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High efficiency energy harvesting device with magnetic coupling for resonance
frequency tuning
Article in Proceedings of SPIE - The International Society for Optical Engineering · May 2008
DOI: 10.1117/12.776385
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High efficiency energy harvesting device with magnetic coupling for
resonance frequency tuning
Vinod R. Challa, M.G. Prasad and Frank T. Fisher
Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken, NJ USA 07030
ABSTRACT
Wireless sensors are becoming extremely popular for their ability to be employed in hostile and inaccessible locations to
monitor various parameters of importance, and vibration energy harvesting shows great potential in powering these
sensor networks. For efficient operation the device should operate in resonance at the environmental excitation
frequency and hence requires a frequency tuning mechanism. Recently efforts have been attempted to broaden the
frequency range of energy harvesting devices, but in terms of power density an efficient design methodology is lacking.
In this work, a tunable energy harvesting device with high efficiency and power density is presented. The technique
involves two single DOF’s cantilever beams which are coupled in a novel fashion by means of magnetic force for
resonance frequency tuning. Here the magnetic force acts as a variable stiffness coupling the two cantilever beams,
allowing one to alter the corresponding resonance frequencies of the cantilever beams. Magnetic force of attraction and
repulsion can be used to achieve the magnetic coupling and can increase the overall stiffness of either of the cantilever
beams while decreasing the others. The total power output of the device is found to be between 180 µW to 320 µW.
Keywords: vibration energy harvesting, piezoelectric, tunable energy harvesting device, magnetic coupling
1. INTRODUCTION
Vibration energy harvesting is becoming extremely popular due to their potential application in wireless sensors and
wireless sensor networks. The omnipresence of vibrations suggests the possibility to harvest energy to power these
sensors which are placed in inaccessible and remote locations. In addition, minimal maintenance and high life span are
key factors driving efforts in pursuing vibration energy harvesting as a source of power in these applications. While there
are several common energy harvesting mechanisms based on electrostatic, electromagnetic, and piezoelectric techniques,
most efforts to date have focused on electromagnetic and piezoelectric methods. (However, researchers have claimed to
have much higher power density in energy harvesting devices using magnetostrictive technique.[1]) In the early stages of
vibration energy harvesting research, electrostatic energy harvesting techniques were adapted to harvest energy; for
example, an electrostatic based energy harvesting device was developed using a variable capacitor, which was found to
increase the corresponding voltage output by orders of magnitude.[2] Other efforts include developing electrostatic
energy harvesting devices for low frequency applications and for potential MEMS scale design.[3,4] In addition to
electrostatic energy harvesting techniques, researchers have pursued electromagnetic-based energy harvesting devices
such as using two and four magnets configurations for higher power output and power density,[5] investigated MEMS
scale design,[6] and have suggested a novel way of up-converting the frequency to achieve higher power output which is
compatible with MEMS scale technology.[7] Piezoelectric techniques have more recently been pursued due to its
simplicity in experimental setup and high power density. Here cantilever beam-based designs are the most common
vibrating structure employed,[8] while non-uniform thicknesses cantilever designs have also been proposed.[9] Apart from
these designs, a MEMS scale piezoelectric energy harvesting cantilever has also been developed that can have increased
power density and the ability to be fabricated as an on-chip power source.[10,11] Even though much research has been
performed using various techniques and novel materials, most vibration energy harvesting devices are designed as nontunable single degree-of-freedom (DOF) systems having a single resonance frequency, thereby making them applicable
only for a given design frequency. In order for these devices to be efficiently applicable over a range of source
frequencies, a resonance frequency tuning mechanism is needed.
While the easiest way to change the resonance frequency of the device is by altering the mass or length or thickness of
the vibrating beam, this approach is quite challenging for a device in operation. Recently Roundy and Zhang have
examined the possibility of applying electrical potential to a piezoelectric bimorph to alter the resonance frequency.[12]
Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2008,
edited by Masayoshi Tomizuka, Proc. of SPIE Vol. 6932, 69323Q, (2008)
0277-786X/08/$18 · doi: 10.1117/12.776385
Proc. of SPIE Vol. 6932 69323Q-1
2008 SPIE Digital Library -- Subscriber Archive Copy
Similarly Leland and Wright have used compressive loads to alter the resonance frequency of a simply supported
beam.[13] While a multi-frequency piezoelectric energy harvester featuring an array of non-tunable cantilever beams has
been proposed to extend the range of frequency operability,[14] it would by definition have a very low efficiency as only
one or at most a few of the cantilevers would be in resonance and efficiently harvest energy for a given excitation
source.
