Influences of arbitrary-distributed Kerr foundation on free vibration and nonlinear transient response of functionally graded plate in thermal environment

For the first time, a novel theoretical model is presented for analyzing the effects of the arbitrary-distributed Kerr foundation on the free vibration and transient responses of the functionally graded material (FGM) plate in a thermal environment. According to the power law distribution, the mechanical characteristics of FGM plates are assumed to vary with plate thickness. The three-parameter Kerr model is founded on the independence of the upper and lower elastic layers with respect to the shear layer. The shape and location of the elastic foundation can be determined arbitrarily using mathematical functions. In the area of the FGM plate, the distribution of the elastic foundation is assumed to be either centralized or decentralized. The Reddy's third-order shear deformation theory is utilized to express the governing equations. Then, the dynamical characteristics of the FGM plate are obtained by using the Galerkin's method. To validate the accuracy of the current computational model, the achieved results are compared to those derived from published literature. In addition, graphical representations of the effects of stiffness, distributions, and geometrical parameters of elastic foundation, geometrical parameters of plate, material properties, and thermal environment on the vibrational characteristics of the plates are provided.