International Journal of Engineering Trends and Technology (IJETT) – Volume 23 Number 6- May 2015
Identification of damping parameters for particle
damper from the response of SDOF harmonically
forced linear oscillator
Mr.Uttam L.Anuse1, Prof.S.B.Tuljapure2
1
P.G.Student, 2Assistant Professor,
Department of Mechanical Engineering,
Walchand Institute of Technology, Solapur
Solapur University, Solapur, Maharashtra, India
Abstract— This paper deals with Experimental methods for
wide variety of applications including vibration attenuation of
identification of Particle damping parameters from the response
cutting tools, turbine blades, television aerials, structures,
of Single degree of freedom harmonically forced linear oscillator
plates, tubing, and shafts. [3]
when system damped with spring and particle damping ,which
Particle Vibration Damping (PVD for the short) is a
parameter is responsible for the control of resonant response of
vibrating systems, and calculation of damping parameters for the
cases such as spring + particle damper in experimental method
setup have been presented to investigate steady state response
combination of impact damping and friction damping. In a
PVD, metal or ceramic particles or powders of small size
(0.05 to 5 mm in diameter) are placed inside cavities
amplitude xi for SDOF system for different values of amplitude
Within or attached to the vibrating structure. Metal particles of
Yi of the base excitation from this relationship of (Xi ,Yi) for
high density such as lead or tungsten give high damping
particle damping by using half power band-width method and
performance due to dissipation of kinetic energy. Particle
the Frequency f1 and f2 calculated using FFT analyser.
Vibration Damping involves the potential energy absorptions
and dissipation through momentum exchange between moving
Keywords— damping ratio; Damping Coefficient;
Resonant frequency; Excitation frequency;
particles and vibrating walls, friction impact restitution. [4]
Particle Impact Damping (PID for the short) is a means for
1. I. INTRODUCTION
achieving high structural damping by the use of a particle-
Particle Damping
filled enclosure attached to the structure in a region of high
Particle damping technology is a derivative of impact
displacements. The particles absorb kinetic energy of the
damping
dampers
structure and convert it into heat through inelastic collisions
significantly reduce the noise and impact forces generated by
between the particles and the enclosure, and amongst the
an impact damper and are less sensitive to changes in the
particles.
with
several
advantages.
Particle
cavity dimensions or excitation amplitude.[2] The advantages
of impact dampers are that these dampers are inexpensive,
simple designs that provide effective damping performance
over a range of accelerations and frequencies. In addition,
impact dampers are robust and can operate in environments
that are too harsh for other traditional damping methods.
2. II. RELEVANCE
In many situations, it is important to identify damping
information from a vibration system with both Coulomb and
Viscous sources of damping. Their frequent occurrence in
practical engineering has arised for a long time the interest of
many researchers in the vibration field. Friction dampers (with
Vibration damping with impact dampers has been used in a
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International Journal of Engineering Trends and Technology (IJETT) – Volume 23 Number 6- May 2015
viscous damping as the system damping) are used in gas
turbine engines, high speed turbo pumps, large flexible space
structures under carriage of railway bogie, vehicle suspension
systems etc. These dampers are used to reduce resonant
stresses by providing sliding contact between points
experiencing relative motion due to vibration, thereby
dissipating resonant vibration energy.
The distribution and arrangement of the multiple particle
dampers on the structure usually have a significant impact on
the damping effect of the dampers. It is seen that the
identification and estimation of the numerous forms of
damping present in a dynamic system is helpful in improving
Fig.1 Schematic of the experimental arrangement (b) A
magnified view of the particles inside the enclosure [21]
the control of resonant response. As such, some theoretical
and experimental studies on “Development of Theoretical and
Experimental Methods for Identification of Coulomb, Viscous
and Particle Damping Parameters from the Responses of a
SDOF Harmonically Forced Linear Oscillator” have been
carried out. When a vibrating system is damped with more
than one type of models of damping, it is necessary to
determine which of these types of damping are more effective
to control the resonant response. In such case, it is important
to identify damping parameters from the responses of a
vibrating system. Therefore when a system is damped due to
Coulomb friction, viscous friction and Particle damping, it is
necessary to develop theoretical & Experimental methods for
identification of these damping parameters from the responses
Fig.2The model of a single degree of freedom system of a
particle vibration damper22]
of the vibrating system.
