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Dielectric elastomers (DEs) are a type of multifunctional materials withsalient features that are very attractive in developing soft, lightweight, andsmall-scale transducers and robotics. This paper reviews the mechanics of softDE structures, focusing on their dynamic responses, including vibrations andwaves in typical structures. The basic formulations of nonlinearelectroelasticity are briefly summarized by following the descriptions ofDorfmann and Ogden. The recent advances in the study on linearized dynamicproblems of DE plates and shells are then outlined according to the geometricconfigurations as well as the coordinates thereof adopted. Some interestingobservations from the numerical results are highlighted, and the underlyingphysics is discussed. For completeness, an account of the nonlinear dynamiccharacteristics of DE structures is also given. For DE structures with aperiodic arrangement, i.e., DE phononic crystals (PCs) or metamaterials, thispaper reviews the designs, solutions, and results to illustrate the wide-rangetunability of band structure that is realized by large reversible deformationand electromechanical coupling. The present literature survey could be a usefulguide for future studies on the dynamic topics of DE structures.

Vibrations and waves in soft dielectric elastomer structures