Abstract
In this paper, we consider the application of the piezoelectric energy harvesting using a portal frame structure of two-degrees-of-freedom. The piezoelectric material is considered as a linear device using a capacitive mathematical model. The portal structure is of two-degrees-of-freedom considering with quadratic coupling between the first and second modes of vibration. 2:1 internal resonance between the first and second modes is set, which is a particular condition of this type of system due to the appearance of a saturation phenomenon. As this phenomenon causes the system to start vibrating from the second mode and, at steady-state, vibrates at the first mode, the objective of this work is to verify the energy uptake, considering the different positioning of a piezoelectric material, which is coupled to the supported beam and/or to the column. In addition, the structure is excited by a nonideal DC motor with a limited power supply. The results show a considerably nonlinear behavior due to the nonideal motor, and, with the saturation phenomenon, it is more efficient to collect energy by coupling the PZT to the column. The investigation of the stability of the system due to the piezoelectric coefficient Θ is also taken into account, which is carried out by numerical tools as phase planes, Poincare maps, bifurcation diagrams, and 0–1 test.
Issue Section:
Research Papers
References
1.
Rocha
,
R. T.
,
Balthazar
,
J. M.
,
Tusset
,
A. M.
, and
Quinn
,
D. D.
, 2018
, “
An Analytical Approximated Solution and Numerical Simulations of a Non-Ideal System With Saturation Phenomenon
,” Nonlinear Dyn.
,
94
(1
), pp. 429
–442
.10.1007/s11071-018-4369-92.
Stephen
,
N. G.
, 2006
, “
On Energy Harvesting From Ambient Vibration
,” J. Sound Vib.
,
293
(1–2
), pp. 409
–425
.10.1016/j.jsv.2005.10.0033.
Syta
,
A.
,
Bowen
,
C. R.
,
Kim
,
H. A.
,
Rysak
,
A.
, and
Litak
,
G.
, 2015
, “
Experimental Analysis of the Dynamical Response of Energy Harvesting Devices Based on Bistable Laminated Plates
,” Meccanica
,
50
(8
), pp. 1961
–1970
.10.1007/s11012-015-0140-14.
Triplett
,
A.
, and
Quinn
,
D. D.
, 2009
, “
The Effect of Nonlinear Piezoelectric Coupling on Vibration-Based Energy Harvesting
,” J. Intell. Mater. Syst. Struct.
,
20
(16
), pp. 1959
–1967
.10.1177/1045389X093432185.
Daqaq
,
M. F.
,
Masana
,
R.
,
Erturk
,
A.
, and
Quinn
,
D. D.
, 2014
, “
On the Role of Nonlinearities in Vibratory Energy Harvesting: A Critical Review and Discussion
,” ASME Appl. Mech. Rev.
,
66
(4
), pp. 040801.10.1115/1.40262786.
Iliuk
,
I.
,
Balthazar
,
J. M.
,
Tusset
,
A. M.
,
Piqueira
,
J. R. C.
,
de Pontes
,
B. R.
,
Felix
,
J. L. P.
, and
Bueno
,
A. M.
, 2013
, “
A Non-Ideal Portal Frame Energy Harvester Controlled Using a Pendulum
,” Eur. Phys. J. Spec. Top.
,
222
(7
), pp. 1575
–1586
.10.1140/epjst/e2013-01946-47.
Iliuk
,
I.
,
Balthazar
,
J. M.
,
Tusset
,
A. M.
,
Piqueira
,
J. R. C.
,
Pontes
,
B. R.
, Jr.
,
Felix
,
J. L. P.
, and
Bueno
,
A. M.
, 2014
, “
Application of Passive Control to Energy Harvester Efficiency Using a Non-Ideal Portal Frame Structural Support System
,” J. Intell. Mater. Syst. Struct.
,
25
(4
), pp. 417
–429
.10.1177/1045389X135005708.