As such, it is proposed to develop methods for identification
of Coulomb and Viscous friction (and also with Particle
damping) parameters responsible for the control of resonant
response of vibrating systems.
For this purpose, following work has been carried out.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 23 Number 6- May 2015
Fig. 3 particle vibration damper (left) and the particle contacts
the base of the springs has been excited by an electrodynamic
(right).[22]
exciter.
The Viscous damper is attached between Centers of the mass
and the “C” frame. Two Particle dampers have been attached.
One end of the particle damper is connected to the mass and
other end of the damper is kept free. Two Coulomb dampers
have been attached between the mass and end plate of the “C‟
frame. The frequency response curve of the system is obtained
using the accelerometer pick up with its necessary attendant
equipment and a FFT analyzer, over a small range of
•
excitation frequency.
Half Power Band-Width Method:
•
To estimate damping ratio from frequency domain, (frequency
response curve) half-power bandwidth method can be used. In
SYSTEM PARAMETERS k, m
A plate of 1.0 kg has been used and the natural frequency of
system alone was chosen as 8.75 Hz, (54.97 rad/sec) and
this method, resonant amplitude of the system is obtained
first. Corresponding to each natural frequency, there is a peak
using the equation, n 
in Frequency Response Function (FRF) amplitude.
On decibel scale, 3 dB down from the peak there are two
points corresponding to half
power point.
The
more the damping, more the frequency range between this two
points. Half-power bandwidth Band width is defined as the
ratio of the frequency range (f2-f1) between the two half power
points to the natural frequency (fn) at this mode. It is
related to damping ratio as, 2 
f 2  f1
.
fn
IV. EXPERIMENTALTEST SET-UP AND THE
PLAN OF INSTRUMENTATION
A schematic of the experimental test set-up is shown in the
k
spring stiffness k was obtained
m
as 3022 N/m. Thus the values of the parameters of SDOF
system are m=1.0 kg and k= 3022 N/m.

Design of springs of Stiffness k1 /2
Two parallel springs each of stiffness of k1/2 = 1511 N/m have
been designed for the experimental work. The springs selected
are helical compression with both ends squared and ground.
The dimensions of springs are obtained using standard
formulae of design of helical compression spring. The
material of springs is selected as high grade spring steel. The
final dimensions of the spring are as follows.
Following are the design specifications.
TABLE 1 – DESIGN SPECIFICATION OF SPRINGS FOR
fig. (4.1).A plate which is made to move in the horizontal
SDOF SYSTEM
direction in two guide bars, represents the mass m of the
system. It is connected on two parallel springs of equal
Parameters
stiffness k1/2 each as shown in figure (4.1). Linear bearings
Spring stiffness
k1/2=1511 N/m
Number of turns (N)
14
and guide bars. A heavy “C” frame has been used for fixing
Wire diameter (d)
4mm
the guide bars as shown in figure. On the left side of mass, a
Mean diameter (D)
38 mm
Outer diameter (D0)
42 mm
Inner diameter (Di)
34 mm
Spring index (C)
10
have been used to reduce friction in between the mass plate
viscous damper, two Coulomb dampers and two particle
dampers have been attached. While, on the right side of mass,
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International Journal of Engineering Trends and Technology (IJETT) – Volume 23 Number 6- May 2015

The frequency response curve for 300 balls inside the
Determination of system damping + particle
pipe case is shown in figure (4.9). Using the half power band-
damping (s+p )
Particle Vibration Damping is a combination of impact
width method, the value of system damping ratio s+pwith no
damping and friction damping. In a PVD, metal or ceramic
balls has been determined as,
particles or powders of small size (0.05 to 5 mm in diameter)
s p 
are placed inside cavities within or attached to the vibrating
f 2  f1 8.037  7.102
=
= 0.06233
2  fn
2  7.5
structure. The particles absorb kinetic energy of the structure
and convert it into heat through inelastic collisions between
iv) Particle damping with fully filled balls inside pipe
The frequency response curve for fully filled balls
the particles and the enclosure, and amongst the particles.