Recently the authors have introduced a magnetic force resonance frequency tuning technique that uses attractive and
repulsive magnetic forces to induce an additional stiffness in the system, thereby altering the overall stiffness and the
corresponding resonance frequency of the energy harvesting device. Using this technique the authors were able to tune a
prototype device to either lower or higher source frequencies with respect to the unturned resonance frequency of the
device by ±20%.[15] However, in terms of power density and efficiency over the frequency range of operation,
enhancements are still necessary for a robust energy harvesting device methodology to be realized. Finally, while active
techniques can be employed to tune the energy harvesting devices, one must of course consider the energy requirements
of active tuning and the implications of active tuning on the overall efficiency energy harvesting system. The semi-active
technique seems promising especially in terms of frequency range operability; still enhancements are needed to have
higher power densities compatible in various applications where the frequency of the excitation source is either not
known or changing with time.
In this paper, a high efficiency energy harvesting device which consists of two independent single DOF systems are
magnetically coupled to enable resonance frequency tuning and hence efficient energy harvesting from a source
frequency which is somewhat greater than the natural frequency of either of the cantilever beams. The resonance
frequency tuning of the device is controlled by adjusting the distance between the magnets to allow the required
magnetic force to couple the cantilever beams. Magnetic force of attraction and repulsion are successfully applied to
tune either of the beams to higher frequencies while approximately consuming the same amount of volume as the
tunable single degree of freedom system described previously in the literature.[15]
2. MAGNETICALLY COUPLED TWO SINGLE DEGREE OF FREEDOM SYSTEMS
FOR RESONANCE FREQUENCY TUNING AND HIGHER POWER DENSITY
The proposed technique utilizes magnetic forces of attraction and repulsion to couple two independent single degree of
freedom systems, enabling one to tune the resonance frequency of one of the beam to match the source frequency. Here
the amount of magnetic force determines the change in effective stiffness of the beam and can be varied by adjusting the
distance between the magnets coupling the two beams. While the technique demonstrated here uses a cantilever beam
structure (due to its simplicity and the low resonant frequency of cantilever beams), it can be readily employed to other
geometrical structures.
The experimental setup involves two cantilever beams, of which one of the cantilever beams is fixed to a permanent
clamp, while the other beam is placed on a vertically displaceable clamp via a screw-spring mechanism.[15] Both
cantilevers are made of piezoelectric material, which produces electrical energy upon application of mechanical stresses.
Permanent magnets are placed at the tip of each cantilever beam (along with appropriate tip masses used to alter the
resonance frequency of the beams), providing a magnetic force of interaction whose magnitude is controlled by changing
the separation distance between the magnets as shown in figure 1. Each cantilever beam is initially designed to have
approximately the same resonance frequency. If the source frequency matches the natural frequencies of the cantilever
beams (with no magnetic coupling present), they would harvest energy as two individual cantilever beams. To design for
the case where the source vibration characteristics change over time, resonance frequency tuning of the device is
performed by introducing magnetic coupling of the beams that is introduced by displacing the movable cantilever beam
to the required distance of the fixed cantilever beam. The change in stiffness in the cantilever beams depends on the
amount of magnetic force/stiffness exerted between them. As described in Section 4, depending on the mode of the
magnetic force (either attractive or repulsive depending on how the magnets are configured), the vibrational response of
each cantilever beam is altered. While only one of the beams can be tuned to match the source frequency for a given
mode of magnetic force, the other beam can still harvest a limited (but non-negligible) amount of energy as a
piezoelectric cantilever beam which is not in resonance. This technique can further be customized to enable either wider
tunable frequency range or higher power density based on the application. For example, if the source frequency is such
Proc. of SPIE Vol. 6932 69323Q-2
that a wide frequency range tunable device is desired, then the cantilevers can be made to have different natural
frequencies, with the desired tunable range falling in between the frequencies of those cantilever beams. Depending on
the mode of the magnetic force either of the beams can be tuned to match the source frequency. In terms of power
density, the volume occupied is approximately the same as a single tunable cantilever beam developed previously by our
group, [15] thus resulting in a higher power density for the device.
