Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
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IssuesArchive of Issues2016-5pp.576-582

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Total articles in the database: 10864
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A.O. Vatul'yan and V.O. Yurov, "On the Dispersion Relations for an Inhomogeneous Waveguide with Attenuation," Mech. Solids. 51 (5), 576-582 (2016)
Year 2016 Volume 51 Number 5 Pages 576-582
DOI 10.3103/S0025654416050101
Title On the Dispersion Relations for an Inhomogeneous Waveguide with Attenuation
Author(s) A.O. Vatul'yan (South Federal University, ul. Mil'chakova 8a, Rostov-on-Don, 344090 Russia; South Mathematical Institute, ul. Markusa 22, Vladikavkaz, 362027 Russia,
V.O. Yurov (South Federal University, ul. Mil'chakova 8a, Rostov-on-Don, 344090 Russia,
Abstract Some general laws concerning the structure of dispersion relations for solid inhomogeneous waveguides with attenuation are studied. An approach based on the analysis of a first-order matrix differential equation is presented in the framework of the concept of complex moduli. Some laws concerning the structure of components of the dispersion set for a viscoelastic inhomogeneous cylindrical waveguide are studied analytically and numerically, and the asymptotics of components of the dispersion set are constructed for arbitrary inhomogeneity laws in the low-frequency region.
Keywords attenuation, dispersion set, cylindrical waveguide, asymptotic analysis, inhomogeneity
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3.  I. P. Getman and Yu. A. Ustinov, Mathematical Theory of Irregular Solid Waveguides (Izdat. RGU, Rostov-on-Don, 1993) [in Russian].
4.  A. O. Vatul'yan and A. V. Morgunova, "Study of Dispersion Properties of Cylindrical Waveguides with Variable Properties," Akust. Zh. 61 (3), 295-301 (2015).
5.  A. O. Vatul'yan and V. O. Yurlov, "On Dispersion Relations for a Hollow Cylinder in the Field of Inhomogeneous Prestresses," Ekolog. Vestnik Nauchn. Tsentrov Chernomorsk. Ekon. Sotrudn., No. 2, 22-29 (2015).
6.  C. Hohne, J. Prager, and H. Gravenkamp, "Computation of Dispersion Relations for Axially Symmetric Guided Waves in Cylindrical Structures by Means of a Spectral Decomposition Method," J. Ultrasonics 63, 54-64 (2015).
7.  J. Morsbol and S. V. Sorokin, "Elastic Wave Propagation in Curved Flexible Pipes," Int. J. Solids Struct. 75-76, 143-155 (2015).
8.  R. M. Christensen, Theory of Viscoelasticity: An Introduction (Academic Press, New York, 1971; Mir, Moscow, 1974).
9.  V. G. Karnaukhov, Coupled Problems of Thermoelasticity (Naukova Dumka, Kiev, 1982) [in Russian].
10.  N. S. Anofrikova and N. V. Sergeeva, "Study of Harmonic Waves in a Hereditarily Elastic Layer," Izv. Saratov Univ. Mat. Mekh. Inf. 14 (3), 321-328 (2014).
11.  A. H. Nayfeh, Perturbation Methods (Wiley, New York, 1973; Mir, Moscow, 1976).
Received 30 April 2016
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