Effect of microstructure on vibration analysis of partially cracked thin orthotropic plate based on strain gradient theory

Abstract

An analytical model is proposed to analyze the vibration problem of partially cracked thin orthotropic plate based on a non-classical plate theory. The governing equation for the cracked orthotropic plate is derived using the classical plate theory in conjunction with the strain gradient theory of elasticity. The crack is modeled using appropriate crack compliance coefficients based on the simplified line spring model. The governing equation of cracked plate has been solved analytically to get the relation for fundamental frequency of the plate. To demonstrate the accuracy of the present model, few comparison studies are carried out with the published literature. The fundamental frequency of the cracked plate is studied considering various parameters such as crack length, plate thickness and internal length scale of microstructure. It has been concluded that the frequency is affected by crack length and internal length scale parameter.