Attractive or
Repulsive
Force
Permanent
Magnets
Fig. 1. (left) Schematic of the magnetically coupled two single DOF energy harvesting technique. (right) Photograph of the prototype.
3. EXPERIMENTAL SETUP
As described in section 2, the prototype device consists of two piezoelectric cantilever beams made of Stripe Actuators
(APC International Ltd). Tungsten masses and NdFeB cylindrical magnets are placed at the tip of the cantilevers as
shown in figure 1. Though the beams are designed to have approximately the same natural frequencies, the fixed beam
has a natural frequency of 22.5 Hz and the movable cantilever beam has 23.5 Hz. The built device is mounted on an
electro dynamic shaker (VTS V3 100-6) and the lead wires from the piezoelectric beams are connected to the data
acquisition (DAQ) card (National Instruments) and are in turn connected to the computer by a USB cable. An
accelerometer (Analog Devices) is mounted at the bottom of the enclosure, which is also connected to the DAQ card.
LabView software is used for real time monitoring of voltages from the piezoelectric beams and the accelerometer. The
input frequency and acceleration is provided from a function generator (HP 4120 series) and power amplifier (VTS)
connected to the shaker. The frequency of the vibration shaker is altered and the device is tuned accordingly to monitor
the tunability and output power of the device. For maximum power output, the voltages are captured across the optimal
load resistances of each piezoelectric cantilever beam. A schematic of the experimental setup is shown in figure 2.
Initially the beams produced a total power output of approximately 320 µW when the source vibration was 22.5 Hz,
which is the natural frequency of the fixed cantilever beam. A magnetic attractive force is then applied between the two
cantilever beams by adjusting the distance between them to monitor the resonance frequency tunability. It is found that
by increasing the magnetic force of attraction, the resonance frequency of the fixed cantilever beam is shifted from 22.5
Hz to 32 Hz, whereas the power output from both the beams is recorded at each of the tuned resonance frequencies of
the fixed cantilever beam and found to decrease from 320 µW to 200 µW over this frequency range. Later the magnetic
force of repulsion is been employed between the two cantilever beams and it is found that the resonance frequency of the
movable cantilever beam increased from 23.5 Hz to 34 Hz with an increase in repulsive magnetic force. The power
output from both beams when the magnetic repulsive force is applied was also found to decrease from 320 µW to 200
µW over the frequency range tested.
Proc. of SPIE Vol. 6932 69323Q-3
Vibration Energy
Harvesting Device
Disc Msgnets
Piezoelectric Cantil
Variable resistors
Fig. 2. Schematic of the experimental setup.
4. PRELIMINARY RESULTS AND DISCUSSION
The experimental results of power output and damping from both the beams are recorded when subjected to magnetic
forces of attraction and repulsion, respectively. The power density of the device and the resonance frequency tunable
range is determined and compared with an array of non-tunable single DOF energy harvesting cantilevers.
4.1 Attractive mode of coupled magnetic force
4.1.1 Power output of the beams versus tuned resonance frequency of the fixed cantilever beam
The power output and the tunability of each beam is measured with respect to the increase in magnetic force of
attraction. The resonance frequency of the fixed beam increased with increase in the magnitude of magnetic force and
the beam is tuned from 22.5 Hz to 32 Hz. The power output from both the beams at each tuned resonance frequency of
the fixed beam is recorded and is plotted in figure 3, which indicates that the power obtained from the fixed cantilever
varies from 240 µW to 180 µW, while the power from the movable cantilever beam dropped from 90 µW to 10 µW. The
plot on the right in figure 3 suggests that the beams are out of phase due to the effect of attractive magnetic force which
is exciting the movable beam. As the magnetic force of attraction is increased to tune the fixed cantilever beam, an
equivalent and opposite magnetic force acts on the movable cantilever beam making the movable beam experience a
forced vibration from the fixed beam.
— fr, — — —
— fr, .. —
250
———Fixed cantilever beam
— Movable cantilever beam
22 2425283032 34
Frequency (Hz)
Fig. 3. (left) Power output of the fixed and movable cantilever beams versus tuned resonance frequency of the fixed cantilever beam
(right) LabView graph of voltage and phase of the two beams with respect to time.
