Transverse vibration of plate with multiple curved through cracks

Abstract

A modeling method for transverse vibration of cracked plate containing multiple internal curved through cracks is presented and experimental studies are performed to validate its effectiveness. The cracked plate is assumed to be divided into several rectangular and curved trapezoidal domains in the global coordinates system. For each sub-domain, the transverse displacement is expanded as Chebyshev orthogonal polynomials series in local coordinates system. As for the shared edges between neighboring two sub-domains, the local collocation method is adopted and a number of Chebyshev zero points are selected to ensure the displacement continuity condition. To verify the convergence and correctness of the presented model and solutions, the natural frequencies, mode shapes and dynamic responses for several cases are compared with reference results and experimental results, with good agreement observed. In addition, the influence of several significant parameters of cracks are investigated, including the number, location and geometrical shape of the cracks. It is shown that the crack inside the plate presents less influence than that at the boundary on the mode change of the plate. The investigations in the study implies that the present model method is effective and convenient for plate with multiple curved through cracks.