerged as vibration suppression strategy in recent years because of its
Fig. 15. Transient energy redistribution: (a) residual energy ratio in PS (b) overall stored energy ratio in NES-GMM (c) dissipated energy ratio in
NES and (d) converted energy ratio in GMM [91].
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excellent damping dissipation performance. Wu et al. [95] investigated the impact of an elastic sphere with elastic and elas­
tic–perfectly plastic substrates using FEM, and found that there are two major energy dissipation mechanisms: stress wave propagation
and plastic deformation. For impact involving plastic deformation, plastic deformation becomes the main energy dissipation mech­
anism, and the energy loss caused by stress wave propagation is relatively small. The energy loss in deformation of contact surface can
be understood as internal friction from the view of molecular microscale. In practical engineering applications, the movement of the
vibro-impact sphere is both sliding and rolling. Therefore, friction induced heat energy accounts for a portion of energy dissipation
during repeated impact process. The contact-separation energy transfer method performs well in a large range of input energy. Particle
damper is developed as a typical method of repeated contact-separation energy transfer due to its significant energy dissipation in the
interaction/collision process. It is experimentally known that after multiple inelastic collisions, the kinetic energy of the collisional
objects decreases significantly. Therefore, the concept of VI-NES is a potential approach to sustaining energy dissipation. To date,
tremendous endeavors to understand the mechanism of vibration-impact NES have focused on numerical analysis of conserved and
damping mechanism [96–98]. For smooth NESs, based on average and multi-scale analysis, the approximate analytical description of
the transient damping response is obtained by using the singular perturbation method [97,99]. Gendelman [100] reported an
approximate analytical method for analyzing the transient vibration-impact NES model. The dynamic system composed of linear main
oscillator and vibration-shock NES is shown in Fig. 16. The relative energy time series under two different initial conditions are shown
in Fig. 17, where the vibration-shock NES with impact velocity of 0.5 can achieve almost 100% energy dissipation through collision.
This relative energy ratio is calculated as the ratio of transient entire energy and the original impact energy [100]:
Er = E(t)/E(0) =
u̇2 (t) + u2 (t) + εv̇2 (t)
u̇2 (0)
(10)
where (⋅) is the first-order derivative; ε is mass of the collisional particle.
Roveri et al. [64] studied the effect of nonlinearity on interchange of energy via implementing nonlinear interactions between
resonators-elastic collisions and parameter instantaneous changes of additional oscillator stiffness. The prototypical array-like vibroimpact system is described as follows:
Firstly, the schematic diagram of the collision between adjacent oscillators of the 2-DOF system is shown in Fig. 18(a) and (b).
Energy evolution of the master-elastic-impact nonlinear system is presented in Fig. 18(c) and (d), where it can be obviously found that
the novel nonlinear energy pumping is significant (nearly 90% reduction) compared with the counterpart of linear systems.
Impact vibration absorber (IVA) is a kind of structure passive vibration migration which is based on transient momentum exchange
mechanism. Experiments show that IVA is more effective than conventional dynamic dampers around the resonant frequency [101].
To date, four types of IVAs [102] have been developed, namely, (a) single-unit IVAs, (b) multi-unit IVAs, (c) hybrid IVAs, and (d)
compound IVAs [101]. Single-unit IVAs can be regarded as a 1DOF system. Nevertheless, the impact mass in a compound IVA is
attached to the main architecture. A compound IVA can be understood as a 2-DOF system. Osire et al. [103] experimentally studied
passive vibration abatement of the main system by using IVA, as described in Fig. 19. The comparison of vibration suppression per­
formance of compound IVA and simple IVA model is illustrated obviously in Fig. 20, from which it can be easily observed that hump
resonance of the primary mass is scrapped evidently by the compound IVA, and the vibration amplitude of the compound IVA is
reduced by about 65% at its resonant frequency compared with single IVA.
The efficiency of VI-NES is higher under low-intensity excitation and large impact mass conditions. Moreover, the energy trapping
efficiency of VI-NES is significantly dependent on low to high frequency modal reallocation performance and resonance capture. When
the VI-NES configurations are applied to the vibration inhibition of flexible structures with large amplitude oscillation, their damping
efficiency is significant. However, the vibration absorption performance of VI-NES is remarkably discounted if the host structure is
excited by weak and low-frequency excitations due to the critical threshold of energy transfer.
2.3.2. Particle impact dampers (PIDs)
PIDs dissipate energy by means of migrating the unwanted energy to a bunch of particles. The bunch is confined to a cabinet
consolidated with the vibration structure. Thus, collision-induced interactions occur within the container as damped energy is
absorbed. Herein, the dissipative mechanisms are: the collision of particle-to-wall interaction and in-between momentum exchange of
the participated particles; stress wave propagation loss and inelastic deformation dissipation; the frictional loss such as sliding or
Fig. 16. The illustration of a VI-NES [100].
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Fig. 17. The residual energy evolution in time history [100]. (The vertical coordinate is the percentage of residual kinetic energy; the abscissa
represents dimensionless time).
Fig. 18. (a) The two-resonator impact-coupling; (b) Master-attachment prototype system; (c) Energy evolution of the linear system; (d) Energy ratio
evolution of the master system with respect to time [64].
rolling friction induced in the tribological contact mechanical behavior. Energy dissipation caused by stress wave propagation or
plastic deformation is a form of existence similar to mechanical energy. The stress wave propagation may activate acoustic wave
energy which dissipates through air damping. The energy loss in deformation of contact surface can be understood as internal friction
from the view of molecular microscale. Therefore, during impact process multiple energy mechanisms shift and the main destinations
of impact energy are mechanical energy and thermal energy. This transient and discontinuous damping mechanism [104] allows
vacant cabinets to operate at low frequencies. The optimization is usually focused on the particle movement time in the cavity and the
materials of the particle damper. Another paramount mechanism is restricted motion of particles inside related to the existence of
granular media. Lu et al. [105] introduced the basic concepts, research status, engineering applications, and design approaches of PIDs,
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Fig. 19. Experimental illustration: (a) single IVA; (b) compound IVA[103].
Fig. 20. Experimental results of the two IVA modes (The y-ordinate is the displacement amplitude amplification factor; x-ordinate is excitation
frequency) [103].
Fig. 21. (a) The conventional DVA model; (b) The new DVA with application of PIDs [106].
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and discussed their advantages and disadvantages in engineering applications.
A typical innovative particle damper concept is shown in Fig. 21. Due to its significant advantages, such as invulnerable to oil
contamination, lightweight impact [106], insensitivity to ambient temperature, multi-direction flexibility, availability over a wide
frequency range [107], satisfactory damping capacity and efficiency under random vibrations or deterministic excitations [108], they
are extensively employed in aerospace, automotive, energy and medical industries. Since the motion of passive multiple PIDs is un­
predictable and unprogrammable, manipulative collision regulation is difficult to realize. The applications of PIDs include: building
vibration migration [109,110]; gear transmission [111–113]; turbine blades [114,115]; spacecraft components [116,117]; machine
tools [118,119]; wind turbines [120,121] and draught fan [122].
Generally, the principle of collision-induced dampers can be understood as conservation of momentum: during the collision process
the velocity reversal of particle dampers [123] is reversed, thereby the kinetic energy of the main architecture is reduced into a low
scale according to the conservation of momentum. After repeated collision the residual energy of the primary system is decreased step
by step, meanwhile, the energy of particle dampers is transformed into wave propagation dissipation, shape plastic deformation and
friction heat. Therefore, the optimal collision-induced energy absorption strategy can be achieved by means of implementing low to
high frequency modal reallocation. Additionally, the absorbed energy proportion from the primary system can be improved to 80%
and even 90% when the ambient excitations are in large scale.
Particle Impact Dampers (PIDs) are suitable for harsh operating conditions, such as extreme temperatures and severe oil
contamination, without any additional maintenance. The performance of PID is better when it is excited by higher frequency and larger
amplitude. In this regard, the momentum interchange between particles and particles and the combined interaction of inelastic
collision and friction can be effectively triggered, converting more vibration energy into heat energy. But for low frequency micro
vibration, PID vibration reduction effect is not satisfactory due to the slightly weak resonance capture. Therefore, the combination of
NESs and PID is a potential stochastic environment vibration tracking control strategy.
