Abstract
Nonlinear oscillations of dielectric elastomers are widely used in the application of dielectric devices. However, the effects of the dielectric permittivity on the oscillations have been overlooked previously. In this article, an analytical model is proposed to study the nonlinear oscillations of dielectric elastomer actuators. The motion equation is obtained by using Hamilton’s principle. Numerical results of the model show that the stretch-dependent dielectric permittivity can change the thickness of the deformed film by about 65% near the resonance frequency. It is anticipated that this work can provide a new way to adjust the nonlinear oscillations and design more robust DE actuators.
Issue Section:
Research Papers
References
1.
Pelrine
, R.
, Kornbluh
, R.
, Pei
, Q.
, and Joseph
, J.
, 2000
, “High-Speed Electrically Actuated Elastomers With Strain Greater Than 100%
,” Science
, 287
(5454
), pp. 836
–839
. 2.
Kofod
, G.
, Wirges
, W.
, Paajanen
, M.
, and Bauer
, S.
, 2007
, “Energy Minimization for Self-Organized Structure Formation and Actuation
,” Appl. Phys. Lett.
, 90
(8
), p. 081916
. 3.
Huang
, J.
, Li
, T.
, Foo
, C. C.
, Zhu
, J.
, Clarke
, D. R.
, and Suo
, Z.
, 2012
, “Giant, Voltage-Actuated Deformation of a Dielectric Elastomer Under Dead Load
,” Appl. Phys. Lett.
, 100
(4
), p. 041911
. 4.
Liu
, Y.
, Liu
, L.
, Zhang
, Z.
, and Leng
, J.
, 2009
, “Dielectric Elastomer Film Actuators: Characterization, Experiment and Analysis
,” Smart Mater. Struct.
, 18
(9
), p. 095024
. 5.
Paul
, B.
, and Pei
, Q.
, 2010
, “Advances in Dielectric Elastomers for Actuators and Artificial Muscles
,” Macromol. Rapid. Commun.
, 31
(1
), pp. 10
–36
.6.
Rahmati
, A. H.
, Yang
, S.
, Bauer
, S.
, and Sharma
, P.
, 2019
, “Nonlinear Bending Deformation of Soft Electrets and Prospects for Engineering Flexoelectricity and Transverse (d31) Piezoelectricity
,” Soft. Matter.
, 15
(1
), pp. 127
–148
. 7.
Chen
, L.
, Yang
, X.
, Wang
, B.
, Yang
, S.
, Dayal
, K.
, and Sharma
, P.
, 2021
, “The Interplay Between Symmetry-Breaking and Symmetry-Preserving Bifurcations in Soft Dielectric Films and the Emergence of Giant Electro-actuation
,” Extreme Mech. Lett.
, 43
, p. 101151
. 8.
Banet
, P.
, Zeggai
, N.
, Chavanne
, J.
, Nguyen
, G. T. M.
, Chikh
, L.
, Plesse
, C.
, Almanza
, M.
, Martinez
, T.
, Civet
, Y.
, Perriard
, Y.
, and Fichet
, O.
, 2021
, “Evaluation of Dielectric Elastomers to Develop Materials Suitable for Actuation
,” Soft. Matter
, 17
(48
), pp. 10786
–10805
. 9.
Bauer
, S.
, Bauer-Gogonea
, S.
, Graz
, I.
, Kaltenbrunner
, M.
, Keplinger
, C.
, and Schwdiauer
, R.
, 2014
, “25th Anniversary Article: A Soft Future: From Robots and Sensor Skin to Energy Harvesters
,” Adv. Mater.
, 26
(1
), pp. 149
–162
. 10.
Koh
, S. J. A.
, Zhao
, X.
, and Suo
, Z.
, 2009
, “Maximal Energy That Can Be Converted by a Dielectric Elastomer Generator
,” Appl. Phys. Lett.
, 94
(26
), p. 262902
. 11.
Yang
, S.
, Zhao
, X.
, and Sharma
, P.
