Vibratory Characteristics of Timoshenko Beams with Arbitrary Number of Cracks

An analytical approach is proposed for determining vibratory characteristics of cracked Timoshenko beams. Based on the rotational spring model for describing the local flexibility induced by a crack and the developed fundamental solutions, the frequency equation for a Timoshenko beam with any kind of two end supports and an arbitrary number of cracks can be established from a second-order determinant. The decrease in the determinant order can lead to significant savings in the computational time.