3. Syntonic elastic energy strategy
3.1. Acoustic metamaterials (AMMs) based energy strategy
The difference between metamaterials and conventional materials lies in that the material structures designed by special multiscale (macroscopic and meso-mechanical) mechanics can show the supernormal physical properties that natural materials do not
have superphysical properties through topological configuration design and spatial ordered distribution on key physical dimensions of
material microstructure. Sound absorption and sound isolation, vibration reduction and noise reduction are the mainstream research
directions in the field of acoustics for a long time, and also the most widely applied direction of acoustic technology. Conventional
acoustic materials do not provide substantial improvement in noise reduction. However, acoustic metamaterials are providing new
solutions for controlling sound waves, especially in reducing noise propagation. These metamaterials are usually light, compact and
excellent at reducing low-frequency noise by using relatively thin resonance structures. Recent research advances have shown that
acoustic metamaterials can effectively control sound waves and optimize their structures to achieve functions according to new
physical phenomena. Gao et al. [124] reviewed the development of acoustic metamaterials, including the basic classification of passive
and active noise reduction metamaterials, potential physical mechanisms, application scenarios, and predicted the future development
trend of acoustic metamaterials with a focus on noise reduction. Structural potential energy is easily trapped in a singular structure
composed of local resonance substructures. The AMM based DVA design concept is to introduce vibration energy or impulse energy
into the local resonant cells and lock it in as elastic energy or reflect it back as wave energy. Unsurprisingly, the trapped elastic energy
is consumed through local resonance damping dissipation. Metamaterials made of locally resonant [125] topological structures [126]
Fig. 22. The illustration of an ultrathin membrane-type AMM for hyper-absorption [128]. (a) Schematic diagram of cellular composition and
structure; (b) Schematic cross-sectional illustration of the two lowest frequency eigenmodes of a decorated membrane plotted in reference to the
same phase of the incident wave (at the two resonant frequencies).
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emerge wide bandgaps for low-frequency vibration attenuation, guided waves [127]. Ma et al. [128] proposed an ultrathin membranetype AMMs for frequency-tuned hyper-absorption, as described in Fig. 22, they found acoustic wave absorption coefficient attained by
hybrid resonances at tunable multiple frequencies can be close to 100%. Bongard et al. [129] proposed a 1D acoustic negative
refractive index metamaterial, which is composed of an acoustic waveguide loaded with a periodic membrane to achieve a series
“capacitance” function and a transversely connected open channel to achieve a shunt “inductance” function. The novel AMM of Ref.
[129] is given in Fig. 23. Popa and Cummer [130] fabricated and studied extremely nonlinear and non-reciprocal active AMMs based
on piezoelectric membranes, as shown in Fig. 24. To quantify the cell non-reciprocity, they defined the isolation factor F as the dif­
ference between the power transmitted in the forward and reverse orientations. Ignoring the acoustic energy through the passive
structure, the isolation factor can be calculated as F = 19 dB which denote almost complete absorption of sound waves.
)
(∫
∫
F = 10log10
p2f dt/
p2r dt
(11)
ΔT
ΔT
where pf and pr are the pressure fields measured in the forward and reverse orientations, respectively.ΔT = 5 ms is the time interval
containing the transmitted pulses.
Acoustic metamaterials prepared by locally resonant spring-mass arrays are good candidates for obtaining ideal band gaps. A finite
length elastic metamaterial beam consisting of a cantilever beam and a set of mass-spring absorbers performs well in bandgap for­
mation [131]. The model schematic diagram of the locally resonant metamaterial beam is shown in Fig. 25. The theoretical and
experimental results in Fig. 25(b) and (c) indicate that there is nearly 12 Hz bandgap around the neighborhood of the beam funda­
mental frequency when a set of absorbers is attached to the main beam. The Bragg scattering and local resonant mechanisms are the
fundamentals of metamaterials physical theory, and the band gap width is seriously dependent on the configurations of acoustic
resonant lattice and cell shapes. The input energy flow obtains admittance to host structure through the periodic co-continuous
acoustic metamaterials in form of wave propagation. Due to the energy locking-in mechanism induced by lattice elastic deforma­
tion, some frequencies of mechanical and acoustic waves are successfully eliminated. Fig. 26 shows the schematic illustration of
various metamaterials configurations and their band gap working mechanism, from which it can be found enhancing acoustic ab­
sorption/boycott by periodic local resonance units such as phononic crystals and reducing acoustic reflection by sonic black hole are
the main approaches for acoustic waves suppression.
3.2. Elastic metamaterials (EMMs) based energy strategy
EMMs possess abnormal low-frequency bandgap behaviors that can trigger low-frequency vibration attenuation. The working
principle of the EMM is introducing artificial microstructures (local resonators) on a scale much smaller than subwavelength. From the
perspective of energy flow, EMM is easy to activate local resonance which can assimilate most of the vibrational wave energy. Due to
the damping energy dissipation, the trapped energy in the local resonant array decreases gradually. However, the damping factor of a
local resonator is too small to achieve rapid energy dissipation, and the duration is always too long, especially for continuous high
input energy. Chiral isomer is a new type of electron microscopic material with great potential for development. Its structure has good
vibration suppression performances. An EMM beam based on chiral lattice with multiple embedded local resonators was designed to
obtain broadband vibration absorption [138]. Zhu et al. [138] evaluated the bandgap behavior of a chiral honeycomb beam made of
aluminum (Al) beams with a water jet cutter, as presented in Fig. 27, from which it can be observed that bandwidth of approximate
300 Hz for vibration abatement is achieved through EMM beam. Composite laminate materials are good candidates for building
various EMMs structures, Fig. 28(a) presents periodic composite laminate materials based EMMs, EMMs is high-efficiency and costeffective in accomplishing impact energy absorption, Fig. 28(b) and (c) describe the EMMs with multiple folded unit structures
which can be exploited to vibration isolation and transient shock absorption.
In linear systems, decreasing the characteristic scale increases the operating resonance frequency. This provides opportunities for
controlling elastic/acoustic waves, including seismic excitation (Hz), structural vibration (kHz), ultrasonic waves (MHz) in microelectro-mechanical systems (MEMS) devices, and thermal phonons (THz) [142–144]. Advanced manufacturing technologies, such
Fig. 23. The illustration of a plate-type AMM and equivalent circuit model [129].
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Fig. 24. The schematic illustration of the non-reciprocal active AMM vibration suppression [130]. (a) Schematic diagram of sound energy prop­
agation in open oral cavity with different diameters; (b) Nonlinear circuit driving PZM; (c) The time history of acoustic wave amplitude through the
unit AMM; (d) Amplitude-frequency characteristics of sound waves passing through the unit AMM.
Fig. 25. (a) A schematic of a metamaterial beam; (b) A comparison between experimental results and analysis (The y-ordinate is the displacement
amplitude amplification factor); (c) Transmissibility (which denotes the vibration isolation efficiency) with respect to resonant frequency of the
cantilever beam [131].
as 3D additive manufacturing, have advanced availability in micromachining field. Phononic crystals (PCs) are formed by periodic
arrangement of materials or components whose spatial size and elastic properties are controllable. The bandgaps in PCs are derived
from the Bragg scattering mechanism and can be very broad, making them ideal for sound insulation and vibration control [145–147].
Matlack et al. [148] designed and fabricated a different elastic element structure consisting of polycarbonate lattices with embedded
steel cubes as local resonators, as shown in Fig. 29, where a nearly 4000 Hz bandgap is obtained in high stiffness and low stiffness
configurations. The metastructure utilizes the geometry rather than physical characteristics to selectively vary the different local
resonance modal shapes [148]. Furthermore, those metastructures are not typically triggered by conventional PCs, and their bandgaps
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Fig. 26. Schematic illustration of various metamaterials configurations and their band gap working mechanism. (a) the Bragg scattering and local
resonant mechanisms [132]; (b) The geometry of the 2D phononic crystal with concentrated masses and Triply periodic co-continuous acoustic
metamaterials consisting of 2 × 2 × 2 unit cells with simple cubic lattice (SC), body-centered cubic lattice (BCC), face-centered cubic lattice (FCC),
and octettruss lattice (Octet) [133]; (c) Schematic of the bending waveguide structure and acoustic retroreflector composed of a Luneburg lens
[132]; (d) Sketch of an acoustic energy harvesting system [134]; (e) Illustration of wave propagation mode of acoustic resonators from the input
energy flow [135–137].
