Free Vibration Analysis of Sandwich Plates with Auxetic Core and Porous FGM Faces Resting on Winkler/Pasternak/Kerr Elastic Foundations

The paper presents an analytical solution to investigate the free vibration of a sandwich plate with an auxetic core (negative Poisson’s ratio) and functionally graded face sheets containing porosities (PoFGM), based on the four-variable higher-order shear deformation theory (HSDT-4). The plate is assumed to be supported by Winkler, Pasternak, or Kerr elastic foundations. The governing equations were derived using Hamilton’s principle and were solved analytically using the Navier solution for a rectangular plate with simply supported edges. The results were validated through comparisons with previously published studies, demonstrating the accuracy and reliability of the proposed approach. In addition, the effects of material properties (porosity distribution patterns, porosity volume fraction), geometric parameters of the auxetic core unit cell, the geometric dimensions of the plate, and the elastic foundation on the vibration characteristics were thoroughly analyzed.