Closed-form Analytical Solutions for Free Vibration of Rectangular Functionally Graded Thin Plates in Thermal Environment

Abstract

Based on classical small deflection plate theory, the governing equation of functionally graded (FG) plates in thermal environment is derived by using Hamilton’s principle. Closed-form analytical solutions are obtained via separation-of-variable method for free vibration of rectangular FG thin plates with simply supported, clamped and guided edges, especially for the plates with two adjacent clamped edges in thermal environment. The normal modes and frequencies are in an elegant and explicit closed form. Comprehensive numerical comparison and results in dimensionless form validate the present method and reveal a few physical phenomena.