Four-variable Quasi-3D model for nonlinear thermal vibration of FG plates lying on Winkler-Pasternak-Kerr foundation

Abstract

This paper presents the nonlinear thermodynamic results of functionally graded plates lying on Winkler/Pasternak and Kerr foundation through an analytical formulation. The field displacement is defined by only four unknowns, including an indeterminate integral and a new shape function representing the transverse shear stresses. Material properties of the FG plates are temperature-dependent and graded according to a simple power-law distribution. Also, the thermodynamic equations of motion are deduced based on Hamilton's principle.The exactitude of the present theory results is verified with those obtained by various researchers. The effects of temperature-dependence material properties, power-law index, nonlinear temperature rising, elastic foundation parameters, aspect, and slenderness ratio are discussed. The results show that the increase in elastic foundation parameters would enhance the thermodynamic response of the FG plates. Nevertheless, the degree of improvement would be related to the nonlinear temperature change. Moreover, the plate's configuration effect is more significant when the nonlinear temperature difference is high.