An Analytical Study for Nonlinear Vibration Analysis of Twodirectional Functionally Graded Rectangular Plate

In this study, an analytical solution is presented for investigating the nonlinear vibration analysis of twodirectional functionally graded rectangular plate for the first time. On the basis of first order shear deformation theory (FSDT) and Galerkin procedure, the equations of motion are developed. The nonlinear equation of motion is then solved analytically by modified LindstedtPoincare method. Thevolume fraction distribution is assumed to be symmetrical for characterizing the inplane material inhomogeneity. Finally, the effects of some system parameters such as nondimensional vibration amplitude, volume fraction indexes and aspect ratio on the nonlinear to linear frequency ratio are discussed in detail. To validate the analysis, the results of this paper are compared with the published data and good agreements are found.