Abstract

Vibrational energy harvesting has attracted considerable research attention for electrical power collection from ambient vibrations. Thereby, this study first developed an electromagnetic energy harvester of large-scale bistable motion by application of stochastic resonance, to enhance energy harvesting efficiency at a broadly low frequency. The electromagnetic energy harvester is fabricated by a magnet-coil generator and an oblique-supported spring-mass system. In the beginning, a weighting function is originally proposed considering mutual position relationship of the magnet and coil, and a motion equation and an electromagnetic induction equation are simultaneously established considering both elastic spring recovery force and electromagnetic induction Lorentz force. Subsequently, numerical analysis is processed to resolve the simultaneous equations to obtain systematic response displacement and the induced voltage, and the numerical solutions are accurately consistent with the measuring results in validation experiments. Furthermore, a damping coefficient is identified considering the mutual effectiveness of the damping forces from the normal friction and electromagnetic induction, and the influence of electromagnetic induction damping on systematic response displacement is carefully discussed. Eventually, experimental results clarified that the stochastic resonance phenomenon actually occurred as a large-scale bistable motion, and it is further validated that power generation efficiency can be noticeably enhanced following amplitude amplifications of systematic response displacement.

References

1.
Halim
,
M. A.
,
Tao
,
K.
,
Towfighian
,
S.
, and
Zhu
,
D.
,
2019
, “
Vibration Energy Harvesting: Linear, Nonlinear and Rotational Approaches
,”
Shock Vib.
,
2019
, pp.
1
2
.
2.
Harne
,
R. L.
, and
Wang
,
K. W.
,
2013
, “
A Review of the Recent Research on Vibration Energy Harvesting via Bistable Systems
,”
Smart Mater. Struct.
,
22
(
2
), p.
023001
.
3.
Xiao
,
H.
, and
Wang
,
X.
,
2014
, “
A Review of Piezoelectric Vibration Energy Harvesting Techniques
,”
Int. Rev. Mech. Eng.
,
8
(
3
), pp.
609
620
.
4.
Leland
,
E. S.
, and
Wright
,
P. K.
,
2006
, “
Resonance Tuning of Piezoelectric Vibration Energy Scavenging Generators Using Compressive Axial Preload
,”
Smart Mater. Struct.
,
15
(
5
), pp.
1413
1420
.
5.
Chen
,
Z.
,
He
,
J.
, and
Wang
,
G.
,
2019
, “
Vibration Bandgaps of Piezoelectric Metamaterial Plate With Local Resonators for Vibration Energy Harvesting
,”
Shock and Vibration
,
2019
, p.
1397123
.
6.
Shahruz
,
S. M.
,
2006
, “
Design of Mechanical Band-Pass Filters for Energy Scavenging
,”
J. Sound Vib.
,
292
(
3–5
), pp.
987
998
.
7.
Derakhshani
,
M.
, and
Berfield
,
T. A.
,
2019
, “
Snap-Through and Mechanical Strain Analysis of a MEMS Bistable Vibration Energy Harvester
,”
Shock Vib.
,
2019
, pp.
1
10
.
8.
Keshmiri
,
A.
, and
Wu
,
N.
,
2018
, “
A Wideband Piezoelectric Energy Harvester Design by Using Multiple Non-Uniform Bimorphs
,”
Vibration
,
1
(
1
), pp.
93
104
.
9.
Ferrari
,
M.
,
Ferrari
,
V.
,
Guizzetti
,
M.
,
Ando
,
B.
,
Balio
,
S.
, and
Trigona
,
C.
,
2010
, “
Improved Energy Harvesting From Wideband Vibration by Nonlinear Piezoelectric Converters
,”
Sens. Actuators, A
,
162
(
2
), pp.
425
431
.
10.
McInnes
,
C. R.
,
Gorman
,
D. G.
, and
Cartmell
,
M. P.
,
2008
, “
Enhanced Vibrational Energy Harvesting Using Nonlinear Stochastic Resonance
,”
J. Sound Vib.
,
318
(
4–5
), pp.
655
662
.
11.
Gammaitoni
,
L.
