Abstract
A problem of reconstruction of multiple cracks in a beam by means of the natural frequencies corresponding to transverse vibration of the beam is considered. The cracks are simulated by massless rotational springs. It is proved that the cracks can be uniquely identified by three spectra corresponding to three different types of the end conditions. The problem is solved by reducing it to the inverse spectral problem for an ordinary differential equation of fourth order. A method for identifying damage caused by cracks has been developed. The method is based on minimization of the objective function, built with the knowledge of the three spectra. Numerical examples are considered.
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