An analytical state-space solution for free vibration of sandwich piezoelectric plate with functionally graded core

Abstract

The purpose of this paper is to develop an analytical solution for free vibration analysis of smart functionally graded (FG) plates by the Levy solution in conjunction with the state-space approach. The FG substrate is sandwiched between two piezoelectric layers. The rectangular structure has two simply-supported opposite edges while the boundary conditions of the other two edges are arbitrary. Based on the simple but efficient four-variable refined plate theory, the governing equations are extracted employing Maxwell’s equation and Hamilton’s principle. The achieved fourth-order partial differential equations are transformed to first-order ordinary ones using the Levy solution along with the state-space approach and then, they are solved by applying the eigenvalue method. Meanwhile, an iterative algorithm is proposed to obtain the natural frequencies of the structure with various boundary conditions. A comparison is made between the obtained results and those available in the literature which verifies the accuracy of the solution method and numerical algorithm proposed in this study. Finally, the effect of several parameters such as type of boundary conditions, aspect ratio, power-law index, piezoelectric layer thickness, and thickness-to-side ratio is examined on the obtained results.