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 Sibirsk. Mat. Zh., 2012, Volume 53, Number 2, Pages 345–364 (Mi smj2310)

Asymptotics of solutions to the spectral elasticity problem for a spatial body with a thin coupler

S. A. Nazarov

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg

Abstract: We construct asymptotics for the eigenvalues and vector eigenfunctions of the elasticity problem for an anisotropic body with a thin coupler (of diameter h) attached to its surface. In the spectrum we select two series of eigenvalues with stable asymptotics. The first series is formed by eigenvalues $O(h^2)$ corresponding to the transverse oscillations of the rod with rigidly fixed ends, while the second is generated by the longitudinal oscillations and twisting of the rod, as well as eigenoscillations of the body without the coupler. We check the convergence theorem for the first series and derive the error estimates for both series.

Keywords: joint of a massive rod with a thin rod, spectrum of elastic body, asymptotics for eigenvalues.

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English version:
Siberian Mathematical Journal, 2012, 53:2, 274–290

Bibliographic databases:

Document Type: Article
UDC: 517.956.8+517.956.328+539.3(4)

Citation: S. A. Nazarov, “Asymptotics of solutions to the spectral elasticity problem for a spatial body with a thin coupler”, Sibirsk. Mat. Zh., 53:2 (2012), 345–364; Siberian Math. J., 53:2 (2012), 274–290

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/smj/v53/i2/p345

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Bunoiu R., Cardone G., Nazarov S.A., “Scalar Boundary Value Problems on Junctions of Thin Rods and Plates”, ESAIM-Math. Model. Numer. Anal.-Model. Math. Anal. Numer., 48:5 (2014), 1495–1528
2. F. L. Bakharev, S. A. Nazarov, “Gaps in the spectrum of a waveguide composed of domains with different limiting dimensions”, Siberian Math. J., 56:4 (2015), 575–592
3. Yu. I. Dimitrienko, I. D. Dimitrienko, “Modeling of thin composite laminates with general anisotropy under harmonic vibrations by the asymptotic homogenization method”, Int. J. Multiscale Comput. Eng., 15:3 (2017), 219–237
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