Pereira
,
T. L.
,
De Paula
,
A. S.
,
Fabro
,
A. T.
, and
Savi
,
M. A.
, 2019
, “
Random Effects in a Nonlinear Vibration-Based Piezoelectric Energy Harvesting System
,” Int. J. Bifurcation Chaos
,
29
(04
), p. 1950046
.10.1142/S02181274195004699.
Cellular
,
A.
,
da Silva Monteiro
,
L. L.
, and
Savi
,
M. A.
, 2018
, “
Numerical Investigation of Nonlinear Mechanical and Constitutive Effects on Piezoelectric Vibration-Based Energy Harvesting
,” TM—Tech. Mess.
,
85
(9
), pp. 565
–579
.10.1515/teme-2017-007010.
Remick
,
K.
,
Quinn
,
D. D.
,
McFarland
,
D. M.
,
Bergman
,
L.
, and
Vakakis
,
A.
, 2016
, “
High-Frequency Vibration Energy Harvesting From Impulsive Excitation Utilizing Intentional Dynamic Instability Caused by Strong Nonlinearity
,” J. Sound Vib.
,
370
, pp. 259
–279
.10.1016/j.jsv.2016.01.05111.
Erturk
,
A.
, and
Quinn
,
D. D.
, 2011
, Piezoelectric Energy Harvesting
, John
Wiley and Sons
, Chichester, UK
.12.
Sugino
,
C.
,
Ruzzene
,
M.
, and
Erturk
,
A.
, 2020
, “
An Analytical Framework for Locally Resonant Piezoelectric Metamaterial Plates
,” Int. J. Solids Struct.
,
182–183
, pp. 281
–294
.10.1016/j.ijsolstr.2019.08.01113.
Chiacchiari
,
S.
,
Romeo
,
F.
,
McFarland
,
D. M.
,
Bergman
,
L. A.
, and
Vakakis
,
A. F.
, 2019
, “
Vibration Energy Harvesting From Impulsive Excitations Via a Bistable Nonlinear Attachment-Experimental Study
,” Mech. Syst. Signal Process.
,
125
, pp. 185
–201
.10.1016/j.ymssp.2018.06.05814.
Tan
,
D.
,
Yavarow
,
P.
, and
Erturk
,
A.
, 2018
, “
Resonant Nonlinearities of Piezoelectric Macro-Fiber Composite Cantilevers With Interdigitated Electrodes in Energy Harvesting
,” Nonlinear Dyn.
,
92
(4
), pp. 1935
–1945
.10.1007/s11071-018-4172-715.
Quinn
,
D. D.
, 2007
, “
Resonant Dynamics in Strongly Nonlinear Systems
,” Nonlinear Dyn.
,
49
(3
), pp. 361
–373
.10.1007/s11071-006-9126-916.
Nayfeh
,
A. H.
, and
Mook
,
D. T.
, 1979
, Nonlinear Oscillations
,
John Wiley and Sons
, Weinheim, Germany
, p. 720
.17.
Nayfeh
,
A. H.
,
Mook
,
D. T.
, and
Marshall
,
L. R.
, 1973
, “
Nonlinear Coupling of Pitch and Roll Modes in Ship Motions
,” J. Hydrodyn.
,
7
(4
), pp. 145
–152
.10.2514/3.6294918.
Haddow
,
A. G.
,
Barr
,
A. D. S.
, and
Mook
,
A. B. D.
, 1984
, “
Theoretical and Experimental Study of Modal Interaction in a Two-Degree-of-Freedom Structure
,” J. Sound Vib.
,
97
(3
), pp. 451
–473
.10.1016/0022-460X(84)90272-419.
Shaw
,
S. W.
, and
Balachandran
,
B.
, 2008
, “
A Review of Nonlinear Dynamics of Mechanical Systems in Year 2008
,” Jpn. Soc. Mech. Eng.
,
2
(3
), pp. 611
–640
.10.1299/jsdd.2.61120.
Marcelo Tusset
,
A.