,
Hanggi
,
P.
,
Jung
,
P.
, and
Marchesoni
,
F.
,
1998
, “
Stochastic Resonance
,”
Rev. Mod. Phys.
,
70
(
1
), pp.
223
287
.
12.
Benzi
,
R.
,
Parisi
,
G.
,
Sutera
,
A.
, and
Vulpiani
,
A.
,
1982
, “
Stochastic Resonance in Climatic Change
,”
Tellus
,
34
(
1
), pp.
10
16
.
13.
Klamecki
,
B. E.
,
2005
, “
Use of Stochastic Resonance for Enhancement of Low-Level Vibration Signal Components
,”
Mech. Syst. Signal Process
,
19
(
2
), pp.
223
237
.
14.
Leng
,
Y.
,
Wang
,
T.
,
Guo
,
Y.
,
Xu
,
Y.
, and
Fan
,
S.
,
2007
, “
Engineering Signal Processing Based on Bistable Stochastic Resonance
,”
Mech. Syst. Signal Process
,
21
(
1
), pp.
138
150
.
15.
Chapeau-Blondeau
,
F.
,
2000
, “
Stochastic Resonance at Phase Noise in Signal Transmission
,”
Phys. Rev. E
,
61
(
1
), pp.
942
943
.
16.
Jung
,
P.
, and
Hanggi
,
P.
,
1991
, “
Amplification of Small Signal via Stochastic Resonance
,”
Phys. Rev. A
,
44
(
12
), pp.
8032
8042
.
17.
Moss
,
F.
,
Ward
,
M. L.
, and
Sannita
,
W. G.
,
2004
, “
Stochastic Resonance and Sensory Information Processing: A Tutorial and Review of Application
,”
Clin. Neurophysiol.
,
115
(
2
), pp.
267
281
.
18.
Rallabandi
,
V. P.
, and
Roy
,
P. K.
,
2010
, “
Magnetic Resonance Image Enhancement Using Stochastic Resonance in Fourier Domain
,”
Magn. Reson. Imaging
,
28
(
9
), pp.
1361
1373
.
19.
Dylov
,
V. D.
, and
Fleischer
,
J. W.
,
2010
, “
Nonlinear Self-Filtering of Noisy Images via Dynamical Stochastic Resonance
,”
Nat. Photonics
,
4
(
5
), pp.
323
328
.
20.
Pellegrini
,
S. P.
,
Tolou
,
N.
,
Schenk
,
M.
, and
Herder
,
J. L.
,
2012
, “
Bistable Vibration Energy Harvesters: A Review
,”
J. Intell. Mater. Syst. Struct.
,
24
(
11
), pp.
1303
1312
.
21.
Andò
,
B.
,
Baglio
,
S.
,
Maiorca
,
F.
, and
Trigona
,
C.
,
2012
, “
Two Dimensional Bistable Vibration Energy Harvester
,”
Procedia Eng.
,
47
, pp.
1061
1064
.
22.
Arrieta
,
A. F.
,
Depero
,
T.
,
Bergamini
,
A. E.
, and
Ermanni
,
P.
,
2013
, “
Broadband Vibration Energy Harvesting Based on Cantilevered Piezoelectric Bi-Stable Composites
,”
Appl. Phys. Lett.
,
102
(
17
), pp.
1
4
.
23.
Cottone
,
F.
,
Vocca
,
H.
, and
Gammaitoni
,
L.
,
2009
, “
Nonlinear Energy Harvesting
,”
Phys. Rev. Lett.
,
102
(
8
), p.
080601
.
24.
Stanton
,
S. C.
,
McGehee
,
C. C.
, and
Mann
,
B. P.
,
2010
, “
Nonlinear Dynamics for Broadband Energy Harvesting: Investigation of a Bistable Piezoelectric Inertial Generator
,”
Phys. D: Nonlinear Phenom.
,
239
(
10
), pp.
640
653
.
25.
Ferrari
,
M.
,
Ferrari
,
V.
,
Guizzetti
,
M.
, and
Marioli
,
D.
,
2010
, “
A Single-Magnet Nonlinear Piezoelectric Converter for Enhanced Energy Harvesting From Random Vibrations
,”
Procedia Eng.
