An approach based on homotopy iteration algorithm to identify the location and the depth of a cracked beam is studied. In the forward problem, a fully open crack model with the composite element method is employed for the vibration analysis and the dynamic responses of the cracked beam in time domain are obtained from the Newmark direct integration method. In the inverse analysis, the identification equation is derived by minimizing the error between the calculated acceleration response and the simulated measured one. Then, Newton's method with the homotopy equation is used to track the correct path and improve the convergence of the crack parameters. A numerical example is conducted to illustrate the correctness and efficiency of the proposed method and the effects of influencing parameters, such as division of the homotopy parameter and measurement noise are studied.
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