Fig. 27. (a) The chiral grid beam and its amplification unit; (b) Frequency response function comparison between tests and FEM [138].
can be adjusted by local resonance. The elastic metastructures of multiple stiffness 6-unit cell substructures exhibit different bandgaps
between operating frequencies, which can be easily understood theoretically and experimentally, as shown in the right figure of
Fig. 30.
The energy trapping strategy for extracting undesirable energy from multiple directions is to design appropriate multi-stable units
to store the strain energy caused by shock or vibration into self-assembled 3D metamaterials obtained by additive manufacturing
technology. Shan et al. [149] have designed multi-stable building materials for capturing elastic strain energy, as shown in Fig. 31.
These programmed structures contain beam elements whose geometry is specifically designed to achieve large local bi-stable defor­
mation. When these materials undergo mechanical deformation, the beams are locally reconfigured into a higher energy but stable
deformation state, similar to a phase change. Yang and Ma [150] prepared one-dimensional to three-dimensional multi-stable me­
chanical metamaterials by using the multi-material assembly method, as shown in Fig. 32. They claim that flexible geometric
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Fig. 28. Different types of elastic metamaterials. (a) Dissipative lattice system with multiple and infinite resonators [139]; (b) Unit cell of the
hexagonal frame and connection elements [140]; (c) Schematic of the kirigami structure design [141].
Fig. 29. (a) Element structure design; (b) FE simulations and experimental results of the 3D printed metamaterials: A) with high stiffness B) with
low stiffness C) test setup [148].
reconstruction and zero Poisson’s ratio enable large recoverable deformation. The syntonic elastic energy strategy can be realized
when impulse input energy is applied to these metamaterials.
The vibration attenuation mechanism of acoustic and elastic metamaterials composed of multiple local resonant cells is producing
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Fig. 30. (A) high stiffness geometry; (B) medium stiffness geometry; (C) low stiffness geometry, using FE simulation to calculate the dispersion
relationship [148].
Fig. 31. Mechanical response of an elastic multi-stable structure: (A) Schematic diagram of one-, two- and three-dimensional energy capture
metamaterials; (B) Vertically load sequence images of multi-stable architectures [149].
Fig. 32. The design of multi-stable mechanical metamaterials from 1D to 3D configurations [150].
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multiple bandgaps. The bandgap caused by Bragg scattering is the mechanism of bandgap formation in periodic media. In fact, the total
bandgaps observed in elastically deformed structures are the superposition of bending bandgaps, torsional bandgaps and longitudinal
bandgaps. By independently controlling the different wave modes, the full bandgap can be enlarged to a broader and lower frequency
range, hence these elastic element structures are suitable for the absorption of low-frequency vibrations. Note that the innovative metastructures which consist of periodic microstructures are overwhelmingly dependent on additive manufacturing technology. Therefore,
high-precision fabrication technologies are strongly embraced to develop the potential applications of metamaterials. However, due to
the scale of microstructural unit whose natural frequency is upon a few hundred Hertz, metamaterials are restricted to be extensively
exploited in low-frequency vibration suppression.
The syntonic elastic energy strategy involved with metamaterials (AMMs and EMMs) is an effective approach to improve the antidisturbance performance of the protected system when it is subjected to broadband ambient vibrations or acoustic waves. The incident
energy can be unidirectionally assimilated in the local flexible substructures without reflection to the primary system. However,
metamaterials also have some limitations in practical application such as complex structure design, high production cost, single target,
relatively low efficiency, poor reliability and poor manufacturing performance. In order to solve the above problems, a series of
interdisciplinary studies have been introduced into metamaterials in recent years. For example, machine learning algorithms can be
used to assist the parametric design of artificial structures, which can quickly find a large number of complex structures that are
difficult to design by conventional design ideas or optimization algorithms. Therefore, the appropriate design of metamaterials
through intricately programming the artificial unit structures can achieve adequate recompenses such as broadband vibration isola­
tion/absorption and converted electric energy with embedded smart materials.
4. Heat energy dissipation strategy
4.1. Magnetorheological elastomers (MREs)
4.1.1. Robustness study of MRE
MREs are made of high polymer rubber and fine magnetized iron, which have superiority in many aspects such as no sealing device,
good stability, fast response, etc. The viscoelastic properties of MREs can vary greatly under the action of magnetic fields, which can be
used in the design of various controllable stiffness and damping devices. MREs give overall consideration to the characteristics of both
magnetorheological materials and elastomers. Their magneto-mechanics properties are a critical index, which directly determine their
application range and effect. MREs have broad application prospects and have been successfully applied in vibration and noise
reduction fields, such as suspension systems, bushings and vibration absorbers. The shear storage modulus of MRE can be easily tuned
by applying magnetic field [151]. Ginder et al. [152] developed a MREs based adaptive and adjustable vibration absorber. Hoang et al.
[153,154] investigated a torsional adaptive and adjustable shock absorber by employing MRE for migration of powertrain bed vi­
bration. The test observations indicate the active DVA can operate in the range of 10.75–16.5 Hz. Yang et al. [159] proposed a MREs
based shear mode semi-active DVA and studied the working principle of an axial semi-active DVA attached to ship shafting, as given in
Fig. 33. Fig. 34 gives shear storage modulus variation with respect to magnetic flux density. It can be seen from Fig. 34 that the shear
storage modulus increases with the increase of the magnetic intensity, which means the stiffness and damping of MRE can be tuned by
applying magnetic field. Due to magnetic saturation, the shear storage modulus becomes saturated after a remarkable increase in
magnetic field. Therefore, the damping force achieved by MRE is restrained. Additionally, employing MRE structure to reduce vi­
bration will inevitably cause problems such as cumbersome installation and high-power supply intensity.
Fig. 33. (a) MRE sample, d = 50 mm and h = 5 mm; (b) Architecture of a semi-active DVA [159].
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Fig. 34. Shear storage modulus variation with respect to magnetic flux density [159].
The performance of a multi-layer MRE is very attractive. Sun et al. [160] proposed a new adaptive tuned vibration absorber (ATVA)
consisting of an eccentric mass and a multi-layer MRE structure. The prototype design of [160] is shown in Fig. 35. The multi-layer
MRE structure has satisfactory wideband vibration absorption performance, as shown in Fig. 36. As the current increases, a gradu­
ally widening low transmittance band is formed. From Fig. 36(a) it can be easily seen that the significant low-frequency vibration
suppression bandwidth from 5 Hz to 15 Hz is obtained by regulating input current ranging from 0 A to 2.5 A.
4.1.2. Magnetorheological fluid dampers
Magnetorheological (MR) fluid is a new kind of intelligent material. The preferred application of MR as a material mainly takes into
account the following important characteristics of MR: large damping force, fast response, insensitive to impurity pollution, simple
design, relatively large range of MR fluid’s relative working temperature and low power consumption. MR damper is a novel semiactive device application, since it has a good tunable damping performance under the condition of changing magnetic field. Rah­
man et al. [155] presented an overview on the advantages of semi-active systems over passive and active systems, the general ap­
plications of MR dampers, and the preparation of various MR dampers, as well as their latest design optimization and progress. There
are three commonly used working modes for magnetorheological fluid dampers, which are flow mode, shear mode and squeeze mode,
all of which are based on the principle of plate model in fluid mechanics. In general, the MR damper used in the automobile is not using
the above three models separately, but the combination of flow mode and shear mode, known as mixed mode, mainly considering the
automobile suspension damper trip is large, and on the structure size and structural strength requirement is strict. However, dampers
Fig. 35. The illustration of MREs based ATVA [160].
