Free vibration analysis of twin piezoelectric inclusions embedded in elastic medium

Abstract

The present study is the first attempt to investigate the free vibration behavior of the rectangular plate including two equal (twin) internal parallel piezoelectric inclusions (lying width-wise in the plate) utilizing the 3D exact equations of electroelasticity theory. For the solution, the finite element method is applied. By Hamilton's principle, the equation of motion and boundary conditions are obtained to derive the finite element equations using the electrical energy of the piezoelectric material and the mechanical energy of the structure. Lateral edge surfaces of the plate have zero electrical potential and are simply supported. Ideal contact conditions are satisfied by the interface surfaces between the elastic medium and piezoelectric (abbreviated as PZT) inclusions. After investigating the convergence and validation of the approach, the influence of various parameters on the natural frequencies of the plate behavior, such as the mutual effect of PZT inclusions, coupling effect between the electrical and mechanical fields, the effect of the size, location, material, and polled directions of the PZT inclusions, and the material of the elastic medium, is investigated.