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

The main objective of this study is to develop an analytical solution for free vibration analysis of smart Functionally Graded (FG) plates using Levy solution in conjunction with 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, yet effcient, four-variable rened plate theory, the governing equations are extracted using Maxwell's equation and Hamilton's principle. The obtained fourth-order partial differential equations are transformed into the rst-order ordinary ones using the Levy solution along with the state-space approach and then, they are solved through the eigenvalue method. Meanwhile, an iterative algorithm is proposed to obtain the natural frequencies of the structure under different boundary conditions. A comparison is made between the obtained results and those available in the literature which veries the accuracy of the solution method and numerical algorithm proposed in this study. Finally, the effects of several parameters such as the type of boundary conditions, aspect ratio, power-law index, piezoelectric layer thickness, and thickness-to-side ratio on the obtained results are examined.