Abstract 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.

中文翻译：

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应变硬化和电致伸缩对可压缩介电弹性体层压板中可调弹性波的影响

摘要 本文介绍了无限周期可压缩介电弹性体 (DE) 层压板在厚度方向上受到静电激励和预应力的非线性静态响应和叠加小振幅波特性的机电分析。使用丰富的 Gent 材料模型来解释 DE 层压板的应变硬化和电致伸缩的影响。利用非线性电弹性理论和相关的线性化增量理论，推导出非线性响应的控制方程以及增量横波和纵波的色散关系。数值结果表明，由几何和材料非线性引起的 Gent DE 层压板的快速通过不稳定性可用于实现波段间隙位置和宽度的急剧转变。此外，详细讨论了材料特性（包括根特常数、第二应变不变量和电致伸缩参数）和预应力对剪切波不稳定性和带隙静电可调性的影响，包括横波和纵波。电致伸缩效应和预应力有利于稳定周期性 DE 层压板。根据是否发生快速通过不稳定性，可以通过改变电刺激来实现波段间隙的连续变化或急剧转变。