Analytical modelling for vibration analysis of partially cracked orthotropic rectangular plates

An analytical model is presented for vibration analysis of a thin orthotropic plate containing a partial crack located at the centre of the plate. The continuous line crack is parallel to one of the edges of the plate. The equation of motion of an orthotropic plate is derived using the equilibrium principle based on Classical Plate Theory. The crack terms are formulated using the Line Spring Model. Using Berger's formulation for the in-plane forces and Galerkin's method for solution, the derived equation involving a cubic nonlinear term is converted into the Duffing equation. The effect of nonlinearity is established by deriving the frequency response equation for the cracked plate using the method of multiple scales. The influence of crack length and boundary conditions on the fundamental frequency of square and rectangular plate is demonstrated for three boundary conditions. It is found that the vibration characteristics are affected by the presence of crack. Further, it is deduced that the presence of a crack across the fibres affects the fundamental frequency more as compared to a crack along the fibres. The effect of varying elasticity ratio on fundamental frequency of cracked plate is also established. •Vibration analysis of cracked orthotropic rectangular plates is presented.•In the analytical model, crack terms for line crack are based on line spring model.•The nonlinear bending hardening or softening phenomenon is demonstrated.•The effect of increase in crack length on fundamental frequency is deduced.•The effect of elasticity ratio on fundamental frequency is established.