Free vibration analysis of functionally graded material beams with transverse crack

In this research, for the first time, the free vibration of the functionally graded beam containing transverse crack under clamped-clamped boundary condition studied based on Reddy high order theory. It was assumed that mechanical properties of beam vary exponentially in the thickness direction. To drive the closed form solution for natural frequencies of functionally graded beams containing a transverse crack, Ritz method was used. The effects of slender ratio, the location of crack, depth of crack and material gradients on natural frequency were also examined. Finally, the results of the analytical method were analyzed and compared with results of modeling by ABAQUS software and other studies. This research shows that due to more complex equations of Reddy beam theory, using Reddy beam theory for a thick beam and Timoshenko beam theory for a thin beam are more suitable. In addition, a relation between the depth of crack and the necessity of using functionally graded beam is confirmed.