Natural frequencies of a Timoshenko beam with cracks

A problem of calculating of natural frequencies of a Timoshenko beam weakened by a finite number of transverse open cracks is considered. The problem is solved for both known crack models. In one model every crack is simulated by a single, massless rotational spring. In the other model every crack is simulated by two massless springs (one extensional and another one rotational). An effective method for calculation of the natural frequencies of a vibrating beam with cracks, which was previously successfully applied to Euler-Bernoulli beams, is extended to the case of Timoshenko beam. The developed method makes it possible to significantly reduce the order of the determinant, the zeros of which are natural frequencies. Numerical examples are considered. The results are compared with the known where it is possible.