,
5
, pp.
1156
1159
.
26.
Friswell
,
M. I.
,
Ali
,
S. F.
,
Bilgen
,
O.
,
Adhikari
,
S.
,
Lees
,
A. W.
, and
Litak
,
G.
,
2012
, “
Non-Linear Piezoelectric Vibration Energy Harvesting From a Vertical Cantilever Beam With Tip Mass
,”
J. Intell. Mater. Syst. Struct.
,
23
(
13
), pp.
1505
1521
.
27.
Lan
,
C. B.
, and
Qin
,
W. Y.
,
2014
, “
Energy Harvesting From Coherent Resonance of Horizontal Vibration of Beam Excited by Vertical Base Motion
,”
Appl. Phys. Lett.
,
105
(
11
), p.
113901
.
28.
Kawano
,
M.
,
Zhang
,
Y.
,
Zheng
,
R.
,
Nakano
,
K.
, and
Kim
,
B.
,
2015
, “
Design and Manufacture of Perpendicular bi-Stable Cantilever for Vibrational Energy Harvesting on the Basis of Stochastic Resonance
,”
J. Phys.: Conf. Ser.
,
660
, p.
012104
.
29.
Zhu
,
D.
, and
Beeby
,
S. P.
,
2013
, “
A Broadband Electromagnetic Energy Harvester With a Coupled Bistable Structure
,”
J. Phys.: Conf. Ser.
,
476
, p.
012070
.
30.
Zhou
,
S.
,
Cao
,
J.
,
Wang
,
W.
,
Liu
,
S.
, and
Lin
,
J.
,
2015
, “
Modeling and Experimental Verification of Doubly Nonlinear Magnet-Coupled Piezoelectric Energy Harvesting From Ambient Vibration
,”
Smart Mater. Struct.
,
24
(
5
), p.
055008
.
31.
Gao
,
Y.
,
Leng
,
Y.
,
Javey
,
A.
,
Tan
,
D.
,
Liu
,
J.
,
Fan
,
S.
, and
Lai
,
Z.
,
2016
, “
Theoretical and Applied Research on Bistable Dual-Piezoelectric-Cantilever Vibration Energy Harvesting Toward Realistic Ambience
,”
Smart Mater. Struct.
,
25
(
11
), p.
115032
.
32.
Erturk
,
A.
, and
Inman
,
D. J.
,
2011
, “
Broadband Piezoelectric Power Generation on High-Energy Orbits of the Bistable Duffing Oscillator With Electromechanical Coupling
,”
J. Sound Vib.
,
330
(
10
), pp.
2339
2353
.
33.
Zhou
,
S.
,
Cao
,
J.
,
Inman
,
D.
,
Lin
,
J.
,
Liu
,
S.
, and
Wang
,
Z.
,
2014
, “
Broadband Tristable Energy Harvester: Modeling and Experiment Verification
,”
Appl. Energy
,
133
, pp.
33
39
.
34.
Zou
,
H.
,
Zhang
,
W.
,
Li
,
W.
,
Hu
,
K.
,
Wei
,
K.
,
Peng
,
Z.
, and
Meng
,
G.
,
2017
, “
A Broadband Compressive-Mode Vibration Energy Harvester Enhanced by Magnetic Force Intervention Approach
,”
Appl. Phys. Lett.
,
110
(
16
), p.
163904
.
35.
Zou
,
H.
,
Zhang
,
W.
,
Li
,
W.
,
Wei
,
K.
,
Hu
,
K.
,
Peng
,
Z.
, and
Meng
,
G.
,
2018
, “
Magnetically Coupled Flextensional Transducer for Wideband Vibration Energy Harvesting: Design, Modeling and Experiments
,”
J. Sound Vib.
,
416
, pp.
55
79
.
36.
Derakhshani
,
M.
,
Berfield
,
T.
, and
Murphy
,
K. D.
,
2017
, “
Dynamic Analysis of a Bi-Stable Buckled Structure for Vibration Energy Harvester
,”
Dyn. Behav. Mater.
