Identification of Transverse Cracks in a Rod Using Eigenfrequencies of Transverse Vibrations

A problem on identification of multiple cracks in a rod by means of eigenfrequencies of transverse vibrations is considered. The cracks are modeled by weightless rotational springs. It has been proven that cracks can be uniquely identified using three spectra corresponding to three different types of boundary conditions. A numerical method for assessing fracture caused by cracks has been developed. The method is based on minimizing the objective function obtained by taking into account three spectra. Theoretically, fracture reconstruction is possible using several different spectra triplets. In the article, by means of various examples and using the developed numerical method, a comparative performance analysis of using various theoretically acceptable triplets of spectra is carried out.