Vibration energy harvesting can be an effective method for scavenging wasted mechanical energy for use by wireless sensors that have limited battery life. Two major goals in designing energy harvesters are enhancing the power scavenged at low frequency and improving efficiency by increasing the frequency bandwidth. To achieve these goals, we derived a magnetoelastic beam operated at the transition between mono- and bi-stable regions. By improving the mathematical model of the interaction of magnetic force and beam dynamics, we obtained a precise prediction of natural frequencies as the distance of magnets varies. Using the shooting technique for the improved model, we present a fundamental understanding of interesting combined softening and hardening responses that happen at the transition between the two regimes. The transition regime is proposed as the optimal region for energy conversion in terms of frequency bandwidth and output voltage. Using this technique, low-frequency vibration energy harvesting at around 17 Hz was possible. The theoretical results were in good agreement with the experimental results. The target application is to power wildlife biologging devices from bird flights that have consistent high power density around 16 Hz (Shafer et al., 2015, “The Case for Energy Harvesting on Wildlife in Flight,” Smart Mater. Struct., 24(2), p. 025031).

References

References
1.
Shafer
,
M. W.
,
MacCurdy
,
R.
,
Shipley
,
J. R.
,
Winkler
,
D.
,
Guglielmo
,
C. G.
, and
Garcia
,
E.
,
2015
, “
The Case for Energy Harvesting on Wildlife in Flight
,”
Smart Mater. Struct.
,
24
(
2
), p.
025031
.
2.
Roundy
,
S.
,
Wright
,
P. K.
, and
Rabaey
,
J.
,
2003
, “
A Study of Low Level Vibrations as a Power Source for Wireless Sensor Nodes
,”
Comput. Commun.
,
26
(
11
), pp.
1131
1144
.
3.
Mitcheson
,
P. D.
,
Green
,
T. C.
,
Yeatman
,
E. M.
, and
Holmes
,
A. S.
,
2004
, “
Architectures for Vibration-Driven Micropower Generators
,”
J. Microelectromech. Syst.
,
13
(
3
), pp.
429
440
.
4.
Cook-Chennault
,
K.
,
Thambi
,
N.
, and
Sastry
,
A.
,
2008
, “
Powering MEMS Portable Devices—A Review of Non-Regenerative and Regenerative Power Supply Systems With Special Emphasis on Piezoelectric Energy Harvesting Systems
,”
Smart Mater. Struct.
,
17
(
4
), p.
043001
.
5.
González
,
J. L.
,
Rubio
,
A.
, and
Moll
,
F.
,
2002
, “
Human Powered Piezoelectric Batteries to Supply Power to Wearable Electronic Devices
,”
Int. J. Soc. Mater. Eng. Resour.
,
10
(
1
), pp.
34
40
.
6.
Mathúna
,
C. Ó.
,
O'Donnell
,
T.
,
Martinez-Catala
,
R. V.
,
Rohan
,
J.
, and
O'Flynn
,
B.
,
2008
, “
Energy Scavenging for Long-Term Deployable Wireless Sensor Networks
,”
Talanta
,
75
(
3
), pp.
613
623
.
7.
Torah
,
R.
,
Glynne-Jones
,
P.
,
Tudor
,
M.
,
O'Donnell
,
T.
,
Roy
,
S.
, and
Beeby
,
S.
,
2008
, “
Self-Powered Autonomous Wireless Sensor Node Using Vibration Energy Harvesting
,”
Meas. Sci. Technol.
,
19
(
12
), p.
125202
.
8.
Gregori
,
S.
,
Li
,
Y.
,
Li
,
H.
,
Liu
,
J.
, and
Maloberti
,
F.
,
2004
, “
2.45 GHZ Power and Data Transmission for a Low-Power Autonomous Sensors Platform
,”
International Symposium on Low Power Electronics and Design
(
ISLPED’04
), Newport Beach, CA, Aug. 11, pp.
269
273
.
9.
Kim
,
J.-W.
,
Takao
,
H.
,
Sawada
,
K.
, and
Ishida
,
M.
,
2007
, “
Integrated Inductors for RF Transmitters in CMOS/MEMS Smart Microsensor Systems
,”
Sensors
,
7
(
8
), pp.
