Identification of crack location and crack size in a simply supported beam by measurement of natural frequencies

Abstract

In this paper, theoretical and experimental analysis of a vibrating, simply supported beam with a crack is carried out. This method is used to address the inverse problem of assessing the crack location and crack size in various beam structures. The method is based on measurement of natural frequencies, which are of global parameter and can be easily measured from any point on the structure. In theoretical analysis the crack is simulated by an equivalent spring, connecting the two segments of the beam. Analysis of this approximate model results in algebraic equations, which relate the natural frequencies of the beam, and crack location. Also the relationship between the natural frequencies, crack location and crack size has also been developed. For identification of the crack location and crack size, it was shown that data on the variation of the first two natural frequencies is sufficient. The computation of natural frequencies of an uncracked and cracked beam is facilitated by a finite element method package. This database is to be utilized in an analytical method to address the inverse problem to identify the crack location and crack size. Experiments have also been performed on a simply supported beam. The experimental analysis is done to verify the practical applicability of the theoretical method developed. A good agreement between the predicted and actual crack location and crack size is obtained. The results obtained by theoretical and experimental methods are compared graphically.