Acta Mechanica Solida Sinica

, Volume 27, Issue 2, pp 210–220

# Homotopy Perturbation Solution and Periodicity Analysis of Nonlinear Vibration of Thin Rectangular Functionally Graded Plates

• M. J. Mahjoob
• M. H. Naei
Article

## Abstract

In this paper nonlinear analysis of a thin rectangular functionally graded plate is formulated in terms of von-Karman’s 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 Duffing’s equation. The homotopy perturbation solution of generated Duffing’s 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 Green’s function and Schauder’s fixed point theorem.

## Key Words

nonlinear vibration FGM rectangular plate Schauder’s fixed point theorem homotopy perturbation method

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© The Chinese Society of Theoretical and Applied Mechanics and Technology 2014

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