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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2012, Volume 53, Issue 2, Pages 137–147 (Mi pmtf1353)  
This article is cited in 4 scientific papers (total in 4 papers)

One method of determining the elastic properties of inhomogeneous solids

A. O. Vatulyana, O. V. Bocharovab

a Southern Federal University, Rostov-on-Don, 344090, Russia
b Southern Scientific Center, Russian Academy of Sciences, Rostov-on-Don, 344006, Russia
Full-text PDF (269 kB) Citations (4)
Abstract: This paper considers the inverse problem of reconstructing three inhomogeneous characteristics of a rod (Young’s modulus, shear modulus, and density) from amplitude-frequency characteristics for the regime of steady-state longitudinal, flexural, and torsional vibrations. The unknown characteristics are identified by constructing iterative processes based on the apparatus of the Fredholm integral equations of the first and the second kind. Results of numerical experiments are presented.
Keywords: inhomogeneous elastic rod, elastic moduli, ill-posed problem, Fredholm equations.
Received: 11.03.2011
English version:
Journal of Applied Mechanics and Technical Physics, 2012, Volume 53, Issue 2, Pages 266–274
DOI: https://doi.org/10.1134/S0021894412020150
Bibliographic databases:
Document Type: Article
UDC: 539.3
Language: Russian
Citation: A. O. Vatulyan, O. V. Bocharova, “One method of determining the elastic properties of inhomogeneous solids”, Prikl. Mekh. Tekh. Fiz., 53:2 (2012), 137–147; J. Appl. Mech. Tech. Phys., 53:2 (2012), 266–274
Citation in format AMSBIB
\Bibitem{VatBoc12}
\by A.~O.~Vatulyan, O.~V.~Bocharova
\paper One method of determining the elastic properties of inhomogeneous solids
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2012
\vol 53
\issue 2
\pages 137--147
\mathnet{http://mi.mathnet.ru/pmtf1353}
\elib{https://elibrary.ru/item.asp?id=17651510}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2012
\vol 53
\issue 2
\pages 266--274
\crossref{https://doi.org/10.1134/S0021894412020150}
Linking options:
  • https://www.mathnet.ru/eng/pmtf1353
  • https://www.mathnet.ru/eng/pmtf/v53/i2/p137
    • This publication is cited in the following 4 articles:
    1. Grigory V. FEDOTENKOV, Dmitry I. MAKAREVSKII, Yana A. VAHTEROVA, Trah Quyet THANG, “The inverse non-stationary problem of identification of defects in an elastic rod”, INCAS BULLETIN, 13:S (2021), 57  crossref
    2. O.V. Bocharova, I.E. Andzjikovich, A.V. Sedov, V.V. Kalinchuk, “Low frequency method for monitoring the state of structural heterogeneous objects”, Procedia Structural Integrity, 32 (2021), 299  crossref
    3. S. N. Tsarenko, “Torsional vibrations of a rod with an axial geometric inhomogeneity”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 11:1 (2019), 50–58  mathnet  mathnet  crossref
    4. O.V. Bocharova, I.E. Andzjikovich, A.V. Sedov, V.V. Kalinchuk, “An effective method of signal processing in problems of low-frequency defectoscopy.”, Procedia Engineering, 199 (2017), 2034  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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