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Fig. 36. The wideband vibration absorption and tuned frequency with respect to increasing current: (a) Transmissibility; (b) Tuned fundamental
frequency [160].
based on these three modes are also used separately. Extrusion mode, due to its relatively small stroke, is mainly used in small in­
struments, such as optics. Liao et al. [156–158] demonstrated the feasibility for improving the ride quality of railway vehicles with
semi-active secondary suspension systems using MR dampers, and found that the vibration suppression performance of car body under
random track irregularities can be significantly improved by employing semi-active MR dampers.
4.1.3. Damping effect description of magneto-rheological visco-elastomer (MRVE)
Due to the randomness of ambient excitation, the adjustability of structural dynamics is indispensable. Smart materials like MRVE
can provide adjustable damping and stiffness, which have a significant impact on vibration suppression performance of the host
structure. MRVE is widely favored because of its obvious advantages such as flexible adjustment of dynamic characteristics, antiaggregation ability and applicability in composite sandwich structure. The energy dissipation principle of MRVE is to convert the
input energy into magnetic energy, deformation energy and internal energy of viscous fluid. MRVE is an intelligent composite material
consisting of magnetically polarized particles and non-magnetic polymers [161]. It incorporates the advantages of magnetorheological
fluids and viscoelastic substrate materials, including reversible stiffness and damping changes within milliseconds under an applied
magnetic field. A tunable vibration absorber and MR composite damper based on MRVE have been designed and used for vibration
control applications [162–165]. In order to obtain excellent vibration control effect, Ying et al. [166,167] proposed an optimal
bounded parameter control method for MRVE sandwich beam with supporting mass under random deterministic supporting motion
excitation, and studied the stochastic and shock vibration suppression performance of the optimal control beam with multi-mode
coupling. Ying et al. [168] investigated the micro-vibration response of sandwich plate with MRVE core under random support
Fig. 37. MR-PTMD prototype CAD model [163].
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motion excitation to evaluate its vibration suppression ability, and found that the MRVE sandwich plate has a good damping capacity
under the excitation of random bracing motion. In order to inhibit the multi-storey building in a wider frequency range of catastrophic
vibration, a novel fast response magnetorheological material can be employed to achieve variable resonance. Christie et al. [163]
designed a prototype of an MR-based DVA by incorporating a differential gearbox to produce a damp-controlled transmission, as
shown in Fig. 37, and experimentally studied the seismic vibration suppression performance of the magnetorheological-fluid-based
pendulum tuned mass damper (MR-PTMD). This semi-active control resulted in a maximum reduction of 79.1% at 3.52 Hz
compared to the passive-off case, and a maximum reduction of 53.3% at 2.80 Hz compared to the passive-on case, as clearly shown in
Fig. 38. The benefits of this semi-active control are particularly evident in the resonance of a building, where similar full-size structures
are most susceptible to potentially catastrophic vibrations.
The semi-active DVA based on MREs is better than the passive DVA in terms of frequency shifting characteristics and vibration
absorption capacity, especially for multi-frequency vibration, it has stronger damping capacity. By adjusting the modulus of the
laminated MRE structure, the frequency bandwidth can be expanded according to varying ambient excitations. According to the
relationship between the MRES modulus and the displacement of the main structure, the adaptive control is realized by monitoring the
displacement of the main structure. However, for space devices the controllable power source is the difficulty in adjusting the
structural modulus of MRE. Hence, the combination of energy harvesting technology and energy conversion/storage technology is of
great value for wider development of MREs based absorbers. Advanced and efficient energy conversion technologies, such as multistable energy conversion devices, have been widely employed in various domains, and optimal energy conversion structures are
designed according to varying ambient vibrations and transient impulse excitations.
4.2. Eddy current dampers (ECDs)
The eddy current damper (ECD) is different from the constrained layer damper, which can significantly affect the dynamic
characteristics of the structure. ECDs operate in contactless mode, thus eliminating the mass loads and increased stiffness shared by
most damping technologies. The concept of ECD can be understood as: vibration energy is firstly converted into eddy induced electrical
energy, and then dissipated as heat energy. The damping force of eddy current is proportional to the relative velocity; however, eddy
current damping coefficient is independent of relative velocity. The eddy current damping coefficient is related to the thickness of the
conductor plate, the volume of permanent magnet, the thickness of the guide plate, the distance between magnets, the gap between the
conductor plate and magnets, etc. In a dynamic system, the magnetic flux undergoes a continuous change due to the continuous
movement of the conducting metal. The changing magnetic flux produces an electromotive force (EMF), which in turn induces current
regeneration and eventually electromagnetic repulsion. This triggers the vortex, which acts like a viscous damper, dissipating energy
and making the vibration disappear faster. ECDs based engineering practices have been widely employed especially for damping of
high-speed components [169,170]. Teshima et al. [171] studied the effect of ECD on superconducting suspension vibration charac­
teristics. Matsuzaki et al. [172] developed a new vibration control strategy that uses the electromagnetic force to suppress the vibration
of a periodically magnetized beam along the span. Graves et al. [173] studied physical models of electromagnetic dampers based on
motion electromotive force and transformer electromotive force devices. A simple conductive plate ECD is shown in Fig. 39(a), and the
mechanism of vortex generation is shown in Fig. 39(b) and (c). The damping force caused by eddy current is defined as Eq.(12), for
which detailed derivation can be found in Ref.[174]. Bae et al. [175] studied the performance of a magnetically DVA consisting of
classic tuned mass damper (TMD) and ECD, and experimentally studied the effect of magnetically tuned-mass-damper (MTMD) on
vibration suppression of the main beam. They found almost 50 dB reduction in FRF amplitude at the fundamental frequency of the
main beam attached with a MTMD is obtained.
∫
∫ 2π ∫ r c
∫ rc
(
)
(
)
F = J × BdV = − kσ δv
(12)
yB2y y, lg dydϕ = − k2πσδv
yB2y y, lg dy
V
0
0
0
Fig. 38. Scale building 5th floor transmissibility (The vertical coordinate denotes displacement transmissibility; passive-off means absence of active
magnetic field; passive-on with 1.8 A indicates the application of stable active magnetic field) [163].
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Fig. 39. (a) Schematic diagram of the ECD effect in a cantilever beam [174]; The principle illustration of ECD: (b) Conductor moving and oscillating
perpendicularly to the magnetization direction; (c) Generation mechanism of eddy currents [175].
The ECDs do not change the desired performance of the system, while increasing the damping ratio and rapidly restraining
oscillation range of the main structure. However, due to the eddy current induced electromotive force is proportional to the velocity,
eddy current damping force in low-frequency vibration circumstances is not satisfactory. Therefore, in order to improve the ECD
damping performance, increasing the eddy current damping coefficient is a direct solution for low-frequency vibration suppression.
Measures to boosting the eddy current damping coefficient (such as optimizing magnet array configuration, enhancing magnetic
circuit and composite laminated conductor plate) can increase the energy dissipation efficiency and improve the low-frequency vi­
bration suppression efficiency of the ECD.
4.3. Switched-coupling based energy dissipation
The concept of switching stiffness [176,177] is suitable for suppressing the structural vibrations of dynamic systems due to its
excellent TET effect and high-efficiency energy dissipation. A typical switched stiffness approach for structural vibration control is
described in Fig. 40. In Fig. 40(a), the connection between the primary structure and the attached oscillator is a friction contact pair
whose frictional force is controlled by the piezoelectric actuators. The principle of energy dissipation is cyclic separation between the
primary structure and the attached oscillator at the switching point where the total potential energy of the system reaches its
maximum, and cyclic incorporation between the primary structure and the attached oscillator at the switching point where the total
potential energy of the system reaches its minimum (equilibrium position). Therefore, the transferred energy from the primary
structure to the attached oscillator can be dissipated through internal damping or introduced damping during the time from switchingon state to switching-off state. Due to the high natural frequency and damping force of the attached vibrator, the extracted energy can
be dissipated rapidly. Therefore, this energy dissipation strategy is suitable for high-frequency input energy. As seen from Fig. 40(b),
the connection stiffness can be adjusted between low state and high state through hard switching or on–off (relay) control. By changing
the spring stiffness value, the potential energy dissipates at the maximum deflection, causing the total energy of the system to “drop”,
thus inhibiting the displacement of the main system. The amount of energy dissipated in a given period is proportional to the difference
Fig. 40. Stiffness modulation strategy in vibration control: (a) “Smart Spring” according to [176]; (b) Switched stiffness concept between low state
and high state [177].
