Identification of crack locations and depths in a multi-cracks beam by using local adaptive differential quadrature method

Abstract

In this article, we propose a new simplified sectional flexibility method to simulate multi-cracks in a beam. The crack is considered as a line spring model which is related to the ratio of crack depth to the beam height ( a/ h). The transfer matrix method was derived and employed to construct the eigenvalue system. The local adaptive differential quadrature method was applied to evaluate the natural frequencies of cracked beams. The results of natural frequencies are in excellent agreement with literature results. For identification of multiple cracks in a beam, the Newton–Raphson iteration method was applied to predict the locations and depths of cracks. Numerical results were compared with results of other investigators and this method was found to be more accurate.