Summary
Cracks and resonance stand out as primary factors contributing to the failure of engineering components subjected to dynamic loading. Numerous studies have affirmed that the existence of cracks can alter modal frequencies, thereby increasing the likelihood of resonance occurring at frequencies other than those originally designed for. Therefore, it is necessary to model for understanding influence of crack on modal coupling. In this work, we employ a model of a cantilever beam with a crack by introducing a singularity in the material stiffness within the dynamic equation of motion to study its effect on modal coupling. We derived equation of beam considering presence of shortening effect as well as geometric nonlinearities. We observe that mode shapes alters modal frequencies relative to a regular beam, which can lead to internal resonance.