1387
1398
.
10.
Bracke
,
W.
,
Merken
,
P.
,
Puers
,
R.
, and
Van Hoof
,
C.
,
2007
, “
Generic Architectures and Design Methods for Autonomous Sensors
,”
Sens. Actuators A
,
135
(
2
), pp.
881
888
.
11.
Baert
,
K.
,
Gyselinckx
,
B.
,
Torfs
,
T.
,
Leonov
,
V.
,
Yazicioglu
,
F.
,
Brebels
,
S.
,
Donnay
,
S.
,
Vanfleteren
,
J.
,
Beyne
,
E.
, and
Van Hoof
,
C.
,
2006
, “
Technologies for Highly Miniaturized Autonomous Sensor Networks
,”
Microelectron. J.
,
37
(
12
), pp.
1563
1568
.
12.
Sodano
,
H. A.
,
Inman
,
D. J.
, and
Park
,
G.
,
2004
, “
A Review of Power Harvesting From Vibration Using Piezoelectric Materials
,”
Shock Vib. Dig.
,
36
(
3
), pp.
197
206
.
13.
Sodano
,
H. A.
,
Inman
,
D. J.
, and
Park
,
G.
,
2005
, “
Generation and Storage of Electricity From Power Harvesting Devices
,”
J. Intell. Mater. Syst. Struct.
,
16
(
1
), pp.
67
75
.
14.
Roundy
,
S.
,
2005
, “
On the Effectiveness of Vibration-Based Energy Harvesting
,”
J. Intell. Mater. Syst. Struct.
,
16
(
10
), pp.
809
823
.
15.
Daqaq
,
M. F.
,
2010
, “
Response of Uni-Modal Duffing-Type Harvesters to Random Forced Excitations
,”
J. Sound Vib.
,
329
(
18
), pp.
3621
3631
.
16.
Mann
,
B.
, and
Owens
,
B.
,
2010
, “
Investigations of a Nonlinear Energy Harvester With a Bistable Potential Well
,”
J. Sound Vib.
,
329
(
9
), pp.
1215
1226
.
17.
Cammarano
,
A.
,
Burrow
,
S.
, and
Barton
,
D.
,
2011
, “
Modelling and Experimental Characterization of an Energy Harvester With Bi-Stable Compliance Characteristics
,”
Proc. Inst. Mech. Eng., Part I
,
225
(
4
), pp.
475
484
.
18.
Ando
,
B.
,
Baglio
,
S.
,
Trigona
,
C.
,
Dumas
,
N.
,
Latorre
,
L.
, and
Nouet
,
P.
,
2010
, “
Nonlinear Mechanism in MEMS Devices for Energy Harvesting Applications
,”
J. Micromech. Microeng.
,
20
(
12
), p.
125020
.
19.
Nguyen
,
S. D.
,
Halvorsen
,
E.
, and
Paprotny
,
I.
,
2013
, “
Bistable Springs for Wideband Microelectromechanical Energy Harvesters
,”
Appl. Phys. Lett.
,
102
(
2
), p.
023904
.
20.
Ibrahim
,
A.
,
Towfighian
,
S.
,
Younis
,
M.
, and
Su
,
Q.
,
2016
, “
Magnetoelastic Beam With Extended Polymer for Low Frequency Vibration Energy Harvesting
,”
Proc. SPIE
,
9806
, p.
98060B
.
21.
Beeby
,
S. P.
,
Tudor
,
M. J.
, and
White
,
N.
,
2006
, “
Energy Harvesting Vibration Sources for Microsystems Applications
,”
Meas. Sci. Technol.
,
17
(
12
), p.
R175
.
22.
Mitcheson
,
P. D.
,
Yeatman
,
E. M.
,
Rao
,
G. K.
,
Holmes
,
A. S.
, and
Green
,
T. C.
,
2008
, “
Energy Harvesting From Human and Machine Motion for Wireless Electronic Devices
,”
Proc. IEEE
,
96
(
9
), pp.
1457
1486
.
23.
Sterken
,
T.
,
Baert
,
K.
,
Van Hoof
,
C.
,
Puers
,
R.
,
Borghs
,
G.
, and
Fiorini
,
P.
