Analytical and numerical free vibration analysis of porous functionally graded materials (FGPMs) sandwich plate using Rayleigh-Ritz method

Abstract

Purpose: This study introduces a new approximated analytical solution of the free vibration analysis to evaluate the natural frequencies of functionally graded rectangular sandwich plates with porosities. Design/methodology/approach: The kinematic relations are developed based on the classical plate theory (CPT), and the governing differential equation is derived by employing the Rayleigh-Ritz approximate method. The FGM plate is assumed made of an isotropic material that has an even distribution of porosities. The materials properties varying smoothly in the thickness direction only according to the power-law scheme. Findings: The influences of changing the gradient index, porosity distribution, boundary conditions, and geometrical properties on the free vibration characteristics of functionally graded sandwich plates are analysed. Research limitations/implications: A detailed numerical investigation is carried out using the finite element method with the help of ANSYS 2020 R2 software to validate the results of the proposed analytical solution. Originality/value: The results with different boundary conditions show the influence of porosity distribution on the free vibration characteristics of FG sandwich plates. The results indicated a good agreement between the approximated method such as the Rayleigh-Ritz and the finite element method with an error percentage of no more than 5%.