Dielectric elastomers (DEs) are a type of multifunctional materials with salient features that are very attractive in developing soft, lightweight, and small-scale transducers and robotics. This paper reviews the mechanics of soft DE structures, focusing on their dynamic responses, including vibrations and waves in typical structures. The basic formulations of nonlinear electroelasticity are briefly summarized by following the descriptions of Dorfmann and Ogden. The recent advances in the study on linearized dynamic problems of DE plates and shells are then outlined according to the geometric configurations as well as the coordinates thereof adopted. Some interesting observations from the numerical results are highlighted, and the underlying physics is discussed. For completeness, an account of the nonlinear dynamic characteristics of DE structures is also given. For DE structures with a periodic arrangement, i.e., DE phononic crystals (PCs) or metamaterials, this paper reviews the designs, solutions, and results to illustrate the wide-range tunability of band structure that is realized by large reversible deformation and electromechanical coupling. The present literature survey could be a useful guide for future studies on the dynamic topics of DE structures.
