Influence of saturated porosity distributions on the geometrically nonlinear behavior of functionally graded porous plates in a thermal environment

Abstract

The nonlinear vibration behavior of functionally graded saturated porous (FGSP) plates in thermal environments is a complex problem influenced by material gradients, pore saturation, and temperature effects. Accurately capturing the impact of saturated porosity distributions and geometric nonlinearity on the dynamic behavior of these plates presents a key challenge. This study investigates the linear and nonlinear vibration characteristics of FGSP plates under thermal gradients, focusing on the role of saturated porosities. A modified power-law defines the temperature-dependent effective material properties through the plate’s thickness, while Biot’s theory models the effects of saturated pores. The governing equations are developed using the refined shear deformation plate theory combined with von Karman’s nonlinear relations and Hamilton’s principle. Numerical simulations via the direct iterative model provide insights into the linear and large-amplitude frequencies and the nonlinear central deflection of FGSP plates. Results indicate that saturated fluids within the pores significantly affect both vibrational frequencies and deflections, emphasizing the importance of considering porosity and thermal effects in modeling. This study highlights the necessity of incorporating saturated porosities and temperature-dependent properties for precise performance prediction, offering valuable guidance for designing porous materials in thermomechanical applications. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.