Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories

TLDR

Porosities in functionally graded materials necessitate studying wave propagation in porous plates. The study develops various higher‑order shear deformation plate theories for wave propagation in functionally graded plates. The authors modify the rule of mixture for porous FGMs, derive governing equations via Hamilton’s principle, solve an eigenvalue problem to obtain analytic dispersion relations, and analyze the influence of volume‑fraction distributions and porosity on wave propagation. The refined theories reduce unknowns compared to first‑order shear deformation theory while capturing transverse shear effects without shear correction factors, and the results are applicable to ultrasonic inspection and structural health monitoring.

Abstract

In this work, various higher-order shear deformation plate theories for wave propagation in functionally graded plates are developed. Due to porosities, possibly occurring inside functionally graded materials (FGMs) during fabrication, it is therefore necessary to consider the wave propagation in plates having porosities in this study. The developed refined plate theories have fewer number of unknowns and equations of motion than the first-order shear deformation theory, but accounts for the transverse shear deformation effects without requiring shear correction factors. The rule of mixture is modified to describe and approximate material properties of the functionally graded plates with porosity phases. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton's principle. The analytic dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions and porosity volume fraction on wave propagation of functionally graded plate are discussed in detail. The results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.