  This paper presents an electromechanical analysis of the nonlinear static
response and the superimposed small-amplitude wave characteristics in an
infinite periodic compressible dielectric elastomer (DE) laminate subjected to
electrostatic excitations and prestress in the thickness direction. The
enriched Gent material model is employed to account for the effects of strain
stiffening and electrostriction of the DE laminate. The theory of nonlinear
electroelasticity and related linearized incremental theory are exploited to
derive the governing equations of nonlinear response and the dispersion
relations of incremental shear and longitudinal waves. Numerical results reveal
that the snap-through instability of a Gent DE laminate resulting from
geometrical and material nonlinearities can be used to achieve a sharp
transition in the position and width of wave band gaps. Furthermore, the
influence of material properties (including Gent constants, the second strain
invariant and electrostrictive parameters) and that of prestress on the
snap-through instability and the electrostatic tunability of band gaps for both
shear and longitudinal waves are discussed in detail. The electrostrictive
effect and prestress are beneficial to stabilizing the periodic DE laminate.
Depending on whether the snap-through instability occurs or not, a continuous
variation or a sharp transition in wave band gaps can be realized by varying
the electric stimuli. Our numerical findings are expected to provide a solid
guidance for the design and manufacture of soft DE wave devices with tunable
band structures.