In the experimental set-up, stainless steel balls of small size
inside the pipe case is shown in figure (4.10). Using the half
(3.18 mm in diameter) are placed inside pipe (of diameter
power band-width method, the value of system damping ratio
20mm and length 80 mm). The pipe is closed from both ends.
s+pwith no balls has been determined as,
One end of pipe is attached to the vibrating mass and other
s p 
end is kept free.
In this case, the SDOF spring mass system with particle
f 2  f1 8.08  6.92
=
= 0.07784
2  fn
2  7.5
TABLE 2. DAMPING RATIO  OF VARIOUS DAMPING COMBINATION
damping has been excited from 5 Hz to 12 Hz using
electro dynamic exciter and the steady state response X has
been measured using an accelerometer and FFT analyzer. The
readings were taken by increasing the number of balls inside
the pipe, starting from no balls to full filled balls inside the
pipe.
i) Particle damping with no balls inside pipe
The frequency response curve for no balls inside the
pipe case is shown in figure (4.7). Using the half power bandwidth method, the value of system damping ratio s+pwith no
Type of
damping
S
S+P(T:No balls)
S+P(T:200 balls)
S+P(T:300 balls)
S+P(T:fully filled
with balls)
fr(Hz)
Xr
(microns)
f1
f2

8.75
4647.5
8.314
9.243
0.053
7.5
6815
7.289
7.9
0.04
7.5
6325
7.308
8.2
0.059
7.5
6095
7.102
8.037
0.0623
7.5
4395
6.92
8.08
0.0778
balls has been determined as,
s p 
f 2  f1 7.9  7.289
=
= 0.04
2  fn
2  7.5
ii) Particle damping with 200 balls inside pipe
The frequency response curve for 200 balls inside the
pipe case is shown in figure (4.8). Using the half power bandwidth method, the value of system damping ratio s+pwith no
balls has been determined as,
s p 
f 2  f1 8.2  7.308
=
= 0.059
2  fn
2  7.5
iii) Particle damping with 300 balls inside pipe
Fig.4. Experimental Setup with particle damper
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International Journal of Engineering Trends and Technology (IJETT) – Volume 23 Number 6- May 2015
S+P(full balls)
5000
4500
X (microns)
4000
3500
3000
2500
2000
1500
1000
500
0
4
5
6
7
8
9
10
11
12
f (Hz)
Fig.4.9. Frequency response curve for ξs+p
fn=7.5 Hz ; f1= 6.92 Hz ;f2= 8.08 Hz
ξ=0.0778; Xr=4395 µm
3. V. CONCLUSION
Particle dampers significantly reduce the noise and impact
forces generated by an impact damper and are less sensitive to
changes in the cavity dimensions or excitation amplitude.[2]
The advantages of impact dampers are that these dampers are
inexpensive, simple designs that provide effective damping
performance over a range of accelerations and frequencies.
i)
For s+p(no ball condition)with resonant frequency equal to
7.5 Hz . Using the half power band-width method, the value of
system damping ratio has been determined as s+p = 0.04.
For s+p(200 balls) with resonant frequency equal to 7.5 Hz .
Using the half power band-width method, the value of system
damping ratio has been determined as s+p = 0.059
For s+p(300 balls)with resonant frequency equal to 7.5 Hz .
Using the half power band-width method, the value of system
damping ratio has been determined as
s = 0.0623.
iv) For s+p(fully filled) with resonant frequency equal to 7.5
Hz. Using the half power band-width method, the value of
system damping ratio has been determined as
s+p = 0.0778
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International Journal of Engineering Trends and Technology (IJETT) – Volume 23 Number 6- May 2015
7.
REFERENCES
1.
2.
3.
4.
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6.
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[4] Mao, K. M., Wang, M. Y., Xu, Z. W., and Chen, T. N., 2004,
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