Influence of Kerr's elastic foundation on free vibration of functionally graded plate

Abstract

The introduction of the paper presents an overview of composite materials. Emphasis is placed on their continuing importance as a key area of research and their significant impact on various industrial applications. Special attention is paid to functionally graded materials (FGM), which are classified as modern composites. The primary objective of this study is to develop analytical formulations and solutions for the analysis of free vibrations of functionally graded plates supported on Kerr elastic foundation. The kinematic displacement‐strain relations are represented using a higher‐order shear deformation theory based on shape functions. The material properties of FG plates are assumed to vary through the thickness following a power law distribution. The applied shape functions ensure that the boundary conditions are satisfied without stresses at the plate surfaces, eliminating the need for shear correction factors. Various numerical examples are given to highlight the effects of different values of the power law index, aspect ratio and aspect‐to‐thickness ratio. The results are compared with those from the quasi‐3D theory and the conclusions suggest that the proposed theory is both accurate and effective in predicting the vibration behavior of functionally graded plates.