Nonlinear Vibration Analysis of Specially Orthotropic Tapered Plate with Arbitrarily Oriented Crack: An Analytical Approach

The current work aims to investigate nonlinear vibrations in a partially cracked orthotropic plate with linearly varying thickness. The orientation of this crack is arbitrary and can vary from 0° to 90°. The equilibrium principle is used, and the governing equation of a tapered orthotropic plate is derived using classical plate theory. The simplified line spring model, which incorporates in-plane forces and bending moments, is used to consider the impact of a partial crack on plate dynamics. The inclusion of Berger’s formulation introduces nonlinearity into the model in terms of in-plane forces. For converting the derived governing equation into time-dependent modal coordinates, Galerkin’s method was chosen, which employs an approximate solution technique to solve the nonlinear Duffing equation. The effects of the taper constants, crack orientation, and crack length on the fundamental frequency are investigated for SSSS and CCSS boundary conditions.