,
2004
, “
Comparative Modelling for Vibration Scavengers [MEMS Energy Scavengers]
,” 3rd IEEE Conference on Sensors (
SENSORS
), Vienna, Austria, Oct. 24–27, pp.
1249
1252
.
24.
James
,
E.
,
Tudor
,
M.
,
Beeby
,
S.
,
Harris
,
N.
,
Glynne-Jones
,
P.
,
Ross
,
J.
, and
White
,
N.
,
2004
, “
An Investigation of Self-Powered Systems for Condition Monitoring Applications
,”
Sens. Actuators A
,
110
(
1
), pp.
171
176
.
25.
Roundy
,
S.
, and
Wright
,
P. K.
,
2004
, “
A Piezoelectric Vibration Based Generator for Wireless Electronics
,”
Smart Mater. Struct.
,
13
(
5
), p.
1131
.
26.
Ottman
,
G. K.
,
Hofmann
,
H. F.
,
Bhatt
,
A. C.
, and
Lesieutre
,
G. A.
,
2002
, “
Adaptive Piezoelectric Energy Harvesting Circuit for Wireless Remote Power Supply
,”
IEEE Trans. Power Electron.
,
17
(
5
), pp.
669
676
.
27.
Ferrari
,
M.
,
Ferrari
,
V.
,
Marioli
,
D.
, and
Taroni
,
A.
,
2006
, “
Modeling, Fabrication and Performance Measurements of a Piezoelectric Energy Converter for Power Harvesting in Autonomous Microsystems
,”
IEEE Trans. Instrum. Meas.
,
55
(
6
), pp.
2096
2101
.
28.
Ferrari
,
M.
,
Ferrari
,
V.
,
Guizzetti
,
M.
, and
Marioli
,
D.
,
2009
, “
An Autonomous Battery-Less Sensor Module Powered by Piezoelectric Energy Harvesting With RF Transmission of Multiple Measurement Signals
,”
Smart Mater. Struct.
,
18
(
8
), p.
085023
.
29.
Masana
,
R.
, and
Daqaq
,
M. F.
,
2011
, “
Relative Performance of a Vibratory Energy Harvester in Mono- and Bi-Stable Potentials
,”
J. Sound Vib.
,
330
(
24
), pp.
6036
6052
.
30.
Sneller
,
A.
,
Cette
,
P.
, and
Mann
,
B.
,
2011
, “
Experimental Investigation of a Post-Buckled Piezoelectric Beam With an Attached Central Mass Used to Harvest Energy
,”
Proc. Inst. Mech. Eng., Part I
,
225
(
4
), pp.
497
509
.
31.
Arrieta
,
A.
,
Hagedorn
,
P.
,
Erturk
,
A.
, and
Inman
,
D.
,
2010
, “
A Piezoelectric Bistable Plate for Nonlinear Broadband Energy Harvesting
,”
Appl. Phys. Lett.
,
97
(
10
), p.
104102
.
32.
Masana
,
R.
, and
Daqaq
,
M. F.
,
2012
, “
Energy Harvesting in the Super-Harmonic Frequency Region of a Twin-Well Oscillator
,”
J. Appl. Phys.
,
111
(
4
), p.
044501
.
33.
Ferrari
,
M.
,
Bau
,
M.
,
Guizzetti
,
M.
, and
Ferrari
,
V.
,
2011
, “
A Single-Magnet Nonlinear Piezoelectric Converter for Enhanced Energy Harvesting From Random Vibrations
,”
Sens. Actuators A
,
172
(
1
), pp.
287
292
.
34.
Ferrari
,
M.
,
Ferrari
,
V.
,
Guizzetti
,
M.
,
Andò
,
B.
,
Baglio
,
S.
, and
Trigona
,
C.
,
2010
, “
Improved Energy Harvesting From Wideband Vibrations by Nonlinear Piezoelectric Converters
,”
Sens. Actuators A
,
162
(
2
), pp.
425
431
.
35.
Litak
,
G.
,
Friswell
,
M.
, and
Adhikari
,
S.
,
2010
, “
Magnetopiezoelastic Energy Harvesting Driven by Random Excitations
,”
Appl. Phys. Lett.
,
96
(
21
), p.
214103
.
36.
