Investigation on the effect of porosity on wave propagation in FGM plates resting on elastic foundations via a quasi-3D HSDT

Abstract

In this paper, wave propagation in functionally graded (FG) porous plates resting on Winkler-Pasternak foundation is studied using a quasi-3D shear deformation theory. The proposed theory has a new displacement field that includes indeterminate integral terms and contains fewer unknown variables taking into account the effect of transverse shear and thickness stretching. The parameters of the elastic foundation are introduced in the present formulation following the mathematical model of Pasternak. In addition, the effect of porosity is studied. The material of the FG plate is inhomogeneous and the material properties are assumed to vary continuously in the thickness direction according to a power law of the volume fraction. The equations governing wave propagation in the plates resting on an elastic foundation are derived using Hamilton's principle. Then, the dispersion relationship between frequency and wave number is solved analytically. A comprehensive numerical result is accomplished to evaluate the effects of the volume fraction index, the porosity, thickness ratio (h/a), and the wave number on the wave propagation in functionally graded porous plates are discussed in detail.