Nonlinear free vibration analysis of functionally graded rectangular plate using modified Lindstedt-Poincare method

In this research, the nonlinear free vibration analysis of functionally graded (FG) rectangular plate is investigated analytically using first order shear deformation theory (FSDT) for the first time. For this purpose, firstly, using Hamilton principle, the partial differential equations of motion are developed based on first order shear deformation theory (FSDT) and von Karman nonlinearity strain displacement relations. Afterward, by applying Galerkin method, the nonlinear partial differential equations are transformed into nonlinear ordinary differential equations. Then, using the modified Lindstedt-Poincare method, the nonlinear equation of transverse motion of the FG plate is solved analytically to determine nonlinear frequency ratio. The material properties of the plate are assumed to be graded continuously according to power law distribution in the thickness direction. The effects of some key system parameters such as vibration amplitude, volume fraction index and aspect ratio on the nonlinear natural frequency ratio to linear natural frequency are discussed. To validate the analysis, the results of this study are compared with the results of previously published papers and numerical solution and good agreement has been observed.