Lin
,
J.-T.
,
Lee
,
B.
, and
Alphenaar
,
B.
,
2010
, “
The Magnetic Coupling of a Piezoelectric Cantilever for Enhanced Energy Harvesting Efficiency
,”
Smart Mater. Struct.
,
19
(
4
), p.
045012
.
37.
Ali
,
S.
,
Adhikari
,
S.
,
Friswell
,
M.
, and
Narayanan
,
S.
,
2011
, “
The Analysis of Piezomagnetoelastic Energy Harvesters Under Broadband Random Excitations
,”
J. Appl. Phys.
,
109
(
7
), p.
074904
.
38.
Roundy
,
S.
, and
Zhang
,
Y.
,
2005
, “
Toward Self-Tuning Adaptive Vibration-Based Microgenerators
,”
Proc. SPIE
,
5649
, pp.
373
384
.
39.
Wu
,
W.-J.
,
Chen
,
Y.-Y.
,
Lee
,
B.-S.
,
He
,
J.-J.
, and
Peng
,
Y.-T.
,
2006
, “
Tunable Resonant Frequency Power Harvesting Devices
,”
Proc. SPIE
,
6169
, p.
61690A
.
40.
Challa
,
V. R.
,
Prasad
,
M.
,
Shi
,
Y.
, and
Fisher
,
F. T.
,
2008
, “
A Vibration Energy Harvesting Device With Bidirectional Resonance Frequency Tunability
,”
Smart Mater. Struct.
,
17
(
1
), p.
015035
.
41.
Shahruz
,
S.
,
2006
, “
Design of Mechanical Band-Pass Filters for Energy Scavenging
,”
J. Sound Vib.
,
292
(
3
), pp.
987
998
.
42.
Shahruz
,
S.
,
2006
, “
Limits of Performance of Mechanical Band-Pass Filters Used in Energy Scavenging
,”
J. Sound Vib.
,
293
(
1
), pp.
449
461
.
43.
Baker
,
J.
,
Roundy
,
S.
, and
Wright
,
P.
,
2005
, “
Alternative Geometries for Increasing Power Density in Vibration Energy Scavenging for Wireless Sensor Networks
,”
3rd International Energy Conversion Engineering Conference
(
IECEC
), San Francisco, CA, Aug. 15–18, pp.
959
970
.
44.
Rastegar
,
J.
,
Pereira
,
C.
, and
Nguyen
,
H.-L.
,
2006
, “
Piezoelectric-Based Power Sources for Harvesting Energy From Platforms With Low-Frequency Vibration
,”
Proc. SPIE
,
6171
, p.
617101
.
45.
Al-Ashtari
,
W.
,
Hunstig
,
M.
,
Hemsel
,
T.
, and
Sextro
,
W.
,
2012
, “
Frequency Tuning of Piezoelectric Energy Harvesters by Magnetic Force
,”
Smart Mater. Struct.
,
21
(
3
), p.
035019
.
46.
Yang
,
W.
, and
Towfighian
,
S.
,
2017
, “
A Hybrid Nonlinear Vibration Energy Harvester
,”
Mech. Syst. Signal Process.
,
90
, pp.
317
333
.
47.
Moon
,
F.
, and
Holmes
,
P. J.
,
1979
, “
A Magnetoelastic Strange Attractor
,”
J. Sound Vib.
,
65
(
2
), pp.
275
296
.
48.
Quinn
,
D. D.
,
Vakakis
,
A. F.
, and
Bergman
,
L. A.
,
2007
, “
Vibration-Based Energy Harvesting With Essential Nonlinearities
,”
ASME
Paper No. DETC2007-35457.
49.
Mann
,
B.
, and
Sims
,
N.
,
2009
, “
Energy Harvesting From the Nonlinear Oscillations of Magnetic Levitation
,”
J. Sound Vib.
,
319
(
1
), pp.
515
530
.
50.
Burrow
,
S.
, and
Clare
,
L.
,
2007
, “
A Resonant Generator With Non-Linear Compliance for Energy Harvesting in High Vibrational Environments
,”
IEEE International Electric Machines and Drives Conference
(
IEMDC
), Antalya, Turkey, May 3–5, Vol.
1
, pp.
715
720
.
