Non-linear Vibration Analysis of Isotropic Plate with Perpendicular Surface Cracks

Abstract

A novel analytical model is presented for nonlinear vibration analysis of a thin isotropic plate containing two perpendicular, partial surface cracks located at the centre of the plate. The two cracks are continuous line cracks and each is parallel to one of the edges of the plate. Using classical plate theory, the equation of motion of the cracked plate is derived based on equilibrium principle. The crack terms are formulated using the Line Spring Model (LSM) and Berger’s formulation for the in-plane forces converts the equation of motion of cracked plate into a cubic nonlinear system. Further, a nonlinear Duffing equation is obtained by applying the Galerkin’s method. The frequency response relation for the cracked plate showing geometric nonlinearity and peak amplitude is obtained using the perturbation method of multiple scales. The influence of crack length ratios and boundary conditions on the natural frequencies of square and rectangular plate is demonstrated. The variation in the vibration characteristic of plate with two perpendicular cracks is presented in this paper.