Nonlinear Free and Forced Vibrations of In-Plane Bi-Directional Functionally Graded Rectangular Plate with Temperature-Dependent Properties

In this paper, the nonlinear free and forced vibrations analysis of in-plane bi-directional functionally graded (IBFG) rectangular plate with temperature-dependent properties is studied for the first time. For this purpose, with the aid of von Karman nonlinearity strain-displacement relations, the partial differential equations of motion are developed based on the first-order shear deformation theory (FSDT). Then, the nonlinear partial differential equations are transformed into the time-dependent nonlinear ordinary differential equations by applying the Galerkin method. The primary and super harmonic resonances are analyzed by the method of multiple scales (MMS). The material properties are assumed to be temperature-dependent and graded in the thickness direction according to the power-law distribution. The effects of some system parameters, such as vibration amplitude, volume fraction indexes, length-to-thickness ratio, temperature and aspect ratio on the nonlinear frequency and also frequency responses curve, are discussed in detail. To validate the analysis, the results of this paper are compared with the published data and good agreements are found.