, 2017
, “Avoiding the Pull-In Instability of a Dielectric Elastomer Film and the Potential for Increased Actuation and Energy Harvesting
,” Soft. Matter
, 13
(26
), pp. 4552
–4558
. 12.
Invernizzi
, F.
, Dulio
, S.
, Patrini
, M.
, Guizzetti
, G.
, and Mustarelli
, P.
, 2016
, “Energy Harvesting From Human Motion: Materials and Techniques
,” Chem. Soc. Rev.
, 45
(20
), pp. 5455
–5473
. 13.
Chen
, L.
, and Yang
, S.
, 2021
, “Enhancing the Electromechanical Coupling in Soft Energy Harvesters by Using Graded Dielectric Elastomers
,” Micromachines
, 12
(10
), p. 1187
. 14.
Carpi
, F.
, Frediani
, G.
, Turco
, S.
, and De Rossi
, D.
, 2011
, “Bioinspired Tunable Lens With Muscle-Like Electroactive Elastomers
,” Adv. Funct. Mater.
, 21
(21
), pp. 4002
–4002
. 15.
Acome
, E.
, Mitchell
, S. K.
, Morrissey
, T. G.
, Emmett
, M. B.
, Benjamin
, C.
, King
, M.
, Radakovitz
, M.
, and Keplinger
, C.
, 2018
, “Hydraulically Amplified Self-Healing Electrostatic Actuators With Muscle-Like Performance
,” Science
, 359
(6371
), pp. 61
–65
. 16.
Pal
, A.
, Restrepo
, V.
, Goswami
, D.
, and Martinez
, R. V.
, 2021
, “Exploiting Mechanical Instabilities in Soft Robotics: Control, Sensing, and Actuation
,” Adv. Mater.
, 33
(19
), p. 2006939
. 17.
Torbati
, M.
, Mozaffari
, K.
, Liu
, L.
, and Sharma
, P.
, 2022
, “Coupling of Mechanical Deformation and Electromagnetic Fields in Biological Cells
,” Rev. Mod. Phys.
, 94
(2
), p. 025003
. 18.
Deng
, Q.
, Ahmadpoor
, F.
, Brownell
, W. E.
, and Sharma
, P.
, 2019
, “The Collusion of Flexoelectricity and Hopf Bifurcation in the Hearing Mechanism
,” J. Mech. Phys. Solids.
, 130
, pp. 245
–261
. 19.
Yang
, S.
, Zhao
, X.
, and Sharma
, P.
, 2017
, “Revisiting the Instability and Bifurcation Behavior of Soft Dielectrics
,” ASME J. Appl. Mech. Trans.
, 84
(3
), p. 031008
. 20.
Yang
, S.
, and Sharma
, P.
, 2020
, “A Tutorial on the Stability and Bifurcation Analysis of the Electromechanical Behaviour of Soft Materials
,” preprint arXiv:2011.08665.21.
Zhu
, J.
, Cai
, S.
, and Suo
, Z.
, 2010
, “Resonant Behavior of a Membrane of a Dielectric Elastomer
,” Int. J. Solids. Struct.
, 47
(24
), pp. 3254
–3262
. 22.
Li
, T.
, Qu
, S.
, and Yang
, W.
, 2012
, “Electromechanical and Dynamic Analyses of Tunable Dielectric Elastomer Resonator
,” Int. J. Solids. Struct.
, 49
(26
), pp. 3754
–3761
. 23.
Xu
, B.-X.
, Mueller
, R.
, Theis
, A.
, Klassen
, M.
, and Gross
, D.
, 2012
, “Dynamic Analysis of Dielectric Elastomer Actuators
,” Appl. Phys. Lett.
, 100
(11
), p. 112903
. 24.
Joglekar
, M. M.
, 2014
, “An Energy-Based Approach to Extract the Dynamic Instability Parameters of Dielectric Elastomer Actuators
,” J. Appl. Mech.
, 81
(9
), p. 091010
. 25.
