Nonlinear dynamic characteristics of a dielectric elastomer membrane undergoing in-plane deformation

This paper proposes a free energy model to study the dynamic characteristics of a dielectric elastomer membrane undergoing in-plane deformation, subject to the combined loads of a mechanical press and an electric field. The natural frequency of the small-amplitude perturbation around the state of equilibrium is calculated with focus on the damping effects and the resonance phenomenon. The numerical results, such as the oscillation, phase diagrams and Poincare maps, are presented to show the influence of the damping on the nonlinear dynamic characteristics of the dielectric elastomer. The numerical results indicate that pre-stresses, damping effects and applied voltages could tune the natural frequency and modify the dynamic behavior of the dielectric elastomer. There is a stability transition when taking the damping effect into account. The damping effect could cause the dynamic responses to constant vibration and decrease the amplitude. These conclusions may guide the exploration of high-performance dielectric elastomers under dynamic mechanical and electrical loads.

[1]  W. Hong,et al.  Modeling Viscoelastic Dielectrics , 2011 .

[2]  Jinsong Leng,et al.  An investigation on electromechanical stability of dielectric elastomers undergoing large deformation , 2009 .

[3]  Jinsong Leng,et al.  Comment on “Method to analyze electromechanical stability of dielectric elastomers”[Appl. Phys. Lett. 91, 061921 (2007)] , 2008 .

[4]  Z. Suo,et al.  A nonlinear field theory of deformable dielectrics , 2008 .

[5]  R. Lerch,et al.  Dynamic performance of dielectric elastomers utilized as acoustic actuators , 2012, Applied Physics A.

[6]  Paulo B. Gonçalves,et al.  Nonlinear vibrations of a radially stretched circular hyperelastic membrane , 2009 .

[7]  Zhigang Suo,et al.  Nonlinear oscillation of a dielectric elastomer balloon , 2010 .

[8]  Zhigang Suo,et al.  Resonant behavior of a membrane of a dielectric elastomer , 2010 .

[9]  Junhua Qiang,et al.  A model for conditional polarization of the actuation enhancement of a dielectric elastomer , 2012 .

[10]  M. Dadras,et al.  Voltage Control of the Resonance Frequency of Dielectric Electroactive Polymer (DEAP) Membranes , 2008, Journal of Microelectromechanical Systems.

[11]  Shaoxing Qu,et al.  Electromechanical and dynamic analyses of tunable dielectric elastomer resonator , 2012 .

[12]  D. De Rossi,et al.  Stretching Dielectric Elastomer Performance , 2010, Science.

[13]  S. Dubowsky,et al.  Large-scale failure modes of dielectric elastomer actuators , 2006 .

[14]  Bai-Xiang Xu,et al.  Dynamic analysis of dielectric elastomer actuators , 2011 .

[15]  Bai-Xiang Xu,et al.  Dynamic analysis of dielectric elastomer actuators , 2011 .

[16]  Z. Suo.  Theory of dielectric elastomers , 2010 .

[17]  Iain A. Anderson,et al.  Self-priming dielectric elastomer generators , 2010 .

[18]  A. Gent.  A New Constitutive Relation for Rubber , 1996 .

[19]  Q. Pei,et al.  Advances in dielectric elastomers for actuators and artificial muscles. , 2010, Macromolecular rapid communications.

[20]  Yanju Liu,et al.  Electromechanical stability of dielectric elastomer , 2009 .

[21]  Z. Suo,et al.  Method to analyze programmable deformation of dielectric elastomer layers , 2008 .

[22]  Q. Pei,et al.  High-speed electrically actuated elastomers with strain greater than 100% , 2000, Science.

[23]  Hualing Chen,et al.  Effect of temperature on the stability of dielectric elastomers , 2011 .

[24]  Yanju Liu,et al.  Electromechanical instability and snap-through instability of dielectric elastomers undergoing polarization saturation , 2012 .

[25]  Choon Chiang Foo,et al.  Model of dissipative dielectric elastomers , 2012 .

[26]  Kai Wolf,et al.  An electroactive polymer based concept for vibration reduction via adaptive supports , 2008, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[27]  Jinsong Leng,et al.  Analysis and manufacture of an energy harvester based on a Mooney-Rivlin–type dielectric elastomer , 2010 .

[28]  Helmut F. Schlaak,et al.  Vibrotactile display for mobile applications based on dielectric elastomer stack actuators , 2010, Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[29]  Eric Mockensturm,et al.  Dynamic response of dielectric elastomers , 2006 .

[30]  N. C. Goulbourne,et al.  On the dynamic electromechanical loading of dielectric elastomer membranes , 2008 .

[31]  Jinsong Leng,et al.  Dielectric elastomer film actuators: characterization, experiment and analysis , 2009 .

[32]  Youhe Zhou,et al.  Dynamics of a thick-walled dielectric elastomer spherical shell , 2011 .

[33]  Z. Suo,et al.  Complex interplay of nonlinear processes in dielectric elastomers. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Zhigang Suo,et al.  Extension limit, polarization saturation, and snap-through instability of dielectric elastomers , 2011 .

[35]  Liying Jiang,et al.  Dynamic characteristics of a dielectric elastomer-based microbeam resonator with small vibration amplitude , 2011 .