Thickness waves in electroelastic plates

Abstract

Within the linear theory developed in [J. Struct. Control 5 (2) (1998) 73] for coherently oriented, transversely isotropic electroelastic plates capable of thickness changes, the general boundary-value problem uncouples into a “membrane” problem and a “flexure” problem. When progressive waves for the membrane problem are investigated, the relative propagation condition reveals that three different types of solutions exist involving oscillatory thickness distension and contraction accompanied by in-plane motion. In the special case of no electroelastic coupling in the material response the propagation condition can be explicitly solved; one purely electrical and two purely mechanical waves obtain. A simple argument based on kinematical similarities indicates that the two mechanical waves can be regarded as two-dimensional counterparts of the first equivoluminal and dilatational modes of the three-dimensional Rayleigh–Lamb theory.