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IssuesArchive of Issues2016-5pp.576-582

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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, vatulyan@math.rsu.ru)
V.O. Yurov (South Federal University, ul. Mil'chakova 8a, Rostov-on-Don, 344090 Russia, vitia.jurov@yandex.ru)
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
References
1.  V. T. Grinchenko and V. V. Meleshko, Harmonic Vibrations and Waves in Elastic Bodies (Naukova Dumka, Kiev, 1981) [in Russian].
2.  I. I. Vorovich and V. A. Babeshko, Dynamic Mixed Problems of Elasticity for Nonclassical Domains (Nauka, Moscow, 1979) [in Russian].
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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