Dynamic equations for a fully anisotropic piezoelectric rectangular plate

•Equations for an anisotropic piezoelectric plate without any planes of symmetry.•A hierarchy of equations based on 3D theory that are asymptotically correct.•Analytical expressions for orthotropic plate equations for different orders.•Eigenfrequencies and field distributions over the plate cross section.

A hierarchy of dynamic plate equations based on the three dimensional piezoelectric theory is derived for a fully anisotropic piezoelectric rectangular plate. Using power series expansions results in sets of equations that may be truncated to arbitrary order, where each order set is hyperbolic, variationally consistent and asymptotically correct (to all studied orders). Numerical examples for eigenfrequencies and plots on mode shapes, electric potential and stress distributions curves are presented for orthotropic plate structures. The results illustrate that the present approach renders benchmark solutions provided higher order truncations are used, and act as engineering plate equations using low order truncation.