 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| I.M. Lebedev and E.I. Shifrin, "Solution of the Inverse Spectral Problem for a Rod Weakened by Transverse Cracks by the Levenberg-Marquardt Optimization Algorithm," Mech. Solids. 54 (6), 857-872 (2019) |
| Year |
2019 |
Volume |
54 |
Number |
6 |
Pages |
857-872 |
| DOI |
10.3103/S0025654419060025 |
| Title |
Solution of the Inverse Spectral Problem for a Rod Weakened by Transverse Cracks by the Levenberg-Marquardt Optimization Algorithm |
| Author(s) |
I.M. Lebedev (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia)
E.I. Shifrin (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, shifrin@ipmnet.ru) |
| Abstract |
The longitudinal vibrations of a rod weakened by transverse cracks are considered. Cracks are assumed to be open and modeled by translational springs. The stiffness of the springs corresponds to the size of the cracks. A method has been developed for identifying the number and position of transverse cracks, as well as the stiffness of the corresponding springs according to two spectra that correspond to two types of conditions at the ends of the rod: free-free and fixed-free. The developed method is based on minimizing the objective function that characterizes the difference between the given (measured) natural frequencies and natural frequencies calculated during the implementation of the algorithm. The objective function is minimized using the Levenberg-Marquardt algorithm. Numerical examples are considered. The stability of the obtained results with respect to noise in the initial data is investigated. |
| Keywords |
longitudinal oscillations of the rod, multiple cracks, inverse spectral problem, Levenberg-Marquardt method |
| Received |
14 January 2019 |
| Link to Fulltext |
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