Inverse spectral problem for a rod with multiple cracks

A problem of identification of multiple cracks in a rod using spectral data is considered. The cracks are simulated by translational springs. A method for determination of the number of springs, their locations and flexibilities is developed. The problem is reduced to the problem which can be solved by Krein׳s method. The Krein method enables to reconstruct the damage parameters by means of the use of natural frequencies for longitudinal vibration of the rod with free-free and fixed-free end conditions.