Nonlinear Vibrations of Initially Stressed Functionally Graded Plates Using Homotopy Perturbation Method

In this paper, the homotopy perturbation method (HPM) is used to analysis the nonlinear vibration of thin functionally graded material (FGM) plates subjected to compressive normal biaxial initial stresses. Due to FGM’s excellent performance in high temperature environments, they have wide applications in aerospace structures. Based on Von Karman’s strain-displacement relations and using Galerkin method, the nonlinear differential equation of free vibrations is obtained. The material properties are graded continuously in the thickness direction of the FGM plate according to power law exponent. The effects of compressive initial stresses, initial deflection and aspect ratio on the frequency behavior are investigated. According to the results, the present first order approximation of HPM involves sufficiently accurate solution and less computational effort in comparison with other perturbation techniques for the present nonlinear problem.