Free vibration analysis of uniform and stepped cracked beams with circular cross sections

This paper presents a novel numerical technique applicable to analyse the free vibration analysis of uniform and stepped cracked beams with circular cross section. In this approach in which the finite element and component mode synthesis methods are used together, the beam is detached into parts from the crack section. These substructures are joined by using the flexibility matrices taking into account the interaction forces derived by virtue of fracture mechanics theory as the inverse of the compliance matrix found with the appropriate stress intensity factors and strain energy release rate expressions. To reveal the accuracy and effectiveness of the offered method, a number of numerical examples are given for free vibration analysis of beams with transverse non-propagating open cracks. Numerical results showing good agreement with the results of other available studies, address the effects of the location and depth of the cracks on the natural frequencies and mode shapes of the cracked beams. Modal characteristics of a cracked beam can be employed in the crack recognition process. The outcomes of the study verified that presented method is appropriate for the vibration analysis of uniform and stepped cracked beams with circular cross section.