Natural frequencies of a bar with multiple cracks

In this paper the smooth function method, previously proposed for bending vibrations, is extended to the calculation of longitudinal natural frequencies of a vibrating isotropic bar with an arbitrary finite number of symmetric transverse open cracks. Moreover, the transfer matrix approach and the finite element method are considered to deal with the same problem. The paper includes several examples related to bars with three cracks which permit the comparison of natural frequencies predicted by these three methods.