Free Vibration Analysis of the Functionally Graded Porous Plates with Auxetic Honeycomb Core Laid on Kerr-Type Elastic Foundation

The aim of this work is to analyze the free vibration behavior of sand-wich plates with two porous functionally graded skins and an auxetic honeycomb core resting on a Kerr-type elastic foundation. To accomplish this, a new quasi-3D trigonometric shear deformation theory is presented. This theory considers both shear strain and normal deformation but only requires five variables to approximate the displacement field, regardless of the shear correction factor. The governing equations of the plates on the Kerr-type elastic foundation are derived using Hamilton’s principle, and closed-form analytical solutions are obtained using Navier’s approach. Additionally, a comprehensive set of parametric simulations is conducted to investigate the influence of geometrical, material, and foundation parameters on the fundamental frequency of the plates.