Free vibration of multi-cracked beams

Abstract

A new method is presented to study the free vibrations of multi-cracked beams with arbitrary boundary conditions. In the literature, the method based on changes in modal strain energy was used to perform the dynamic analysis of beams with just one crack. In this paper, the changes in modal strain energy are used iteratively to study the dynamic behavior of beams with multiple cracks. The iterative method consists in finding the dynamic frequencies in steps by considering the effects of cracks one by one. First, the beam is assumed intact, for it a single crack is taken into account via the method based on changes in modal strain energy. Then, this procedure is repeated iteratively by taking at steps (i+1), the frequencies obtained at step (i). The end is detected when the total number of cracks is reached. This developed iterative approach is used to analyze the effect of multiple open cracks on the modal parameters of a cantilever beam subjected to free vibration. The results are in good agreement with finite element and experimental methods. This developed method may also be used to generate training data for pattern recognition approaches to health monitoring.