Crack Detection in Stepped Beam Carrying Slowly Moving Mass

Abstract

A crack identification algorithm based on a mathematical model has been developed to identify crack location and depth in stepped cantilever Euler—Bernoulli beam carrying concentrated masses. In order to estimate crack location and depth in the beam the proposed algorithm utilizes the variation of the difference between the natural frequencies of cracked and intact systems versus single mass location along the beam span. The assumed mode method is used to derive the mathematical model for the system under investigation, in which the crack's effect is introduced to the system as a global effect. The advantage of the proposed algorithm is to identify the crack by monitoring a single natural frequency of the system. The algorithm can utilize the measurements of the first few system natural frequencies to check/reconfirm its identification results. Furthermore, it is efficient and can be simply implemented for any structure that has a slowly moving mass, as in the case of overhead gantry and girder cranes. The identification algorithm is tested using the first system's natural frequency obtained from an experimental work as well as from a finite element analysis. Moreover, the algorithm is tested once more using the second system's natural frequency obtained from finite element analysis. The tests' results show that the crack depth and location can be predicted with sound accuracy.