Nonlinear free and forced vibrations of porous sigmoid functionally graded plates on nonlinear elastic foundations

This paper focuses on the nonlinear free and forced vibrations of porous sigmoid functionally graded material plates resting on nonlinear elastic foundations. Two types of porosity distributions, even and uneven, were considered. A nonlinear three-parameter foundation model was employed to estimate the plate-foundation interactions. The material properties of the plates, described by the sigmoid distribution law, were assumed to be graded in the thickness direction. All four edges of the plates were simply supported and had no in-plane displacements. Based on a higher-order shear deformation plate theory and general von Karman-type equation, the equations of motion with the effects of nonlinear elastic foundations were developed. The equations of motion were solved by an improved perturbation technique to determine the nonlinear frequencies and dynamic responses of the plates. The numerical illustrations are presented in both tabular and graphical forms to show the effects of the nonlinear foundation parameters, pore volume fraction, and material volume fraction on the nonlinear vibration and dynamic responses of the plates.