Modal analysis of multi-cracked beams with circular cross section

This paper proposes a numerical model that combines the finite element and component mode synthesis methods for the modal analysis of beams with circular cross section and containing multiple non-propagating open cracks. The model virtually divides a beam into a number of parts from the crack sections and couples them by flexibility matrices considering the interaction forces that are derived from the fracture mechanics theory. The main feature of the presented approach is that the natural frequencies and mode shapes of a beam with an arbitrary number of cracks and any kind of two end conditions can be conveniently determined with a reasonable computational time. Three numerical examples are given to investigate the effects of location and depth of cracks on the natural frequencies and mode shapes of the beams. Moreover, it is shown through these examples that the evaluation of modal data obtained by the proposed model gives valuable information about the location and size of defects in the beams.