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between high and low values. Therefore, a significant vibration suppression and total system energy (including kinetic energy and
potential energy) reduction can be implemented by cyclic stiffness switching such as square wave stiffness.
The MR dampers and switched-coupling based energy dissipation strategy have similar characteristics that the energy pumping
mechanism is dynamic stiffness and damping modulation, and the dissipation of trapped energy in DVAs is structural damping. The
two dissipation strategies mentioned above always function as semi-active dampers whose frequency shift is altered by DC/AC current
input, and their energy absorption efficiency is up to over 50% when the related parameters are optimized. In addition to highly robust
energy migration performance and energy trapping capacity, the energy dissipation strategy can be utilized as a supplementary vi­
bration control method without appending cumbersome architectonics.
5. Regenerative energy strategy
The concept of energy decomposition and transformation mentioned in this chapter refers to the transformation of the existing form
of vibration energy, that is, the vibration energy is decomposed into potential energy and kinetic energy of the system, and then the
kinetic energy is transferred to the additional structure through nonlinear multi-steady state mechanism, and finally the captured
kinetic energy is converted into electrical energy by high-energy inter-well motion. Compared with the conventional ways of energy
consumption, vibration control method based on the decomposition of energy transformation under micro-disturbances and broad­
band excitations has better applicability and robustness, and compared with the conventional way of vibration absorption and vi­
bration control method based on the decomposition of energy conversion can really reduce the kinetic energy of the controlled system,
realize the stable vibration suppression. In essence, the vibration control strategy of energy conversion realizes energy redistribution
and active regulation through nonlinear energy transfer and conversion mechanism from the perspective of energy flow.
5.1. Smart materials-based energy conversion
With the development of microelectronics and wireless sensor network technology, smart city, smart home, smart medical, smart
transportation and smart grid have been proposed successively. Self-powered micro electro mechanical system (MEMS) sensors can be
exploited to monitor and estimate the on-time health conditions of MEMS components by means of harvesting and converting wind
energy, solar energy, hydro energy and vibration energy into available energy without depending on the use of toxic and contami­
native chemical batteries. The future energy networks cover land, space and oceans, and hybrid energy utilizations become unam­
biguous weathervanes for efficient use of energy. Due to the satisfactory achievements in Internet of things (IoT), smart city, smart
home, smart medical, smart transportation and smart grid are generated and connected with each other. The intelligent applications of
energy harvesting strategies and their neoteric characteristics are presented in Fig. 41. The presented diversified energy harvesting
strategies are potential to power intelligent facilities that are equipped with state-of-the-art algorithm systems including supervised
machine learning algorithms, unsupervised recommender algorithms, fuzzy logic and methods, natural-inspired and evolutionary
algorithms, and deep learning.
Due to the friendly economic behavior, naturally abundant and easy to design, vibration based renewable energy technology has
been favored by many researchers [178,179,183]. In general, vibration suppression and energy conversion are similar in terms of
energy transfer and energy trapping [182,184]. Vibration control includes the energy migration to small attachments and the con­
version and storage of energy from the attached battery to a portable rechargeable battery. Therefore, the DVA unit can be properly
designed as a renewable energy device to achieve vibration control and self-powered wireless nodes. Piezoelectric, triboelectric,
ferrofluid-electric and thermoelectric energy conversion principles are illustrated in Fig. 42, from which it can be understood that
relative motion may induce charge or electromotive force in piezoelectric, triboelectric and ferrofluid-electric mechanism.
Different energy conversion strategies can be adopted according to the type of environmental vibration. Since the high energy
density behavior, piezoelectric composites are widely used to convert unwanted vibration energy and preserve it as available energy.
Cai and Zhu [185] summarized the nexus between vibration-based energy harvesting and structural vibration control and presented a
critical review on co-prosperity of multiple energy conversion techniques and vibration suppression science. Hydraulic shock ab­
sorbers have been widely used in vehicle suspensions for decades to reduce acceleration and keep tires in contact with the ground in
irregular conditions. Unlike conventional suspension systems, which transform vibration energy into waste heat to suppress vibration,
regenerative suspension with energy-harvesting shock absorbers converts unwanted energy into available energy. Abdelkareem et al.
[186] reviewed the automotive suspension systems based on energy conversion and compared the advantages and limitations of the
commonly used energy conversion systems in automotive suspension, and then they discussed some challenging issues concerning the
future regenerative automotive suspension systems. It is assumed that the input energy is stabilized for the specific vibration, hence the
energy harvesting performance can be exploited to evaluate the performance of the attached absorbers. One strategy to improve the
vibration-based regenerative energy efficiency in low-frequency circumstances is the utilization of frequency-up conversion. The
implementation of frequency up-conversion in engineering practice is always mechanical plucking and transient shock [187,188]. A
further strategy for regenerating energy on piezoelectric beams using the frequency-up technique is developed in [189,190]. Monostable and bi-stable regenerative energy methods are exploited into frequency up-conversion [178,180,181]. However, these
methods require large accelerations to achieve low-frequency resonance, especially bi-stable methods with high inter-well/cross-well
motion thresholds. Multi-stable [184] nonlinear (more than two stable equilibrium states) coupling frequency up-conversion is a
potential approach to obtain regenerated energy from extremely weak and low-frequency sources [191,192]. The capacity of trapping
energy from broadband stochastic ambient vibrations is a critical challenge for energy conversion based DVAs. Wang et al. [193]
proposed a piezoelectric wideband frequency up-conversion regenerative energy structure, which is induced by the four-well potential
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Fig. 41. The intelligent applications of energy harvesting strategies.
Fig. 42. Schematic diagrams of four common energy conversion principles based smart materials.
caused by the cantilever-surface contact nonlinearity and magneto-elastic coupling. The prototype of a low-frequency wideband fourstabilized oscillator is shown in Fig. 43. Although some energy harvesting techniques concerning efficient energy conversion are not
directly related to vibration control, the introduction of nonlinearity, piecewise stiffness and multi-stable configuration provides a
good imitation foundation for the realization of broadband vibration suppression.
In general, DVA and vibration energy harvester (VEH) have the uniform structure. Therefore, it is feasible to develop a composite
energy harvester [194,195] to suppress the vibration of the main structure and harvest electric energy. The electronic output power
can be used to provide wireless network sensors for health monitoring of the primary structure. Rezaei and Talebitooti [196] inves­
tigated simultaneous energy harvesting and vibration isolation through a tri-stable magneto-piezoelastic absorber (TMPA) whose
prototype is given in Fig. 44. They comprehensively examined the potential of a TMPA for simultaneous vibration annihilation and
energy scavenging and found that compared with the linear dynamic vibration absorber (LDVA), TMPA can reduce the vibration of
main beam more quickly and efficiently, meanwhile, it obtains more energy by implementing large and high-energy inter-well
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Fig. 43. (a) the proposed four-stable regenerative energy structure based on vibration; (b) the cross-section diagram of the cantilever beam; and (c)
a photo of the prototype [193].
motions. Li [197] investigated the dynamics of an electromagnetic vibro-impact nonlinear energy sink (VINES) whose schematic
illustration is presented in Fig. 45. In terms of vibration suppression, they found that the novel electromagnetic VINES enhanced the
robustness of TET efficiency, and hence had better performance than conventional VINES.
