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A Journal of Russian Academy of Sciences
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IssuesArchive of Issues2020-4pp.496-513

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I.M. Lebedev and E.I. Shifrin, "Identification of Transverse Cracks in a Rod Using Eigenfrequencies of Transverse Vibrations," Mech. Solids. 55 (4), 496-513 (2020)
Year 2020 Volume 55 Number 4 Pages 496-513
DOI 10.3103/S002565442004007X
Title Identification of Transverse Cracks in a Rod Using Eigenfrequencies of Transverse Vibrations
Author(s) I.M. Lebedev (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, 119526 Russia)
E.I. Shifrin (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, 119526 Russia, shifrin@ipmnet.ru)
Abstract 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.
Keywords transverse vibrations of a rod, multiple cracks, inverse spectral problem, numerical identification algorithm
Received 05 February 2020Revised 23 February 2020Accepted 25 March 2020
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