A method for crack identification in functionally graded Timoshenko beam

In this paper, a method is proposed to detect a single crack in functionally graded Timoshenko beam by measurements of natural frequencies. First, a consistent theory of vibration is formulated for cracked FGM Timoshenko beam that is a useful tool for modal analysis of the beam. The frequency equation obtained in the theory provides a simple approach to solve not only the forward but also inverse problems for the cracked beam. It allows one to propose an efficient method for crack identification in FGM Timoshenko beam from lowest natural frequencies. Usefulness of the theoretical development was validated by numerical results.