Ambient energy sources are available in railway vehicles and tracks, including mechanical energy from interaction of the wheel-rail
and the acoustical energy from the structural and airborne noises. The induced-wind of passing train causes unpleasant noise and highfrequency wheel and body shaking. Therefore, hybrid energy conversion technology can be applied to improve high-speed train
running stability, comfort and safety, as shown in Fig. 46. Based on advanced energy conversion and storage technology the
dependable monitoring networks of railway surrounding safety can be supported by using transient electric energy from the smart
energy harvesting device [198]. Although the combination of nonlinear vibration suppression (VS) and energy harvesting (EH) has
received much attention in recent decades, how to improve the performance of both simultaneously and extend the operating range to
weak excitation scenarios remains an unsolved problem. Fang et al. [181] proposed a tuned bistable nonlinear energy sink (TBNES) to
outperform the typical bistable nonlinear energy sink (BNES), as shown in Fig. 47. They surprisingly found that the trapped energy
efficiency is dependent on the level of ambient excitations, as shown in Fig. 48, from which it can be easily seen that the mean optimal
trapped energy ratio of TBNES is almost 80%, much larger than its counterpart of BNES.
Jamshidi et al. [199] introduced the design and application of a new self-powered hybrid electromagnetic damper, which can
simultaneously suppress structural vibration and achieve energy conversion. The damping effect of the hybrid damper is evaluated by
numerical evaluation of a bridge cable-stayed cable under wind excitation. It was understood that the hybrid design is superior to the
passive case without external power supply. Furthermore, they also found the decoupling method of passive mode and semi-active
mode can enlarge the force range and improve the vibration performance of the cable. Marian and Giaralis [200] investigated pas­
sive vibration control and energy conversion of tuned mass dampers (TMDI) in harmonically excited structures. They found that
compared with TMD of the same weight, TMDI can suppress the vibration close to the fundamental frequency of the main system more
Fig. 44. Schematic diagram of a magneto-electromechanical coupling system consisting of a simply-supported main beam and a tri-stable magnetopiezoelastic absorber [196].
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Fig. 45. (a) Configuration of a two degree of freedom system consisting of a fixed LO coil with an VINES magnet; (b) The associated harvesting
circuit [197].
Fig. 46. Vehicle-borne hybrid energy conversion technologies and railway industry requirement of electrical power [198].
effectively and has stronger robustness to the detuning effect. Tsushima and Su [201] successfully addressed active and passive flutter
suppression in highly flexible airfoils using piezoelectric multifunctional beams, as described in Fig. 49. They found active multi­
functional wing technology can improve aircraft performance from aeroelastic stability and energy consumption.
Du et al. [202] presented an energy transfer approach that achieve a reciprocity in which vibration enhancement and vibration
attenuation are both flourished, relying on local resonance to accomplish energy redistribution. This energy transfer method is based
on a 2-DOF resonance system with an internal triboelectric nano-generating spring, as shown in Fig. 50. The satisfactory energy
transfer and redistribution phenomenon is observed in Fig. 51, from which it can be easily found that the vibration suppression
performance is improved. It is experimentally demonstrated that almost 95.8% of the retained energy can be converted and the vi­
bration suppression of the protected object is improved nearly 55% [202]. Thereby, there is a potential co-prosperity between
vibrational energy conversion and vibration migration, namely appropriate energy redistribution.
Excessive vibration caused by wind load is the main obstacle affecting the structural safety and comfort of high-rise buildings.
Energy conversion from wind vibration is a new and promising strategy for vibration suppression of high-rise buildings. Sun et al.
[203] proposed a regenerative electromagnetic tuned mass damper (RETMD) to weaken the dynamic response of building structures
under wind loads and convert vibration energy into electrical energy. In aerospace field, structural vibration in steady flows can
introduce fluctuant aerodynamic forces, due to Bernoulli principle the lift force and drag force on the surface of the airfoil are
oscillating when the airflow ranges from moderate to violent, consequently, the airfoil structure experiences flutter which is a sort of
flow-induced vibrations (FIV). In order to verify the feasibility of energy harvesting, Zhu and Gao [204] numerically studied the vortex
induced vibration (VIV) response of a riser attached to a freely rotating impeller and the rotational response of the impeller; they
demonstrated vibration suppression and high energy extraction can be achieved simultaneously when the reduced velocity is larger
than 9.85 for a riser with a free-to-rotate impeller. Although FIVs may cause some structural health problems and comfort challenges, it
also has a great potential for utilization and can be employed to harvest the hydraulic energy and wind energy [206]. Inspiration from
nature, many bionic appearances are exploited to strengthen the performance of FIV and capture more vibration energy, Fig. 52 shows
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Fig. 47. (a) A simply supported, hinged–hinged beam (HHB); (b) TBNES and the BNES layouts; (c) Dynamic descriptions of TBNES and the
BNES [181].
Fig. 48. The mean trapped energy ratio comparison between TBNES and BNES with respect to the impact amplitude [181].
some FIV based bionic piezoelectric energy harvesting applications, from which it can be easily seen that piezoelectric beam
configuration [205] is widely used to convert fluid kinetic energy into electricity from wind energy and hydro energy. Karman vortex
street is always exploited to enhance the energy conversion performance of FIV, Wang et al. [209] introduced a downstream rect­
angular plate as an interference in in the wake of the circular cylinder, and conducted a series of wind tunnel experiments to
demonstrate the usefulness of the downstream rectangular plate and influence on energy conversion efficiency (See Fig. 52).
Ferrofluid is a colloidal liquid containing magnetic nanoparticles that are coated with a surfactant to prevent their agglomeration
suspended in a water or organic carrier liquid. The ferrofluid based electromagnetic energy converters, which convert ambient
vibratory energy into electric energy through the sloshing motion of a ferrofluid have been exploited over recent decades [211–213].
Liu et al. [211] studied the theoretical model of ferrofluid-based electromagnetic energy converters by solving the magnetic field
dynamic behavior and fluid motion coupled by Maxwell equations and Navier-Stokes equations, and conducted an experimental study
to improve the energy conversion efficiency by means of different magnetic field configurations, as shown in Fig. 53. Ferrofluid-based
renewable energy technologies are explored extensively by exploiting wind energy, ocean energy, vibration energy and etc., as shown
in Fig. 54. Pathak et al. [214] designed a highly efficient wind energy harvester by using ultra-low friction surface formation of
ferrofluids and passive levitation, the exclusive configuration is described in Fig. 54(a). Seol et al. [213] proposed a ferrofluid-based
hybrid triboelectric-electromagnetic actuator vibration energy converter, as seen in Fig. 54(b) where the schematic mechanisms of
TEG and EMG are illustrated. The experimental results show that the hybrid energy converter has a lower threshold amplitude and a
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Fig. 49. (a) Piezoelectric multifunctional beam with energy conversion and equivalent circuit (b) The beam frame along the direction of the
reference line; (c) Airfoil coordinate system and velocity components [201].
Fig. 50. The illustration of the 2-DOF energy redistribution system: (a) The prototype design; (b) Triboelectric nanogenerating spring (TENG-S); (c)
Electricity generation principle of the TENG-S [202].
wider operating frequency range than the solid–solid contact generator. This requires a minimum threshold energy to overcome the
friction. The ferrofluid is vulnerable to the whims of a magnetic field, thus the relative motion of the inductor coil and the controlled
ferrofluid causes electromotive force which can be extracted through electronic circuit and meanwhile hampers ferrofluid oscillations.
As a consequence, the primary system coupled to ferrofluid is forced by an additional damping resistance. Therefore, ferrofluid
inspired regenerative energy strategy is an appropriate approach to implement vibration absorption of concerned devices which
usually operate under low-intensity and broadband unsteady ambient vibrations.
5.2. Electromagnetic coupling-based energy conversion
The ideology that transfers input energy to small attachments and harvests the trapped energy is the core design concept of energy
conversion-based vibration suppression. Electromagnetic coupling composed of a coil and a permanent magnet has good nonlinear
characteristics and good energy conversion capacity. The nonlinear vibration control system based on electromagnetic coupling is of
significance to solve the nonlinear vibration problem in mechanical application under harsh environment. By improving the efficiency
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Fig. 51. The dynamic behavior of the proposed 2-DOF resonance system: (a) The displacement response in frequency domain; (b) The comparison
of vibration amplitude of the protected object with or without TENG-S; (c) The acceleration response of the protected system; (d) Energy redis­
tribution in a 2-DOF resonant system [202].
