Damped free vibration analysis of a beam with a fatigue crack using energy balance method

In this paper, a new approach based on the energy balance method is proposed for free vibration analysis of a cracked cantilever beam by taking into account both the structural damping and the damping due to the crack. Also, by taking into account the effect of opening and closing the crack during the beam vibration, the stiffness changes at the crack location are considered to be a nonlinear amplitude-dependent function which causes the frequencies and mode shapes of the beam to vary continuously with time. The results show that neglecting the effects of structural damping and nonlinear behavior of the crack will be a source of considerable error in obtaining the dynamic response and vibration characteristics of the cracked beam. In order to validate the results obtained through the proposed method, some experimental test have been conducted.

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