Identification of the parameters of a rod with a longitudinal rectangular groove using two spectra of natural frequencies of bending vibrations
- Authors: Utyashev I.M.1, Fatkhelislamov A.F.2
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Affiliations:
- Mavlyutov Institute of Mechanics, Ufa Centre RAS
- Ufa University of Science and Technology
- Issue: Vol 28, No 2 (2024)
- Pages: 378-389
- Section: Short Communications
- URL: https://journal-vniispk.ru/1991-8615/article/view/311032
- DOI: https://doi.org/10.14498/vsgtu2061
- EDN: https://elibrary.ru/WTKDQB
- ID: 311032
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Abstract
The inverse coefficient problem involves determining the geometric parameters of a longitudinal rectangular groove based on the natural frequencies of the bending vibrations of a rectangular rod. It is assumed that the groove does not extend along the entire length of the rod, but rather from a certain point to the right end. To solve the problem, the rod with the longitudinal groove is modeled as two sections: the first section without a groove and the second section with a groove.
Mating conditions are applied at the connection point, where deflection values, rotation angles, bending moments, and shear forces are equated. The behavior of the natural frequencies of bending vibrations when changing the length of the groove was investigated. A solution method is proposed that allows for determining the required parameters based on a finite number of natural frequencies of bending vibrations. It is shown that the solution is unambiguous when using frequency spectra with respect to mutually perpendicular axes.
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##article.viewOnOriginalSite##About the authors
Ilnur M. Utyashev
Mavlyutov Institute of Mechanics, Ufa Centre RAS
Author for correspondence.
Email: utyashevim@mail.ru
ORCID iD: 0000-0002-2342-0492
SPIN-code: 7856-5351
Scopus Author ID: 56966700200
ResearcherId: J-1064-2018
https://www.mathnet.ru/person139311
Cand. Phys. & Math. Sci.; Researcher; Lab. of Solid Mechanics
Russian Federation, 450054, Ufa, prosp. Oktyabrya, 71Alfir F. Fatkhelislamov
Ufa University of Science and Technology
Email: alfir93@mail.ru
ORCID iD: 0000-0002-8494-9592
https://www.mathnet.ru/person203542
Senior Lecturer; Dep. of Information Security Management
Russian Federation, 450076, Ufa, Zaki Validi st., 32References
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