Fig. 52. Some FIV based bionic piezoelectric energy harvesting applications. (a) Different bluff bodies in wind tunnel test [207]; (b) Bio-stream tail
[206]; (c) Inverted flag [208]; (d) A hybrid energy harvester [210].
of TET and the energy conversion efficiency of available energy from mechanical energy to electric energy, the vibration absorption
performance of DVAs can be significantly improved. Gu et al. [215] developed a new planar multidirectional vibrating electromagnetic
energy converter by using a magnetic ball moving that covered with a goblet-like structure on a 2D surface generated by the rotation of
a 1D bi-stable potential function curve. Nguyen et al. [216] provided an experimental and theoretical foundation for the design
guidance and analysis of magnetic spring involved in vibration-based energy harvesting. The prototype energy collector consisting of a
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Fig. 53. (a) The test scheme; (b) The illustration of 4 configurations [211].
Fig. 54. Ferrofluid-based renewable energy technologies. (a) Schematic diagram of wind energy harvester based on magnetic fluid bearing [214];
(b) Structure of the ferrofluid-based hybrid triboelectric-electromagnetic energy converter [213].
suspended magnet and two fixed ring magnets is described in Fig. 55.
In order to reduce vibration, different methods have been put forward, among which TMD is one of the most ideal methods and has
been widely used in practice. Tang and Zuo [217] presented a new method to convert vibration energy of high-rise buildings into
available energy by using a regenerative electromagnetic TMD instead of viscous damper which consumes vibration energy as waste
heat. They demonstrated that vibration suppression and energy conversion can be achieved simultaneously using a power-generating
TMD. Fig. 56 presents frequency response of passive, electricity-generating, and active TMDs, from which it can be easily observed that
regenerative semi-active TMD provides more excellent vibration mitigation performance than the optimal passive TMD. Zhu et al.
[218] introduced a new application of linear moving electromagnetic (EM) device, hereinafter referred to linear EM damper, to reduce
vibration and convert waste energy. Kinetic energy caused by earthquake, wind, or traffic loads is not only dissipated by the EM
damper, but is also stored by an energy conversion circuit connected to the damper. The energy conversion efficiency of the linear EM
damper increases with the frequency and amplitude of displacement oscillation, and its maximum can be up to 33.1% when suitable
external loads are employed.
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Fig. 55. The conventional magnetic spring based vibration energy harvester: (a) cross-view; (b) schematic of the scalar potential and force
interaction [216].
Fig. 56. Frequency response of passive, electricity-generating, and active TMDs (passive TMD (solid line), regenerative semi-active TMD (dotted
line), self-powered active TMD (fine dotted line), and active TMD (dash dot line)) [217].
Fig. 57. Hybrid aeroelastic structure for FIV [220].
Kakou and Barry [219] presented an innovative nonlinear electromagnetic resonance shunt tuned mass damper within two
different configurations to obtain both vibration mitigation and energy harvesting. Fluid-induced vibration (FIV) caused by air vortex
effect is commonly encountered in aerospace. Bolat et al. [220] designed a piezoelectric and electromagnetic hybrid energy harvester
by adopting a cantilever beam whose tail end is mounted with an airfoil profile. Piezoelectric patches are attached to the cantilever
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beam and the tip mass (coupled to airfoil structure) is connected with demonstrative Cu coils by a straight rod, as shown in Fig. 57,
where the aerodynamic lift force is generated by the inflow from air nozzle. The electromagnetic-Lorentz induction is connected to the
airfoil element at the end of this beam, and energy is generated simultaneously with the vibration of the beam using electromagnetic
induction and piezoelectric transduction. In turn, piezoelectric damping and electromagnetic damping are applied to the vibrational
beam and tail end, respectively. Therefore, flutter suppression can be achieved during energy conversion.
Remick et al. [221] investigated comprehensive studies on a 2-DOF dynamic system with fundamental cubic stiffness and elec­
tromagnetic damping, demonstrating that high frequency instability can be achieved in a system with moderate viscous damping
under a single impulsive excitation. The 2-DOF dynamic electromagnetic system herein is described in Fig. 58. Chiacchiari et al.
[222,223] theoretically and experimentally evaluated the energy conversion performance of bi-stable nonlinear attachments from
impulse excitations including single and repeated impulses. Parametric sensitivity analysis on energy conversion efficiency by
Chiacchiari et al. [222] is presented in Fig. 59. From Fig. 59 it can be found that the efficiency measure η% resulting from a single
impulse excitation is satisfactory under low initial velocity conditions when the bi-stable attachment is adopted.
5.3. Related works
The negative stiffness term of a buckled beam can be implemented by means of controlling the side payload of a clamped-tunable
beam. By introducing the tunable buckling technology, we designed a bi-stable regenerative energy structure (BRES) based on a
tunable 2-DOF buckling beam [224]. The BRES prototype is shown in Fig. 65. In Fig. 60 it can be seen that the buckled factor can be
actively modulated by a piezoelectric actuator, electromagnetism actuator or GMM actuator equipped attached with multilevel
amplification mechanism. Single transient impulsive excitation is applied to this BRES, and then the efficiency of regenerative electric
energy is evaluated, as shown in Fig. 61. It can be obviously seen in Fig. 61 that the dynamics of the buckled BRES are significant, and
the total efficiency of regenerative electric energy is sensitive to the mass ratio, the initial impact velocity and buckled factor, addi­
tionally, evident enhancements in transient energy conversion efficiency in chaos regimes including aperiodic intra-well and inter-well
motions are observed in Fig. 61(c) when compared with the cubic stiffness system depicted in Fig. 61(d). Fig. 62 presents the transient
energy conversion efficiency of the buckled BRES against the initial impact velocity, in which it can be found that small initial impact
velocity enhances the energy conversion efficiency of the buckled BRES. Therefore, a conclusion can be drawn that small mass ratio
and small initial impact velocity contribute greatly to high-efficiency vibration absorption of the primary structure by using a buckled
beam based BRES.
This section reviews some advanced energy conversion techniques that can trap and harvest remarkable vibration energy from the
main structure excited by broadband ambient vibration. On account of the distinguished energy conversion capacity and absolutely
passive power generation mechanism, regenerative energy strategy can be combined to the structure design of DVA. By means of
modulating the multi-stable operation mechanism the energy conversion component can easily convert the input energy with variable
amplitude and frequency of wide ranges (from low scale to moderate scale) into electric energy, thereby the challenge of powering
wireless sensor nodes can be solved without any external power supply. The energy conversion efficiency of multi-stable DVAs can be
increased up to 60% by means of applying state-of-the-art semi-active control strategy when the primary system is subjected to
deterministic excitations or stochastic excitations.
Fig. 58. Configuration of 2-DOF electromagnetic dynamic system [221].
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Fig. 59. The distribution of parametric energy harvesting efficiency (The abscissa is viscous damping of the coupling; the vertical coordinate
denotes the amplitude of the initial velocity): (a) mono-stable; (b) bi-stable [222].
Fig. 60. The prototype of 2-DOF buckled beam based BRES device.
6. Conclusions and future prospects
6.1. Ongoing problems
The original intention of this review is to fully investigate the state-of-the-art of unconventional DVAs and their representative
applications from the perspective of energy shunt. The critical aim is to discuss the feasibility of combining vibration control methods
with various energy strategies. It is expected to provide some reliable guidance for the novel and efficient DVA design in the future. The
several representatives of unconventional DVAs reviewed in this work strongly indicate that optimal structural design and energy
conversion technology enjoy exceptional advantage in vibration attenuation. Based on the overview of the reported efforts above, the
applicability of the four energy shunt strategies can be summarized, as described in Fig. 63. From Fig. 63 it can be easily seen that
energy conversion-based strategy is eligible for vibration control of structures subjected to wide and low-frequency weak excitations.