51.
Beeby
,
S. P.
,
Torah
,
R.
,
Tudor
,
M.
,
Glynne-Jones
,
P.
,
O'Donnell
,
T.
,
Saha
,
C.
, and
Roy
,
S.
,
2007
, “
A Micro Electromagnetic Generator for Vibration Energy Harvesting
,”
J. Micromech. Microeng.
,
17
(
7
), p.
1257
.
52.
Cottone
,
F.
,
Vocca
,
H.
, and
Gammaitoni
,
L.
,
2009
, “
Nonlinear Energy Harvesting
,”
Phys. Rev. Lett.
,
102
(
8
), p.
080601
.
53.
Erturk
,
A.
,
Hoffmann
,
J.
, and
Inman
,
D.
,
2009
, “
A Piezomagnetoelastic Structure for Broadband Vibration Energy Harvesting
,”
Appl. Phys. Lett.
,
94
(
25
), p.
254102
.
54.
Barton
,
D. A.
,
Burrow
,
S. G.
, and
Clare
,
L. R.
,
2010
, “
Energy Harvesting From Vibrations With a Nonlinear Oscillator
,”
ASME J. Vib. Acoust.
,
132
(
2
), p.
021009
.
55.
Stanton
,
S. C.
,
McGehee
,
C. C.
, and
Mann
,
B. P.
,
2010
, “
Nonlinear Dynamics for Broadband Energy Harvesting: Investigation of a Bistable Piezoelectric Inertial Generator
,”
Physica D
,
239
(
10
), pp.
640
653
.
56.
Sebald
,
G.
,
Kuwano
,
H.
,
Guyomar
,
D.
, and
Ducharne
,
B.
,
2011
, “
Experimental Duffing Oscillator for Broadband Piezoelectric Energy Harvesting
,”
Smart Mater. Struct.
,
20
(
10
), p.
102001
.
57.
Stanton
,
S. C.
,
Owens
,
B. A.
, and
Mann
,
B. P.
,
2012
, “
Harmonic Balance Analysis of the Bistable Piezoelectric Inertial Generator
,”
J. Sound Vib.
,
331
(
15
), pp.
3617
3627
.
58.
Bilgen
,
O.
,
Friswell
,
M. I.
,
Ali
,
S. F.
, and
Litak
,
G.
,
2015
, “
Broadband Vibration Energy Harvesting From a Vertical Cantilever Piezocomposite Beam With Tip Mass
,”
Int. J. Struct. Stab. Dyn.
,
15
(
2
), p.
1450038
.
59.
Zhou
,
S.
,
Cao
,
J.
,
Inman
,
D. J.
,
Lin
,
J.
,
Liu
,
S.
, and
Wang
,
Z.
,
2014
, “
Broadband Tristable Energy Harvester: Modeling and Experiment Verification
,”
Appl. Energy
,
133
, pp.
33
39
.
60.
Gammaitoni
,
L.
,
Neri
,
I.
, and
Vocca
,
H.
,
2009
, “
Nonlinear Oscillators for Vibration Energy Harvesting
,”
Appl. Phys. Lett.
,
94
(
16
), p.
164102
.
61.
Masana
,
R.
, and
Daqaq
,
M. F.
,
2011
, “
Electromechanical Modeling and Nonlinear Analysis of Axially Loaded Energy Harvesters
,”
ASME J. Vib. Acoust.
,
133
(
1
), p.
011007
.
62.
Marinkovic
,
B.
, and
Koser
,
H.
,
2009
, “
Smart Sand—A Wide Bandwidth Vibration Energy Harvesting Platform
,”
Appl. Phys. Lett.
,
94
(
10
), p.
103505
.
63.
Tvedt
,
L. G. W.
,
Nguyen
,
D. S.
, and
Halvorsen
,
E.
,
2010
, “
Nonlinear Behavior of an Electrostatic Energy Harvester Under Wide-and Narrowband Excitation
,”
J. Microelectromech. Syst.
,
19
(
2
), pp.
305
316
.
64.
Miki
,
D.
,
Honzumi
,
M.
,
Suzuki
,
Y.
, and
Kasagi
,
N.