,
Piccirillo
,
V.
,
Bueno
,
A. M.
,
Manoel Balthazar
,
J.
,
Sado
,
D.
,
Felix
,
J. L. P.
, and
Brasil
,
R. M. L. R. D. F.
, 2016
, “
Chaos Control and Sensitivity Analysis of a Double Pendulum Arm Excited by an RLC Circuit Based Nonlinear Shaker
,” J. Vib. Control
,
22
(17
), pp. 3621
–3637
.10.1177/107754631456478221.
Lee
,
Y.
,
Frank Pai
,
P.
, and
Feng
,
Z.
, 2008
, “
Nonlinear Complex Response of a Parametrically Excited Tuning Fork
,” Mech. Syst. Signal Process.
,
22
(5
), pp. 1146
–1156
.10.1016/j.ymssp.2007.11.01522.
Pai
,
P. F.
, and
Schulz
,
M. J.
, 2000
, “
A Refined Nonlinear Vibration Absorber
,” Int. J. Mech. Sci.
,
42
(3
), pp. 537
–560
.10.1016/S0020-7403(98)00135-023.
Felix
,
J. L. P.
,
Balthazar
,
J. M.
, and
Brasil
,
R. M.
, 2005
, “
On Saturation Control of a Non-Ideal Vibrating Portal Frame Foundation Type Shear-Building
,” J. Vib. Control
,
11
(1
), pp. 121
–136
.10.1177/107754630504765624.
Shoeybi
,
M.
, and
Ghorashi
,
M.
, 2005
, “
Control of a Nonlinear System Using the Saturation Phenomenon
,” Nonlinear Dyn.
,
42
(2
), pp. 113
–136
.10.1007/s11071-005-4123-y25.
Warminski
,
J.
,
Cartmell
,
M. P.
,
Mitura
,
A.
, and
Bochenski
,
M.
, 2013
, “
Active Vibration Control of a Nonlinear Beam With Self-and External Excitations
,” Shock Vib.
,
20
(6
), pp. 1033
–1047
.10.1155/2013/79279526.
Zhao, Y. Y., and Xu, J., 2012. “Using the Delayed Feedback Control and Saturation Control to Suppress the Vibration of the Dynamical System,”
Nonlinear Dyn.
, 67(1), pp. 735–753. 10.1007/s11071-011-0023-527.
Tusset
,
A. M.
,
Janzen
,
F. C.
,
Piccirillo
,
V.
,
Rocha
,
R. T.
,
Balthazar
,
J. M.
, and
Litak
,
G.
, 2018
, “
On Nonlinear Dynamics of a Parametrically Excited Pendulum Using Both Active Control and Passive Rotational (MR) Damper
,” J. Vib. Control
,
24
(9
), pp. 1587
–1599
.10.1177/107754631771488228.
Oueini
,
S. S.
,
Nayfeh
,
A. H.
, and
Golnaraghi
,
M. F.
, 1997
, “
A Theoretical and Experimental Implementation of a Control Method Based on Saturation
,” Nonlinear Dyn.
,
13
(2
), pp. 189
–202
.10.1023/A:100820712493529.
Pai
,
P. F.
,
Wen
,
B.
,
Naser
,
A. S.
, and
Schulz
,
M. J.
, 1998
, “
Structural Vibration Control Using Pzt Patches and Nonlinear Phenomena
,” J. Sound Vib.
,
215
(2
), pp. 273
–296
.10.1006/jsvi.1998.161230.
Pratt
,
J. R.
,
Oueini
,
S. S.
, and
Nayfeh
,
A. H.
, 1999
, “
Terfenol-d Nonlinear Vibration Absorber
,” J. Intell. Mater. Syst. Struct.
,
10
(1
), pp. 29
–35
.10.1177/1045389X990100010431.
Hall
,
B. D.
,
Mook
,
D. T.
,
Nayfeh
,
A. H.
, and
Preidikman
,
S.
