Wave propagation in a linear transversely isotropic electroactive elastomer

Abstract

In the present paper, the linearized theory of a transversely isotropic electroactive elastomer is used to analyze plane and surface wave characteristics. The transversely isotropic elastomer is considered with electroactive particles aligned in a preferred direction in the presence of an external applied field. The equations of motion are specialized to a two-dimensional setting and homogeneous plane and Rayleigh-type surface waves are considered. The two-dimensional governing equations are solved to obtain plane and surface wave solutions. Plane wave solutions of the governing equations lead to a velocity equation which indicates the propagation of two plane waves. The surface wave solutions satisfy the required boundary conditions which lead to a secular equation for Rayleigh-type wave speed. A numerical example is considered to illustrate graphically the wave speeds of plane and Rayleigh-type waves.

Keywords

Transversely isotropic electroactive elastomer Plane waves Rayleigh waves Wave speed

Get full access to this article

View all access options for this article.

References

Bossis

Abbo

Cutillas

. Electroactive and electrostructured elastomers. Int J Mod Phys B 2001; 15: 564–573.

Suo

. Theory of dielectric elastomers. Acta Mech Solida Sinica 2010; 23: 549–577.

Toupin

. A dynamical theory of elastic dielectrics. Int J Eng Sci 1963; 1: 101–126.

Hutter

van de Ven

. Field matter interactions in thermoelastic solids, Lectures notes in Physics, vol. 88. Berlin: Springer, 1978.

Pao

. Electromagnetic forces in deformable continua. In: Nemat-Nasser

(ed.) Mechanics today, vol. 4. New York: Pergamon Press, 1978, pp. 209–306.

Eringen

Maugin

. Electrodynamics of continua I. Foundations and solid media. Berlin: Springer, 1990.

Kovetz

. Electromagnetic theory. Oxford: Oxford University Press, 2000.

Dorfmann

Ogden

. Nonlinear electroelasticity. Acta Mech 2005; 174: 167–183.

Dorfmann

Ogden

. Nonlinear electroelastic deformations. J Elast 2006; 82: 99–127.

10.

Bustamante

. Transversely isotropic non-linear electro-active elastomers. Acta Mech 2009; 206: 237–259.

11.

Tiersten

. Thickness vibrations of piezoelectric plates. J Acoust Soc Am 1963; 35: 53–58.

12.

Tiersten

. Wave propagation in an infinite piezoelectric plate. J Acoust Soc Am 1963; 35: 234–239.

13.

Yang

. Mechanics of electroelastic bodies under biasing fields. Appl Mech Rev 2004; 57: 173–189.

14.

Mockensturm

Goulbourne

. Dynamic response of dielectric elastomers. Int J Nonlinear Mech 2006; 41: 388–395.

15.

Zhu

Cai

Suo

. Nonlinear oscillation of a dielectric elastomer balloon. Polymer Int 2010; 59: 378–383.

16.

Dorfmann

Ogden

. Electroelastic waves in a finitely deformed electroactive material. IMA J Appl Math 2010; 75: 603–636.

17.

Shmuel

Gei

deBotton

. The Rayleigh-Lamb wave propagation in dielectric elastomer layers subjected to large deformations. Int J Non-Linear Mech 2012; 47: 307–316.

18.

Galich

Rudykh

. Manipulating pressure and shear waves in dielectric elastomers via external electric stimuli. Int J Solids Struct 2016; 91: 18–25.

19.

Singh

Ogden

. Reflection of plane waves from the boundary of an incompressible finitely deformed electroactive half-space. Z Angew Math Phys 2018; 69: 149.

20.

Chen

, et al. Effects of strain stiffening and electrostriction on tunable elastic waves in compressible dielectric elastomer laminates. Int J Mech Sci 2020; 176: 105572.

21.

Zhao

Chen

, et al. Vibrations and waves in soft dielectric elastomer structures. Int J Mech Sci 2023; 239: 107885.

22.

Chen

Pan

Chen

. Wave propagation in magneto-electro-elastic multilayered plates. Int J Solids Struct 2007; 44: 1073–1085.

23.

Saxena

Ogden

. On surface waves in a finitely deformed magnetoelastic half-space. Int J Appl Mech 2011; 3: 633–665.

24.

Moshtagh

Pan

Eskandari-Ghadi

. Wave propagation in a multilayered magneto-electro-elastic half-space induced by external/internal circular time-harmonic mechanical loading. Int J Solids Struct 2017; 128: 243–261.

25.

Moshtagh

Pan

Eskandari-Ghadi

. Shear excitation of a multilayered magneto-electro-elastic half-space considering a vast frequency content. Int J Eng Sci 2018; 123: 214–235.

26.

Crampin

. A review of wave motion in anisotropic and cracked elastic media. Wave Motion 1981; 3: 343–391.

27.

Singh

. Wave propagation in a prestressed piezoelectric half-space. Acta Mech 2010; 211: 337–344.

28.

Weis

Gaylord

. Lithium Niobate: summary of physical properties and crystal structure. Appl Phy A 1985; 37: 191–203.