Sheng
, J.
, Chen
, H.
, Li
, B.
, and Wang
, Y.
, 2014
, “Nonlinear Dynamic Characteristics of a Dielectric Elastomer Membrane Undergoing In-Plane Deformation
,” Smart Mater. Struct.
, 23
(4
), p. 045010
. 26.
Gu
, G.-Y.
, Gupta
, U.
, Zhu
, J.
, Zhu
, L.-M.
, and Zhu
, X.-Y.
, 2015
, “Feedforward Deformation Control of a Dielectric Elastomer Actuator Based on a Nonlinear Dynamic Model
,” Appl. Phys. Lett.
, 107
, p. 042907
. 27.
Zhang
, J.
, Chen
, H.
, Li
, B.
, McCoul
, D.
, and Pei
, Q.
, 2015
, “Coupled Nonlinear Oscillation and Stability Evolution of Viscoelastic Dielectric Elastomers
,” Soft. Matter
, 11
, pp. 7483
–7493
. 28.
Eder-Goy
, D.
, Zhao
, Y.
, and Xu
, B.-X.
, 2017
, “Dynamic Pull-In Instability of a Prestretched Viscous Dielectric Elastomer Under Electric Loading
,” Acta Mech.
, 228
, pp. 4293
–4307
. 29.
Li
, Y.
, Oh
, I.
, Chen
, J.
, Zhang
, H.
, and Hu
, Y.
, 2018
, “Nonlinear Dynamic Analysis and Active Control of Visco-Hyperelastic Dielectric Elastomer Membrane
,” Int. J. Solids Struct.
, 152–153
, pp. 28
–38
. 30.
Lowe
, R. L.
, and Cooley
, C. G.
, 2020
, “Nonlinear Dynamics of a Dielectric Elastomer Membrane Under Compressive Loading
,” Volume 12: Mechanics of Solids, Structures, and Fluids of ASME International Mechanical Engineering Congress and Exposition, 11
, Online
.31.
Mrabet
, K.
, Zaouali
, E.
, and Najar
, F.
, 2022
, “Internal Resonance and Nonlinear Dynamics of a Dielectric Elastomer Circular Membrane
,” Int. J. Solids Struct.
, 236–237
(10
), p. 111338
. 32.
Yin
, Y.
, Zhao
, D.
, Liu
, J.
, and Xu
, Z.
, 2022
, “Nonlinear Dynamic Analysis of Dielectric Elastomer Membrane With Electrostriction
,” Appl. Math. Mech.
, 43
(6
), pp. 793
–812
. 33.
Zhang
, Z.
, Li
, J.
, Liu
, Y.
, and Xie
, Y.-X.
, 2022
, “Nonlinear Oscillations of a One-Dimensional Dielectric Elastomer Generator System
,” Extreme Mech. Lett.
, 53
, p. 101718
. 34.
Cooley
, C. G.
, and Lowe
, R. L.
, 2022
, “In-Plane Nonlinear Vibration of Circular Dielectric Elastomer Membranes With Extreme Stretchability
,” Eur. J. Mech.-A/Solids
, 96
(11
), p. 104660
. 35.
Son
, S.
, and Goulbourne
, N. C.
, 2010
, “Dynamic Response of Tubular Dielectric Elastomer Transducers
,” Int. J. Solids Struct.
, 47
(20
), pp. 2672
–2679
. 36.
Bortot
, E.
, 2018
, “Nonlinear Dynamic Response of Soft Thick-Walled Electro-active Tubes
,” Smart Mater. Struct.
, 27
, p. 105025
. 37.
Mockensturm
, E. M.
, and Goulbourne
, N.
, 2006
, “Dynamic Response of Dielectric Elastomers
,” Inter. J. Non-Linear Mech.
, 41
(3
), pp. 388
–395
. 38.
Zhu
, J.
, Cai
, S.
, and Suo
, Z.
, 2010
, “Nonlinear Oscillation of a Dielectric Elastomer Balloon
,” Polym. Int.
