Natural frequency analysis of imperfect FG sandwich plates resting on Winkler-Pasternak foundation

Abstract

The present research analyzes the natural frequencies of the imperfect functionally graded sandwich plate (FGSP) comprised of porous face sheets made of functionally graded materials (FGMs) and an isotropic homogeneous core resting on the elastic foundation. To accomplish this, the material characteristics of the FGSP are taken to be changed incessantly along the thickness direction based on the volume fraction of constituents expressed by the modified rule of the mixture, which includes porosity volume fraction with three diverse kinds of porosity distribution models. Furthermore, to describe the two-parameter elastic foundation's response on the imperfect FGSP, the medium is supposed to be linear, homogenous, and isotropic, and it has been modelled using the Winkler-Pasternak model. Moreover, in the kinematic relationship of the imperfect FGSP resting on the Winkler-Pasternak foundation, third-order shear deformation theory (TSDT) is used, and the motion equations are set up employing Hamilton's principle. For natural frequency analysis of imperfect FGSPs resting on the Winkler-Pasternak foundation with simply supported edges, an analytical solution is obtained. To verify the current formulation, comprehensive comparisons are performed with the available data. The impacts of the two-parameter elastic foundation, porosity volume fraction, porosity distribution types, lay-up scheme, and side to thickness ratio, on the values of the non-dimensional fundamental natural frequency (NDFNF) of the imperfect FGSPs, are investigated, thoroughly.