Homotopy perturbation solution and periodicity analysis of nonlinear vibration of thin rectangular functionally graded plates

In this paper nonlinear analysis of a thin rectangular functionally graded plate is formulated in terms of von-Karmanʹs dynamic equations. Functionally Graded Material (FGM) properties vary through the constant thickness of the plate at ambient temperature. By expansion of the solution as a series of mode functions, we reduce the governing equations of motion to a Duffingʹs equation. The homotopy perturbation solution of generated Duffingʹs equation is also obtained and compared with numerical solutions. The sufficient conditions for the existence of periodic oscillatory behavior of the plate are established by using Greenʹs function and Schauderʹs fixed point theorem.