 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| << Previous article | Volume 51, Issue 5 / 2016 | Next article >> |
| 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 |
| Link to Fulltext |
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