Inverse spectral problem for a non-uniform rod with multiple cracks

An inverse spectral problem for a rod of variable cross-section containing a finite number of transverse cracks is considered. The cracks are simulated by translational springs. It is proved that the number of springs, their locations and flexibilities are uniquely reconstructed by two spectra corresponding to longitudinally vibrating rod with free-free and free-fixed end conditions. A constructive procedure for reconstructing unknown damage parameters is developed. Numerical examples are considered.