Proc. of SPIE Vol. 6932 69323Q-4
4.1.2 Power output of the beams versus tuned resonance frequency of the movable cantilever beam
The effect of attractive magnetic force used to tune the fixed cantilever beam from 22.5 Hz to 32 Hz on the vibrational
response of the movable cantilever beam is studied. In this case it is observed that the natural frequency of the movable
beam is lowered as the magnitude of attractive force is increased. This reduction in natural frequency is attributed to an
increase in damping, which results in the decrease in natural frequency of the movable beam from 23.5 Hz to 20.5 Hz (as
described in the next section, the damping in the movable beam increases from 0.032 to 0.1 as the magnetic force of
attraction increases). The power output from both the beams in the tuned resonance frequency range of the movable
beam is recorded. While the change in resonance frequency of the movable beam is comparably small to that of the fixed
beam, the movable beam can still provide appreciable power at source frequencies slightly below its natural frequency
(and non-negligible power at even lower frequencies). The power output of the movable beam is reduced from 270 µW
to 190 µW and the power from the fixed beam dropped from 70 µW to 5 µW. A real time graph of the voltage outputs
from the two beams is plotted in figure 4 along with the power output plot.
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Fig. 4. (left) Power output of the beams versus tuned resonance frequency of the movable cantilever beam. (right) LabView graph of
voltage and phase of the two beams with respect to time.
4.1.3 Damping versus resonance frequency
The applied magnetic force of attraction for coupling the two piezoelectric cantilever beams induces a certain amount of
additional damping on the device. The damping in each cantilever beam is determined as the device is tuned to higher
frequencies by performing a flick test to obtain an amplitude decay plot with time for every tuned resonance frequency.
It is found that the damping in both the cantilever beams increases with the application of the attractive magnetic force.
the preliminary experimental results show that the damping in the fixed cantilever beam increased only from 0.03-0.036,
while the damping in the movable beam increases from 0.032 to 0.1 in the tuned resonance frequency range of fixed
cantilever beam.
Proc. of SPIE Vol. 6932 69323Q-5
0.12 £ Fixed cantilever beam
• Movable cantilever beam
0.08 -
0.04 -
•
A
A
£
A
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0.02 -
22
24
28
26
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Resonance frequency (Hz)
Fig. 5. Experimentally measured damping in the cantilever beams versus tuned resonance frequency of the fixed cantilever beam
4.1.4 Power output versus load resistance for each cantilever beam
In order to maximize the power output of the device the optimal load resistance (of the electrical circuit used to store the
harvested power) for each cantilever beam at its natural frequency of vibration is determined. The optimal load
resistance is found by performing a load resistance sweep and monitoring the power output of the beams as shown in
figure 6. A power output of 270 µW is obtained for the movable cantilever beam at 42 kΩ when the device is vibrated at
its natural frequency, while a power output of 240 µW is observed for the fixed beam at 39 kΩ.
300
250
200
100
—— — Fixed cantilever beam
—Movable cantilever beam
10
20
30
40
50
Load resistance (kO)
Fig. 6. Power output of each cantilever beam versus load resistance at its natural frequency
4.1.5 Optimal load resistances of the beams versus tuned resonance frequency of the fixed cantilever beam
The device is tuned to various source frequencies in the range of 22.5 Hz to 32 Hz and at every tuned resonance
frequency, the power output from both beams is maximized by employing the optimal load resistances as described
previously. As shown in figure 7, the optimal resistance of the fixed cantilever beam decreased from 41 kΩ to 28 kΩ and
for the movable cantilever beam the optimal resistance decreased from 39 kΩ to 33 kΩ.
Proc. of SPIE Vol. 6932 69323Q-6
'A.
C
I
32
£
£
.
.
. LA
.. £
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.
a
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0
ii 16
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Movable cantilever beam
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24
26
28
Resonance frequency (Hz)
30
32
Fig. 7. Optimal load resistance versus tuned resonance frequency of the fixed cantilever beam.
4.1.6 Device power output versus power output of a single DOF energy harvesting device in resonance
The total power output of the device, which includes the power from the fixed beam and the movable beam, is
determined experimentally at every resonance frequency for which the device is tuned between 22.5 Hz to 32 Hz as
shown in figure 8. The power output from both beams drops with an increase in resonance frequency due to the decrease
in amplitude of the cantilever beams (considering the input acceleration from the source remains the same). The total
power output of the device is found to be approximately 320 µW at 22.5 Hz and is reduced to 200 µW at 32 Hz. The
large drop in power is due to the drop in power from the movable cantilever beam (which is not in resonance).