,
2010
, “
Large-Amplitude MEMS Electret Generator With Nonlinear Spring
,”
IEEE 23rd International Conference on Micro Electro Mechanical Systems
(
MEMS
), Wanchai, Hong Kong, China, Jan. 24–28, pp.
176
179
.
65.
Nguyen
,
D.
,
Halvorsen
,
E.
,
Jensen
,
G.
, and
Vogl
,
A.
,
2010
, “
Fabrication and Characterization of a Wideband MEMS Energy Harvester Utilizing Nonlinear Springs
,”
J. Micromech. Microeng.
,
20
(
12
), p.
125009
.
66.
Erturk
,
A.
, and
Inman
,
D.
,
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
.
67.
Stanton
,
S. C.
, and
Mann
,
B. P.
,
2009
, “
Harvesting Energy From the Nonlinear Oscillations of a Bistable Piezoelectric Inertial Energy Generator
,”
ASME
Paper No. DETC2009-86902.
68.
Tang
,
L.
,
Wu
,
H.
,
Yang
,
Y.
, and
Soh
,
C. K.
,
2011
, “
Optimal Performance of Nonlinear Energy Harvesters
,”
22nd International Conference on Adaptive Structures and Technologies
, Corfu, Greece, Oct. 10–12, Paper No. ICAST2011 #075.
69.
Tang
,
L.
,
Yang
,
Y.
, and
Soh
,
C.-K.
,
2012
, “
Improving Functionality of Vibration Energy Harvesters Using Magnets
,”
J. Intell. Mater. Syst. Struct.
,
23
(13), pp. 1433–1449.
70.
Harne
,
R.
,
Thota
,
M.
, and
Wang
,
K.
,
2013
, “
Concise and High-Fidelity Predictive Criteria for Maximizing Performance and Robustness of Bistable Energy Harvesters
,”
Appl. Phys. Lett.
,
102
(
5
), p.
053903
.
71.
Stanton
,
S. C.
,
Mann
,
B. P.
, and
Owens
,
B. A.
,
2012
, “
Melnikov Theoretic Methods for Characterizing the Dynamics of the Bistable Piezoelectric Inertial Generator in Complex Spectral Environments
,”
Physica D
,
241
(
6
), pp.
711
720
.
72.
Azizi
,
S.
,
Chorsi
,
M. T.
, and
Bakhtiari-Nejad
,
F.
,
2016
, “
On the Secondary Resonance of a MEMS Resonator: A Conceptual Study Based on Shooting and Perturbation Methods
,”
Int. J. Non-Linear Mech.
,
82
, pp.
59
68
.
73.
Karami
,
M. A.
, and
Inman
,
D. J.
,
2011
, “
Electromechanical Modeling of the Low-Frequency Zigzag Micro-Energy Harvester
,”
J. Intell. Mater. Syst. Struct.
,
22
(
3
), pp.
271
282
.
74.
Arrieta
,
A.
,
Delpero
,
T.
,
Bergamini
,
A.
, and
Ermanni
,
P.
,
2013
, “
Broadband Vibration Energy Harvesting Based on Cantilevered Piezoelectric Bi-Stable Composites
,”
Appl. Phys. Lett.
,
102
(
17
), p.
173904
.
75.
Gu
,
L.
,
2011
, “
Low-Frequency Piezoelectric Energy Harvesting Prototype Suitable for the MEMS Implementation
,”
Microelectron. J.
,
42
(
2
), pp.
277
282
.
76.
Karami
,
M. A.
, and
Inman
,
D. J.
,
2011
, “
Equivalent Damping and Frequency Change for Linear and Nonlinear Hybrid Vibrational Energy Harvesting Systems
,”
J. Sound Vib.
,
330
(
23
), pp.
5583
5597
.
77.
Tang
,
L.
, and
Yang
,
Y.
,
2012
, “
A Nonlinear Piezoelectric Energy Harvester With Magnetic Oscillator
,”
Appl. Phys. Lett.
,
101
(
9
), p.
094102
.
78.
Younis
,
M. I.
,
2011
,
MEMS Linear and Nonlinear Statics and Dynamics
, Vol.
20
,
Springer Science and Business Media
, New York.
79.
Wolfram
,
S.
,
1987
, “
Mathematica
,”
Springer
,
New York
.
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