, 2001
, “
Novel Strategy for Suppressing the Utter Oscillations of Aircraft Wings
,” AIAA J.
,
39
(10
), pp. 1843
–1850
.10.2514/2.119032.
Ashour
,
O. N.
, and
Nayfeh
,
A. H.
, 2002
, “
Adaptive Control of Flexible Structures Using a Nonlinear Vibration Absorber
,” Nonlinear Dyn.
,
28
(3/4
), pp. 309
–322
.10.1023/A:101562263038233.
Golnaraghi
,
M. F.
, 1991
, “
Vibration Suppression of Flexible Structures Using Internal Resonance
,” Mech. Res. Commun.
,
18
(2–3
), pp. 135
–143
.10.1016/0093-6413(91)90042-U34.
Nayfeh
,
A. H.
, 2000
, Nonlinear Interactions: Analytical, Computational, and Experimental Methods
(Wiley Series in Nonlinear Science), Wiley-Interscience
, New York
.35.
Mook
,
D. T.
,
Marshall
,
L. R.
, and
Nayfeh
,
A. H.
, 1974
, “
Subharmonic and Superharmonic Resonances in the Pitch and Roll Modes of Ship Motions
,” J. Hydrodyn.
,
8
(1
), pp. 32
–40
.10.2514/3.6297336.
Nayfeh
,
A. H.
, 1988
, “
Numerical-Perturbation Methods in Mechanics
,” Comput. Struct.
,
30
(1–2
), pp. 185
–204
.10.1016/0045-7949(88)90226-X37.
Balachandran
,
B.
, and
Nayfeh
,
A. H.
, 1990
, “
Nonlinear Motions of Beam-Mass Structure
,” Nonlinear Dyn.
,
1
(1
), pp. 39
–61
.10.1007/BF0185758438.
Nayfeh
,
A. H.
, and
Balachandran
,
B.
, 2008
, Applied Nonlinear Dynamics: Analytical, Computational and Experimental Methods
, John
Wiley and Sons
, Weinheim, Germany
.39.
Mook
,
D. T.
,
Plaut
,
R. H.
, and
HaQuang
,
N.
, 1985
, “
The Influence of an Internal Resonance on Nonlinear Structural Vibrations Under Subharmonic Resonance Conditions
,” J. Sound Vib.
,
102
(4
), pp. 473
–492
.10.1016/S0022-460X(85)80108-540.
Alfredsson
,
K. S.
,
Josefson
,
B. L.
, and
Wilson
,
M. A.
, 1996
, “
Use of the Energy Flow Concept in Vibration Design
,” AIAA J.
,
34
(6
), pp. 1250
–1255
.10.2514/3.1322041.
Amin
,
T. M. F.
,
Huda
,
M. Q.
,
Tulip
,
J.
, and
Jäger
,
W.
, 2014
, “
A Virtual Pivot Point MEMS Actuator With Externally Mounted Mirror: Design, Fabrication and Characterization
,” Sens. Transducers
,
183
(12
), pp. 65
–71
.https://search.proquest.com/docview/1645170155/fulltext/91960DA2B647CFPQ42.
Felix
,
J. L. P.
,
Balthazar
,
J. M.
,
Rocha
,
R. T.
,
Tusset
,
A. M.
, and
Janzen
,
F. C.
, 2018
, “
On Vibration Mitigation and Energy Harvesting of a Non-Ideal System With Autoparametric Vibration Absorber System
,” Meccanica
,
53
(13
), pp. 3177
–3188
.10.1007/s11012-018-0881-843.
Rocha
,
R. T.
,
Balthazar
,
J. M.
,
Tusset
,
A. M.
,
Piccirillo
,
V.
, and
Felix
,
J. L. P.
, 2017
, “
Nonlinear Piezoelectric Vibration Energy Harvesting From a Portal Frame With Two-to-One Internal Resonance
,” Meccanica
,
52
(11–12
), pp. 2583
–2602
.10.1007/s11012-017-0633-144.
