Effect of thickness ratio on vibrations of an asymmetric bimorph plate of piezoelectric ceramics

An asymmetric bimorph plate is formed by inverting the polarization of two piezoelectric ceramic plates of unequal thickness (b ₁ and b₂, respectively) and bonding them together. The thickness ratio of the two layers is defined by r_t=b₂/b₁. Exact and close form solutions of the 3-D equations of linear piezoelectricity are obtained for the free vibrations of an infinite, asymmetric bimorph plate of piezoelectric ceramics. These solutions which satisfy the traction-free and electrically shorted face conditions and the continuity conditions of mechanical displacements, tractions, normal electrical displacements and potential at the interface of the two layers. They reduce to those of a homogeneous plate as r_t=0 and to those of a symmetric bimorph plate as r_t=1. Dispersion curves are computed and plotted for real as well as imaginary wave numbers for piezoelectric ceramic bimorphs with various thickness ratios. The effects of changes in thickness ratios on the behavior of various frequency branches are examined in detail