Effects of non-uniform elastic foundation on the nonlinear vibration of nanocomposite plates in thermal environment using Selvadurai methodology

Abstract

This paper focuses on effects of non-uniform elastic foundation, that impact on non-linear thermal dynamics of the simply supported plate reinforced by functionally graded (FG) graphene nanoplatelets (GNPs). The Halpin-Tsai micromechanical model and the rule of mixtures are employed to calculate the material properties. By adjusting the volume fraction of matrix/GNPs in the thickness direction, the various distribution patterns of the plates are considered as the uniform distribution (UD) and functionally graded (FG) reinforcements. The governing equations is expressed by using the classical theory, Von Karman-Donnell geometrical nonlinearity assumption, and combining the temperature change. Then the dynamical behaviors of the FG-GNPs reinforced plates are obtained by applying the Airy's stress function and the Galerkin's method. The obtained results are described by the column charts, the 2D and 3D graphs and written by codes of Wolfram-Mathematica. In addition, the present study scrutinizes the effects of the thermal environment, GNPs weight fraction, GNPs distribution patterns, damping coefficient and geometric parameters. More importantly, the influences of the longitudinal variable thickness of Pasternak’s subgrade model on the dynamical characteristics are analyzed to optimize structures. Altogether these findings have significant applications in industries engineering and lead to breakthroughs in the microstructures design.