Natural frequency of stepped beam having multiple open cracks by transfer matrix method

In this study, the transfer matrix method is used for the dynamic analysis of a stepped beam with arbitrary multiple transverse open cracks. The reduction in bending stiffness due to the presence of transverse open cracks or abrupt changes of cross-section is modelled by kind of massless rotational springs. The advantages are demonstrated through examples. Firstly, it yields purely analytical solutions which are more accurate than the numerical ones. Secondly, the size of the resulting eigen-matrix is small. For beams with all sorts of boundary restraint conditions, having many abrupt changes of cross-sections and/or with arbitrary multiple open cracks, the size of the eigen-matrix is still 4 by 4 (or less). Numerical examples are presented to validate the accuracy and efficiency of the present formulation.