Effect of crack orientation on vibration characteristics of partially cracked FGM plate: An analytical approach

Abstract

A nonlinear analytical model for vibration analysis of partially cracked thin FGM plate as affected by the crack orientation, crack length and plate aspect ratio is presented. The proposed analytical model is based on the Kirchhoff’s classical plate theory. A single partial crack located at the centre and at an arbitrary orientation is considered in a FGM plate. The crack is in the form of a continuous line and the line spring model is used to incorporate it’s effect in the form of moment and in-plane forces. Berger’s formulation is used to introduce the non linearity in the model while the Galerkin’s method is used for obtaining the solution of the governing differential equation. Results for the fundamental frequencies as affected by the plate aspect ratio, gradient index, crack orientation and crack length is presented for all edges simply supported boundary condition. It is found that the crack orientation affects the fundamental frequencies of the partially cracked FGM plates.