For the sake of clearly understanding the features of energy strategies proposed above. Hereby, Table 1 summarizes comparison of
advantages and disadvantages within the proposed energy strategies, from which it can be found that an incorporation among them is
expected to solve the issues of vibration in complex environment. The narrow band and low efficiency of linear regenerative energy
strategy has not been effectively solved in vibration control. The combination of NESs and energy conversion pattern is a potential
method for wide-amplitude and broadband vibration suppression. From the perspective of energy flow, the essence of vibration control
is to manage and decompose the input vibration or impact energy more scientifically and effectively, and the vibration control strategy
based on energy transformation is a better choice. As a result, a possible way to smart vibration control is by introducing nonlinear
energy transfer, energy conversion and the strategy of energy dissipation, input energy can be one-way transfer to additional nonlinear
subsystem from the main system, and will capture energy efficiently into available energy, radically reduce the reside kinetic energy of
the primary system, vibration control is stable. Notwithstanding a mass of related efforts, there are still some intractable vibration
control problems that have not been well disposed.
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Mechanical Systems and Signal Processing 182 (2023) 109496
X. Huang and B. Yang
Fig. 61. The distribution of parametric energy harvesting efficiency as a function of the mass ratio and impulsive velocity): (a) μ = 0.025; (b) μ =
0.05; (c) σ = 0.8; (d) σ = 1.0.
(1) In the field of ultra-precision machining, for example, the vibration performance of the installation platform of the lithography
machine during chip manufacturing directly affects the chip machining accuracy, and its vibration amplitude is small and
difficult to be solved by the conventional energy dissipation technology.
(2) In space engineering, the mass index is very strict, and the payload in the satellite has the characteristics of high flexibility, low
stiffness and low damping ratio in structure. The vibration response of the payload on the satellite subjected to multi-source
micro-disturbance is difficult to dissipate quickly through structural damping.
(3) The vibration suppression performance of conventional dynamic vibration absorbers largely depends on the selection of mass
ratio. Generally, it is difficult to obtain better vibration control effect with smaller mass ratio.
(4) The vibration energy of the flexible structure under transient impulsive scenarios and broadband weak excitations is difficult to
be rapidly and nonreciprocally transferred to the attached substructure for energy conversion or dissipation.
(5) In complex vibration environment, the energy conversion efficiency of conventional dynamic vibration absorber is low and
unstable, and contributes little to the decomposition and transmission of vibration energy of the main system. Additionally, the
high robustness against multi-source vibration interference is lacking in traditional vibration absorption technology.
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X. Huang and B. Yang
Fig. 62. The transient energy conversion efficiency of the buckled BRES with respect to the initial impact velocity.
Fig. 63. The applicability descriptions of the four energy shunt strategies.
6.2. Challenges and prospects
Due to the remarkable broadband performance and high conversion efficiency the emerging regenerative energy strategy is
gradually developed into a novel strategy of vibration energy decomposition and conversion. The significant relative motion of
nonlinear oscillators is an important guarantee for efficient energy conversion. Nonlinear energy transfer mechanism can capture
sufficient energy from broadband ambient excitations. Therefore, the ultimate prototype of future vibration control is enabling the
primary system to unidirectionally transfer energy to small nonlinear attachments and efficiently convert the trapped energy into
available energy by incorporating energy trapping strategy, regenerative energy strategy and energy dissipation strategy. To conclude,
the future design of an eligible DVA should considers the application of smart materials that can be exploited to improve the conversion
efficiency for self-power of wireless sensor networks, the introduction of innovative metamaterials, adoption of the non-contact
nonlinear dissipation technologies. The future nonlinear vibration dampers should be miniaturized, portable, clustered and light­
weight. The challenges and prospects can be summarized as follows:
(1) The optically sensitive payload of a space satellite will be subjected to some micro-disturbances in space, such as cosmic wind,
thermal induced vibration of solar panels, impact of space debris, etc. Due to the microgravity environment, it is difficult to
dissipate energy by relying on structural damping. The imaging, positioning and pointing accuracy of optically sensitive
payload on board depend heavily on the anti-interference performance of the onboard platform, thereby it is of great signifi­
cance to improve the micro-disturbance suppression performance of optically sensitive payload platform on board.
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X. Huang and B. Yang
Table 1
Comparison of advantages and disadvantages within the proposed energy strategies.
Classification
Regression energy strategy
Advantages
LES
NES
VI-NES
Syntonic elastic energy
strategy
Heat energy strategy
AMM
EMM
MR
ECD
Switchedcoupling
Regenerative energy
strategy
Smart materials
Disadvantages
• High energy absorption
• Light-weight
• Low-frequency
•
•
•
•
•
•
•
•
Light-weight
Broadband TET
High robustness
Low-frequency & impulse
Passive
Low to high frequency modal reallocation
Resonance capture
Wide bandgap
• Efficient wave control
• Light-weight
• Low-frequency
Narrow bandwidth
Undamped
Return
Multiple cells
Incident energy threshold
Critical damping ratio,
Complex parameter design
•
•
•
•
Large mass ratio
Easy to damage
Hard to control
Complicated design
Difficult to modify
Poor reliability
Processing difficulties
High cost
Limited control direction
Limited damping force
Dependent control
algorithm
• Continuous power supply
• Low-power dissipation
• High shear yield strength
• Insensitive to impurities
•
•
•
•
•
•
•
Wide temperature range
Semi-active control
High robustness
Non-contact damping
Economic friendly
Simple structure
High reliability
•
•
•
•
•
•
•
•
•
•
•
• Easy maintenance
• Multidirectional damping
• Semi-active
• Substantial stiffness and damping
adjustment
• high-efficiency energy dissipation
• Self-powered
• Energy reuse
Electromagnetic
•
•
•
•
•
•
•
•
•
•
•
•
Broadband
Adaptive
Simple structure
High reliability
Wide range
Enormous size
Heavy body
Large power consumption
Sensitive to ambient
temperature
• Hard to regulate precisely
• Complex parameter design
• High voltage
output
• High power
output
• Light-weight
• Easy tuning
• Large output
current
• High power
output
• High-efficiency
• Easy to enlarge
• High durability
• Broadband tuning
• Low impedance
• Repeated switching
• Low output current
• Low efficiency
• Pulse output
• High impedance
• Low output voltage
• A large number of magnets
• Multiple coils
• Heavy weight
(2) Advanced equipment and facilities in the fields of semiconductors, nanotechnology, laser communications, chip processing and
optical instruments are ultra-precise and vibration-sensitive. However, due to the unavoidable environmental vibration and
self-excited micro-vibration, the performance of advanced instruments is adversely affected. Therefore, improving the antivibration and anti-impact performance of their carrying platform is an important way to improve their work efficiency and
accuracy.
(3) The nonlinear dynamic vibration absorber with small mass ratio is difficult to have significant vibration suppression perfor­
mance. Conventional NESs have strict requirements on mass ratio, and it is difficult for nonlinear oscillators with small mass
40
Mechanical Systems and Signal Processing 182 (2023) 109496
X. Huang and B. Yang
ratio to achieve targeted energy transfer. Therefore, it is of great significance to design nonlinear vibration absorber with small
mass ratio to realize fast and efficient energy transfer and energy conversion.
(4) How to efficiently transfer vibration energy from the main system subjected to wideband weak impulsive scenarios or har­
monics to the nonlinear oscillator and lock it in the subsystem for energy conversion or dissipation is a troublesome problem.
The emerging nonlinear structures such as multi-stable systems have attracted much attention because of their multiple stable
equilibrium positions which can realize high-energy inter-well orbits. The multi-stable energy conversion vibration control
strategy is expected to achieve better vibration suppression effect for the vibration structure under broadband weak ambient
excitations.
(5) Additionally, with the advances of Internet of things (IoT) and artificial intelligence technology (AIT), the vibration control
strategy can be flexibly switched between the energy shunt strategies reviewed above by state-of-the-art control algorithms.
Consequently, the tunable vibration control method of nonlinear energy transfer and conversion is obtained.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to
influence the work reported in this paper.
Acknowledgement
The work is supported by National Natural Science Foundation of China (52173239, 5177349) and the National Key R&D Program
of China (2017YFF0108000), for which the authors are most grateful.
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