Influence of microstructural defects on free flexural vibration of cracked functionally graded plates in thermal medium using XFEM

Abstract

This paper presents the influence of microstructural defects on the vibration characteristics of the cracked functionally graded plate in a thermal environment. Extended finite element formulation is implemented to model the cracked functionally graded plate based on higher-order shear deformation theory (HSDT). The level set function is implemented to track the crack in the functionally graded plate domain. The crack in the functionally graded plate domain is addressed by enriching the primary variable with additional functions using the partition of unity technique. The power-law distribution is implemented for the gradation of the material properties along the thickness direction to form functionally graded material (FGM). The microstructural defects are assumed as porosities in the plate. The porosity index determines the porosity in the FGM plate. The convergence and comparative study have been performed to verify the current formulation’s efficacy, accuracy, and reliability. Further, various numerical examples are presented. The effects of different influential parameters like porosity, volume fraction index, crack length, thickness ratio, and boundary condition on the natural frequencies have been discussed in detail. The presented computational approach is accurate, efficient, and robust enough to investigate the vibration response of the cracked FGM porous plates, which can provide a reference for future research by researchers.