Free vibrations and stability of stepped columns with cracks

In this paper, a solution to the free vibration problem of a stepped column with cracks is presented. The open cracks occur at step changes in the cross-section of the column or at the intermediate points of the uniform segments. The cracks in the column are represented by massless rotational springs. The frequency equation is obtained by using properties of the Green's functions corresponding to the uniform segments of the column. The approach pertains to the vibration of columns consisting of an arbitrary number of uniform segments. The stability of the column, which depends on the position and size of the cracks, is numerically investigated.