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This report gives a summary on our recent studies on dielectric elastomer (DE) structures in general and plates and shells in particular. DEs are usually very soft, and deform significantly when subjected to electric and mechanical stimuli. Thus, to proceed with the analysis, we need to employ the general nonlinear theory of electroelasticity, a typical and most recent version of which was suggested by Dorfmann and Ogden. Also, we need to employ the incremental linear theory for elastic waves superimposed on large deformation. The static large deformation induced by a pre-applied mechanical force or electric stimulus changes the geometry as well as the instantaneous material properties of the structure, and can be an efficient way to tune the dynamic behaviors of soft DE plates and shells.We have therefore examined the vibrations and wave propagation characteristics in typical DE structures, including circular and rectangular plates, cylindrical shells and spherical shells. For these structures with relatively simple geometries, we have been able to derive exact solutions for particular types of pre-deformations. Also, we have taken account of structural periodicity to consider waves in DE phononic crystal structures.

Waves; vibration; dielectric elastomer; plate; shell