Analytical solution for free vibrations of moderately thick hybrid piezoelectric laminated plates

An analytical solution for free vibrations of a hybrid rectangular plate composed of a transversely isotropic, homogeneous and linear elastic core and face sheets made of a linear piezoelectric material is derived by assuming that the plate deformations are governed by the Mindlin plate theory. The electric potential in a piezoelectric layer satisfies Maxwellʹs equation and either open circuit or closed circuit boundary conditions on its major surfaces. For the hybrid plate coupled governing equations obtained from the Hamilton principle are decoupled by introducing four auxiliary scalar functions, and the Levy type analytical solution for free vibrations is derived. Plate frequencies as a function of the piezoelectric layer thickness and the plate aspect ratio are presented and discussed. It is found that the electric boundary conditions on major surfaces of the piezoelectric layers and the aspect ratio of the hybrid plate noticeably influence its frequencies. Significant contributions of the work include proposing the four scalar functions to uncouple the governing equations, providing an analytical solution for frequencies of the hybrid plate, and delineating effects of boundary conditions as well as of aspect ratio of the plate.