Rocha
,
R. T.
,
Haura Junior
,
R.
,
Lenz
,
W. B.
,
Ribeiro
,
M. A.
,
Tusset
,
A. M.
,
Balthazar
,
J. M.
, and
Jarzebowska
,
E.
, 2019
, “
Investigation of Energy Harvesting in a 2DOFs Portal Frame by Means of the Positioning of the Piezoelectric Material
,” 15th International Conference, Dynamical Systems—Theory and Applications
, Theoretical Approaches in Nonlinear Dynamical Systems, Lodz, Poland, Dec. 2–5, pp. 453
–463
.45.
Lee
,
W. K.
, and
Cho
,
D. S.
, 2000
, “
Damping Effect of a Randomly Excited Autoparametric System
,” J. Sound Vib.
,
236
(1
), pp. 23
–31
.10.1006/jsvi.2000.296546.
Rocha
,
R. T.
,
Balthazar
,
J. M.
,
Tusset
,
A. M.
,
Piccirillo
,
V.
, and
Felix
,
J. L. P.
, 2016
, “
Comments on Energy Harvesting on a 2:1 Internal Resonance Portal Frame Support Structure, Using a Nonlinear-Energy Sink as a Passive Controller
,” Int. Rev. Mech. Eng. (IREME)
,
10
(3
), pp. 147
–156
.10.15866/ireme.v10i3.879547.
Cveticanin
,
L.
, and
Zukovic
,
M.
, 2015
, “
Motion of a Motor-Structure Non-Ideal System
,” Eur. J. Mech.-A/Solids
,
53
, pp. 229
–240
.10.1016/j.euromechsol.2015.05.00348.
Cveticanin
,
L.
, and
Zukovic
,
M.
, 2015
, “
Non-Ideal Mechanical System With an Oscillator With Rational Nonlinearity
,” J. Vib. Control
,
21
(11
), pp. 2149
–2164
.10.1177/107754631350829749.
Preumont
,
A.
, 2006
, Mechatronics: Dynamics of Electro-Mechanical and Piezoelectric Systems
, Vol.
136
,
Springer Science & Business Media
, Berlin
.50.
Younis
,
M. I.
, 2011
, “
MEMS Linear and Nonlinear Statics and Dynamics
,” Microsystems
,
Springer US
, Boston, MA
.51.
Thompson
,
R. L.
, and
Soares
,
E. J.
, 2016
, “
Viscoplastic Dimensionless Numbers
,” J. Non-Newtonian Fluid Mech.
,
238
, pp. 57
–64
.10.1016/j.jnnfm.2016.05.00152.
Bernardini
,
D.
, and
Litak
,
G.
, 2016
, “
An Overview of 0–1 Test for Chaos
,” J. Braz. Soc. Mech. Sci. Eng.
,
38
(5
), pp. 1433
–1450
.10.1007/s40430-015-0453-y53.
Bernardini
,
D.
,
Rega
,
G.
,
Litak
,
G.
, and
Syta
,
A.
, 2013
, “
Identification of Regular and Chaotic Isothermal Trajectories of a Shape Memory Oscillator Using the 0–1 Test
,” Proc. Inst. Mech. Eng. Part K
,
227
(1
), pp. 17
–22
.10.1177/146441931244749854.
Litak
,
G.
,
Syta
,
A.
, and
Wiercigroch
,
M.
, 2009
, “
Identification of Chaos in a Cutting Process by the 0–1 Test
,” Chaos Solitons Fractals
,
40
(5
), pp. 2095
–2101
.10.1016/j.chaos.2007.09.09355.
Sun
,
K.
,
Liu
,
X.
, and
Zhu
,
C.
, 2010
, “
The 0-1 Test Algorithm for Chaos and Its Applications
,” Chin Phys B
,
19
(11
), p. 110510
.10.1088/1674-1056/19/11/110510Copyright © 2020 by ASME
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