Nonlinear vibrational response of a single edge cracked beam

The nonlinear vibrational response of a breathing cracked beam was investigated. The study was done by using a new crack stiffness model to examine some of the nonlinear behaviors of a cantilever beam with a breathing crack. The quadratic polynomial stiffness equation of the cracked beam was derived based on the hypothesis that the breathing process of a crack depends on the vibration magnitude. The Galerkin method combined with the stiffness equation was used to simplify the cracked beam into a Single-degree-of-freedom (SDOF) lumped system with nonlinear terms. The multi scale method was adopted to analyze the nonlinear amplitude frequency response of the beam. The applicability of the stiffness model was discussed and parameter sensitivity studies on the dynamic response were carried out by the SDOF model for a cantilever beam. Results indicate that the new stiffness model provides an efficient tool to study the vibrational nonlinearities introuduced by the breathing crack. Therefore, it might be used to develop a nonlinear identification method of a crack in a beam.