Free Vibration Analysis of Multiple Cracked Functionally Graded Timoshenko Beams

In this paper, authors present the study of free vibration of bending multiple cracked functionally graded material (FGM) beam. Vibration equations of multiple cracked FGM beam were established by using the rotational spring model of cracks, dynamic stiffness method (DSM) and actual position of neutral plane. The frequency equation obtained was in a simple form, that provides an effective approach to study not only free vibration of the beams but also inverse problems like identification of material and crack parameters in structure. The obtained numerical results show good agreement with other previous published results. Thence, numerical computation has been carried out to investigate the effect of each crack, the number of cracks, material and geometric parameters on the natural frequencies of multiple cracked Timoshenko FGM beams.