, 59
(3
), pp. 378
–383
. 39.
Yong
, H.
, He
, X.
, and Zhou
, Y.
, 2011
, “Dynamics of a Thick-Walled Dielectric Elastomer Spherical Shell
,” Inter. J. Eng. Sci.
, 49
(8
), pp. 792
–800
. 40.
Chen
, F.
, Zhu
, J.
, and Wang
, M. Y.
, 2015
, “Dynamic Electromechanical Instability of a Dielectric Elastomer Balloon
,” Europhys. Lett.
, 112
(4
), p. 47003
. 41.
Liu
, F.
, and Zhou
, J.
, 2017
, “Shooting and Arc-Length Continuation Method for Periodic Solution and Bifurcation of Nonlinear Oscillation of Viscoelastic Dielectric Elastomers
,” J. Appl. Mech.
, 85
, p. 011005
. 42.
Lv
, X.
, Liu
, L.
, Liu
, Y.
, and Leng
, J.
, 2018
, “Dynamic Performance of Dielectric Elastomer Balloon Incorporating Stiffening and Damping Effect
,” Smart Mater. Struct.
, 27
, p. 105036
. 43.
Sharma
, A. K.
, Arora
, N.
, and Joglekar
, M. M.
, 2018
, “Dc Dynamic Pull-In Instability of a Dielectric Elastomer Balloon: An Energy-Based Approach
,” Proc. R. Soc. A: Math., Phys. Eng. Sci.
, 474
(2211
), p. 20170900
. 44.
Alibakhshi
, A.
, Chen
, W.
, and Destrade
, M.
, 2022
, “Nonlinear Vibration and Stability of a Dielectric Elastomer Balloon Based on a Strain-Stiffening Model
,” J. Elasticity
, pp. 1
–16
. 45.
Khurana
, A.
, Kumar
, A.
, Raut
, S. K.
, Sharma
, A. K.
, and Joglekar
, M.
, 2021
, “Effect of Viscoelasticity on the Nonlinear Dynamic Behavior of Dielectric Elastomer Minimum Energy Structures
,” Int. J. Solids Struct.
, 208–209
, pp. 141
–153
. 46.
Wang
, F.
, Lu
, T.
, and Wang
, T.
, 2016
, “Nonlinear Vibration of Dielectric Elastomer Incorporating Strain Stiffening
,” Int. J. Solids Struct.
, 87
, pp. 70
–80
. 47.
Wissler
, M.
, and Mazza
, E.
, 2007
, “Electromechanical Coupling in Dielectric Elastomer Actuators
,” Sens. Actuators., A.
, 138
(2
), pp. 384
–393
. 48.
McKay
, T. G.
, Calius
, E.
, and Anderson
, I. A.
, 2009
, Electroactive Polymer Actuators and Devices (EAPAD)
, Vol. 7287
, International Society for Optics and Photonics, SPIE
, San Diego
, pp. 209
–218
.49.
Suo
, Z.
, Zhao
, X.
, and Greene
, W. H.
, 2008
, “A Nonlinear Field Theory of Deformable Dielectrics
,” J. Mech. Phys. Solids
, 56
(2
), pp. 467
–486
. 50.
Zhao
, X.
, and Suo
, Z.
, 2008
, “Electrostriction in Elastic Dielectrics Undergoing Large Deformation
,” J. Appl. Phys.
, 104
(12
), p. 123530
. 51.
Li
, H.
, Chen
, L.
, Zhao
, C.
, and Yang
, S.
, 2021
, “Evoking or Suppressing Electromechanical Instabilities in Soft Dielectrics With Deformation-Dependent Dielectric Permittivity
,” Int. J. Mech. Sci.
, 202–203
, p. 106507
. 52.
Geradin
, M.
, and Rixen
, D. J.
, 2015
, Mechanical Vibrations: Theory and Application to Structural Dynamics
, 3rd ed., Wiley
, Hoboken, NJ
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