Crack detection of plate structures using differential quadrature method

Abstract

In this study, the problem of crack identification in plates is investigated using the differential quadrature method. The crack, which is assumed to be open, is modeled by the extended rotational spring. The crack, with finite length, divides the plate into six segments. Then, the differential quadrature is applied to the governing differential equations of motion of each segment and the corresponding boundary and continuity conditions. An eigenvalue analysis will be performed on the resulting system of algebraic equations to obtain the natural frequencies of the cracked plate. Here, the crack detection practice is considered as an optimization problem, and the location, size, and depth of the crack are regarded as the design variables. The weighted sum of the squared errors between the measured and computed natural frequencies is used as the objective function. The Bees algorithm, a swarm-based evolutionary optimization technique, is used to solve the optimization problem. To insure the integrity and robustness of the presented method, extensive experimental case studies are carried out on the cantilever plates having a finite-length open crack parallel to the clamped edge. The results show that the crack parameters can be predicted well by the presented methodology.