In order to evaluate if the power from the coupled device is comparable to a non-tunable device in resonance, a
comparison is made to the amount of power that can be harvested from an individual cantilever beam in resonance at a
given frequency. As shown in figure 8, the power output from the magnetically coupled device is approximately equal to
the power output from a single cantilever beam in resonance at the higher range of frequencies tested. At the lower range
of frequencies in figure 8, the power output from the magnetically coupled device is significantly higher than that
possible from a single individual cantilever beam due to the contribution to the power output provided by the second
(movable) beam.
350
Magnetically coupled device
—Single DOF energy harvesting device
250
150
22
24
26
28
30
32
Resonance frequency (Hz)
Fig. 8. Comparison of device output powers obtained for a single DOF energy harvesting device and the magnetically-coupled twobeam energy harvesting device for the case of an attractive magnetic force.
Proc. of SPIE Vol. 6932 69323Q-7
4.2 Repulsive mode of coupled magnetic force
4.2.1 Power output of the beams versus resonance frequency of movable cantilever beam
The experiments described in section 4.1 were replicated for the case of a repulsive mode of magnetic force coupling the
beams. The power output and the tunability of each beam are again tested with respect to the change in magnitude of the
magnetic force. It is observed that the resonance frequency of the movable beam increased with increase in the repulsive
force and the beam is tuned from 23.5 Hz to 34 Hz (note that this is in contrast to the results described in section 4.1,
where the fixed beam exhibited the resonance frequency tuning effect). The power output of the movable beam
decreased from 270 µW to 190 µW as the beam is tuned from 23.5 Hz to 34 Hz, while the power from the fixed
cantilever beam dropped from 60 µW to 5 µW as shown in figure 9. In the case of repulsive force the beams appear to be
closely in phase as can be seen on the right side of the figure 9; this is again attributed to the forced vibration of the
movable cantilever beam on the fixed beam.
vcke — — — —
vckefl.
nfl ____________________________________________ Paiiath
'0
200
— ——
Fixed cantilever beam
Movable cantilever beam
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-6
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0
0.02
0.04
0.06
0.06
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0.12
0.14
0.16
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20.7
21.2
21.7
22.2
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Frequency (Hz)
Fig. 9. (left) Power output of the beams versus tuned resonance frequency of the movable cantilever beam. (right) LabView graph of
voltage and phase of the two beams with respect to time.
4.2.2 Power output of the beams versus resonance frequency of the fixed cantilever beam
As in the case of attractive mode described in section 4.1, a similar effect is seen in repulsive mode where the resonance
frequency of the fixed cantilever beam is only altered from 22.5 Hz to 20.35 Hz while the movable beam is tuned from
23.5 Hz to 34 Hz. This reduction in natural frequency is again attributed to an increase in damping with increase in
repulsive force as described earlier in section 4.1.2. The power outputs of the cantilever beams are recorded in the tuned
resonance frequency range of the fixed cantilever beam (22.5 Hz - 20.35 Hz). The power output of the fixed cantilever
beam decreased from 240 µW to 180 µW and the power from the fixed beam decreased from 80 µW to 75 µW. A real
time graph of the voltage and power outputs from the two beams is also plotted on the right side of figure 10.
Proc. of SPIE Vol. 6932 69323Q-8
Fig. 10. (left) Power output of the beams versus tuned resonance frequency of the fixed cantilever beam. (right) LabView graph of
voltage and phase of the two beams with respect to time.
4.2.3 Damping versus resonance frequency of the movable cantilever beam
The applied repulsive magnetic force induced an additional damping on the device as observed for the case of the
attractive magnetic force as described in section 4.1.2. The damping in the fixed cantilever beam is found to increase
from 0.03 to 0.18 and the damping in the movable cantilever beam increased from 0.03 to 0.038 in the tuned resonance
frequency range of the movable cantilever beam as shown in figure 11.
0.2
Movable cantilever beam
0.18
A Fixed cantilever beam
0.16
£
0.14
0.12
A
S
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E
0.08
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£
0.04
s
•
0.02
••••.
