A VDQ approach to nonlinear vibration analysis of functionally graded porous circular plates resting on elastic foundation under hygrothermal shock

Abstract

In this paper, a novel numerical approach is proposed to study the geometrically nonlinear large-amplitude vibrations of circular plates subjected to hygrothermal loading resting on an elastic foundation. It is considered that the plates are made of functionally graded (FG) porous materials whose hygro-thermo-mechanical properties are estimated based on the modified Voigt's rule of mixture. Hygroscopic stresses produced because of the nonlinear rise in moisture concentration are taken into account. Moreover, two distribution patterns for porosity (even and uneven) are considered. The Touloukian formula is also employed to assess the temperature-dependence of material properties. Based on the first-order shear deformation plate theory in conjunction with von-Kármán geometrical nonlinear relations, the variational form of the governing equations is derived using Hamilton’s principle. In addition, the effect of the elastic foundation is incorporated into the formulation according to the Winkler-Pasternak model. For solving the problem of nonlinear vibrations, the generalized differential quadrature, variational differential quadrature, and Newmark-beta integration methods are utilized. The influences of important parameters such as temperature distribution, porosity volume fraction, moisture concentration, elastic foundation parameters and FG index on the geometrically nonlinear vibrations of FG porous plates with different boundary conditions induced by hygro-thermal loadings are analyzed. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature.