Free vibration of a circular membrane with a concentric circular crack

The natural vibration of a circular membrane with a discontinuity at the fixed boundary is investigated by an analytical method and the finite element analysis. A new analytical method is developed to consider the mixed boundary value problem using the orthogonality of the Fourier series. The finite element analysis has been done using ANSYS. The results from both simulations agree well as the problem is linear elastic problem. The mode shapes of the cracked membrane show that the vibration of the ligament dominates the vibration of smaller natural frequencies as the angle of the crack become larger because the flexibility of the free part in the ligament provide lower vibration modes.