Analytical Approach for Detection of Multiple Cracks in a Beam

Abstract

An analytical approach for the detection of a beam with multiple cracks is presented in this article. The method is based on the bending vibration theory of Euler-Bernoulli beam and the cracks are treated as massless rotational springs, by which the cracked beam is separated into a number of segments of perfect beams. By using the nontrivial solution condition of the vibration mode of the beam elements, specially using the transfer matrix method for the multiple cracks detection, the crack identification equation of the cracked beam is obtained explicitly, which is a function of natural frequencies, the locations, and depths of the cracks. Since the natural frequencies of a cracked beam can be measured through many of the structural testing methods, then the relations of the locations and the depths of the cracks can be determined explicitly from the identification equation of a cracked beam which geometrical and physical parameters as well as the boundary conditions are given. The results of some examples are shown and the present method is validated with the existing and measured experimental data. The detection for other types of beams with different number of cracks and various boundary conditions can also be obtained by a similar procedure.