The influence of transversal crack geometry on the frequency changes of beams

Global non-destructive testing methods use changes in modal data as damage indicators. Depending on their geometry, damages influence the modal parameters in different way. While breathing cracks influence the natural frequencies due to only stiffness change, open cracks affect supplementary these frequencies due to loss of mass. This paper describes a study devoted to clarify the influence of the damage geometry on the natural frequencies of beams considering the two above mentioned aspects. First, analytical and numerical analyses are performed, in order to highlight the effect of mass changes on the frequency changes. Afterwards, the study focuses on breathing cracks in open and closing stages as well as on open cracks and emphasizes the influence of the geometrical discontinuity. It was demonstrated that, for beams with a breathing crack, a two degrees of freedom model is necessary to characterize its dynamic behavior. Finally, a relation between frequency changes and damage geometry and location is contrived.