U
0
23
25
2]
29
31
33
35
Resonance frequency (Hz)
Fig. 11. Damping in the two cantilever beams versus tuned resonance frequency of the movable cantilever beam
4.2.4 Optimal resistance versus frequency
The optimal resistance for both the cantilevers for every resonance frequency is determined by performing a load
resistance sweep while monitoring the power output as described earlier in section 4.1.4. Figure 12 shows the optimal
resistance of both the beams in the tuned resonance frequency of the movable cantilever beam. It is found that for
movable beam the optimal resistance is decreased from 39 kΩ to 26 kΩ and for fixed cantilever beam the optimal
resistance decreased from 41 kΩ to 28 kΩ.
Proc. of SPIE Vol. 6932 69323Q-9
..
40
C
32
LA
..
A
..
A
£
£
.
£
.
£
•
•A.
24
A Fixed cantilever beam
• Movable cantilever beam
22
24
26
28
30
Resonance frequency (Hz)
34
32
Fig. 12. Optimal load resistance versus tuned resonance frequency of the movable cantilever beam.
4.2.5 Device Power output versus power output of a single DOF energy harvesting device in resonance
The total power output of the device is determined experimentally at every resonance frequency for which the device is
tuned between 23.5 Hz to 34 Hz as shown in figure 13. The power output from both beams drops with an increase in
resonance frequency due to the decrease in amplitude of the cantilever beams (considering the input acceleration from
the source remains the same). The total power output of the device is found to be approximately 324 µW at 23.5 Hz and
is reduced to 180 µW at 34 Hz. For comparison, an individual cantilever (of similar properties and geometry) at
resonance at 34 Hz would generate 170 µW of power. Thus the power output of the tuned device is greater than the
power output of an individual cantilever beam in resonance over this range of frequencies. In addition, the magnetically
coupled device enables one to tune the resonance frequency of the device to match the source frequency over this range
of frequencies. It is noteworthy to know that the power contributed by the fixed cantilever beam is almost negligible as
the device is tuned to farther frequencies from its untuned resonance frequency; in this case the total output power of the
device is mainly due to the movable cantilever beam.
350
•_
300
150
100
— — — Magnetically coupled device
50
—Single DOF energy harvesting device
I
I
I
I
0
23
25
27
29
31
33
35
Resonance frequency (Hz)
Fig. 13. Comparison of device output powers obtained for a single DOF energy harvesting device and the magnetically-coupled twobeam energy harvesting device for the case of repulsive magnetic force.
Proc. of SPIE Vol. 6932 69323Q-10
5. CONCLUSIONS
A magnetic coupling is introduced between two independent single degree of freedom system cantilever beams allowing
one to alter the overall stiffness of the device, and hence the corresponding natural frequencies of the cantilevers, to
enable resonance frequency tuning to match the source excitation frequency. Apart from the frequency responses, the
optimal load resistance conditions were also determined. A prototype has been successfully built and tested with both
modes of magnetic force coupling. It is observed from these preliminary experimental results that the magnetic force of
attraction increases the natural frequency of the fixed beam while decreasing the natural frequency of the movable beam.
On the other hand, the repulsive magnetic force increases the natural frequency of the movable beam and decreases the
natural frequency of the fixed beam. The main advantage of this magnetic coupling technique is that it allows one to tune
the cantilever beam without inducing a large damping. The total output power from both the cantilevers suggests that the
power density of the device is much higher than a single resonance frequency tunable cantilever beam presented
previously.[15] The prototype is tested over the frequency range of 22 - 34 Hz, while altering the magnetic force to match
the source excitation frequency. By performing the designed tuning technique, a continuous power output of 180 µW320 µW is achieved over the entire frequency range of 22 Hz to 34 Hz, irrespective of the mode of the magnetic force
used. The total power output of the magnetically coupled device is comparable to that of a single DOF energy harvesting
device in resonance; further it has the ability to tune the resonance frequency of the device to match the source
frequency. A companion paper describing the theoretical modeling of this technique is underway.
ACKNOWLEDGEMENTS
The authors would like to acknowledge Prof. Dimitri M. Donskoy of the Department of Civil, Environmental and Ocean
Engineering at Stevens Institute of Technology for the vibration equipment.
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