,
1
, pp.
199
208
.
37.
Mehdipour
,
I.
,
Braghin
,
F.
,
Lecis
,
N.
, and
Galassi
,
C.
,
2016
, “
Analytical Modeling and Experimental Verification of a s-Shaped Vibration Energy Harvester
,”
Proceedings of the ASME 2016 Conference on Smart Materials, Adaptive Structures and Intelligent Systems
,
Stowe, VT
,
September
.
38.
Yang
,
W.
, and
Towfighian
,
S.
,
2016
, “
Nonlinear Vibration Energy Harvesting Based on Variable Double Well Potential Function
,”
Proceeding of SPIE Active and Passive Smart Structures and Integrated Systems
,
Las Vegas, NV
,
April
, p.
9799
.
39.
Yang
,
W.
, and
Towfighian
,
S.
,
2016
, “
A Hybrid Nonlinear Vibration Energy Harvester
,”
Mech. Syst. Signal Process
,
90
, pp.
317
333
.
40.
Zheng
,
R.
,
Nakano
,
K.
,
Hu
,
H.
,
Su
,
D.
, and
Cartmell
,
M. P.
,
2014
, “
An Application of Stochastic Resonance for Energy Harvesting in a Bistable Vibrating System
,”
J. Sound Vib.
,
333
(
12
), pp.
2568
2587
.
41.
Nakano
,
K.
,
Cartmell
,
M. P.
,
Hu
,
H.
, and
Zheng
,
R.
,
2014
, “
Feasibility of Energy Harvesting Using Stochastic Resonance Caused by Axial Periodic Force
,”
Strojniski Vestnik-J. Mech. Eng.
,
60
(
5
), pp.
314
320
.
42.
Zhang
,
Y.
,
Zheng
,
R.
,
Ejiri
,
K.
,
Su
,
D.
, and
Nakano
,
K.
,
2016
, “
Modeling Analysis for Vibration Energy Harvesting Excited by Low-Speed Automobile Tires
,”
Trans. Jpn. Soc. Mech. Eng.
,
82
(
840
), pp.
15
00645
.
43.
Zhang
,
Y.
,
Zheng
,
R.
,
Kaizuka
,
T.
,
Su
,
D.
,
Nakano
,
K.
, and
Cartmell
,
M. P.
,
2015
, “
Broadband Vibration Energy Harvesting by Application of Stochastic Resonance From Rotational Environments
,”
Eur. Phys. J. Spec. Top.
,
224
, pp.
2687
2701
.
44.
Zhang
,
Y.
,
Nakano
,
K.
,
Zheng
,
R.
, and
Cartmell
,
M. P.
,
2016
, “
Adjustable Nonlinear Mechanism System for Wideband Energy Harvesting in Rotational Circumstances
,”
J. Phys.: Conf. Ser.
,
744
, p.
012079
.
45.
Zhao
,
W.
,
Wu
,
Q.
,
Zhao
,
X.
,
Nakano
,
K.
, and
Zheng
,
R.
,
2020
, “
Development of Large-Scale Bistable Motion System for Energy Harvesting by Application of Stochastic Resonance
,”
J. Sound Vib.
,
473
, p.
115213
.
46.
Zhao
,
W.
,
Zheng
,
R.
,
Yin
,
X.
,
Zhao
,
X.
, and
Nakano
,
K.
,
2020
, “
Bistable Vibration Harvesting System of Diagonally Supported Spring-Mass Using Piezoelectric Element
,”
Trans. Jpn. Soc. Mech. Eng.
,
86
(
889
), pp.
20
72
.
47.
Yang
,
Z.
,
Zhou
,
S.
,
Zu
,
J.
, and
Inman
,
D.
,
2018
, “
High-Performance Piezoelectric Energy Harvesters and Their Applications
,”
Joule
,
2
(
4
), pp.
642
697
.
48.
Alevras
,
P.
,
2021
, “
On the Effect of the Electrical Load on Vibration Energy Harvesting Under Stochastic Resonance
,”
ASCE-ASME J. Risk Uncertain. Eng. Syst., Part B
,
7
(
1
), p.
010902
.
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