Dispersion relations for cylindrical bending motions of polarized piezoceramic bimorph plates with two facing edges free

Abstract

Dispersion relations of thin parallel bimorph plates with polarized piezoceramics are obtained by using Hamilton’s principle. The coupled variational equations for piezoceramic bimorph plates are derived with the thin plate theory and the extension of electric potential in the thickness direction, which are valid for low frequency range. More specifically, coupled differential equations as well as dispersion relations subject to homogeneous natural-type boundary conditions on the two facing side-edges are derived for the cylindrical bending motions of both fully electroded and unelectroded bimorph plates of which surfaces are free from applied traction for both cases; the derivations are made through the expansions of mechanical displacements in the thickness co-ordinate with plane stress assumptions at major surfaces in the manner of Mindlin and of electric potential with vanishing second order components of electric potentials at major surfaces in the manner of Tiersten. Relations between the deflection gradient of fully electroded bimorph plate and the induced electric current are obtained. The complexity due to the additional inclusion of differential equations for the electric potential components may be alleviated through the reductions of the coupled differential equations. As an illustrative example, dispersion relations for the aforementioned four cases of bimorph plates composed of PZT5 are obtained. The dispersion curves are depicted and compared each other, and some differences and similarities are discussed.