New analytic free vibration solutions of non-Lévy-type porous FGM rectangular plates within the symplectic framework

Abstract

This study reports new analytic free vibration solutions of non-Lévy-type porous functionally graded material (FGM) rectangular plates, i.e., those without two opposite edges simply supported, by the symplectic superposition method (SSM). Such analytic solutions are not accessible through conventional analytic methods as seeking analytic solutions that meet both the governing partial differential equations and various non-Lévy-type boundary conditions is an acknowledged challenge. The primary advantage of the SSM is that it does not require any assumption of solution forms, but is conducted via rigorous mathematical treatments, such as the symplectic space-based separation of variables and the symplectic eigen expansion. Therefore, the intractable problems can be analytically solved. The rapid convergence and high accuracy of the analytic solutions obtained from the SSM have been demonstrated. Comprehensive natural frequency results of porous FGM plates with all possible combinations of clamped and free edges are presented and validated by the finite element method. The effects of various parameters, e.g., porosity distributions, are also investigated by the analytic solutions obtained. All tabulated results can serve as benchmarks for the future studies focusing on porous FGM plates with non-Lévy-type boundary conditions.