Natural frequencies of cracked functionally graded material plates by the extended finite element method

TL;DR

This study investigates the natural frequencies and mode shapes of cracked functionally graded material plates using the extended finite element method, considering various crack parameters and boundary conditions.

Contribution

It introduces an extended finite element approach with a specialized quadrilateral element for analyzing cracked FG plates, including effects of multiple cracks and thickness variations.

Findings

Natural frequencies decrease with increasing crack length and orientation.

Mode shapes are significantly affected by crack position and boundary conditions.

Multiple cracks further alter vibrational characteristics.

Abstract

In this paper, the linear free flexural vibration of cracked functionally graded material plates is studied using the extended finite element method. A 4-noded quadrilateral plate bending element based on field and edge consistency requirement with 20 degrees of freedom per element is used for this study. The natural frequencies and mode shapes of simply supported and clamped square and rectangular plates are computed as a function of gradient index, crack length, crack orientation and crack location. The effect of thickness and influence of multiple cracks is also studied.