| | 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: | | 12804 |
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
In English (Mech. Solids): | | 4760 |
|
<< Previous article | Volume 42, Issue 4 / 2007 | Next article >> |
M. A. Kulesh, V. P. Matveenko, and I. N. Shardakov, "Dispersion and polarization of surface Rayleigh waves for the Cosserat continuum," Mech. Solids. 42 (4), 583-594 (2007) |
Year |
2007 |
Volume |
42 |
Number |
4 |
Pages |
583-594 |
Title |
Dispersion and polarization of surface Rayleigh waves for the Cosserat continuum |
Author(s) |
M. A. Kulesh (Institute of Continuous Media Mechanics, Ural Branch of Russian Academy of Sciences, Akad. Korolyova 1, Perm, 614013, Russia, kma@icmm.ru)
V. P. Matveenko (Institute of Continuous Media Mechanics, Ural Branch of Russian Academy of Sciences, Akad. Korolyova 1, Perm, 614013, Russia, mvp@icmm.ru)
I. N. Shardakov (Institute of Continuous Media Mechanics, Ural Branch of Russian Academy of Sciences, Akad. Korolyova 1, Perm, 614013, Russia, shardakov@icmm.ru) |
Abstract |
In the framework of the nonsymmetric theory of elasticity (the Cosserat contimum), we consider the problem of propagation of a surface acoustic Rayleigh wave in the half-space. The wave is represented as a wave packet of arbitrary form bounded both in the time space and the Fourier space. We assume that the material strain is described by not only the displacement vector but also an independent rotation vector. The general analytic solution of this problem is obtained in displacements. We perform comparative analysis of the obtained solution and the corresponding solution for the classical elastic medium. We introduce and analyze macroparameters characterizing the difference between the stress-strain state and the state predicted by the classical theory of elasticity: the elasticity coefficient, the wave number, and the phase and group velocities. It should be noted that these parameters can be measured experimentally. |
References |
1. | W. Nowacki, Theory of Elasticity (PWN,
Warsaw, 1970; Mir, Moscow, 1975). |
2. | V. A. Pal'mov,
"Fundamental Equations of Nonsymmetric Elasticity Theory,"
Prikl. Mat. Mekh.
28 (3), 401-408 (1964)
[J. Appl. Math. Mech. (Engl. Transl.)]. |
3. | A. C. Eringen,
Microcontinuum Field Theories, Vol. I, Foundations and Solids
(Springer, New York, 1998). |
4. | N. F. Morozov,
Selected Two-Dimensional Problems of Elasticity Theory
(Izd-vo LGU, Leningrad, 1978)
[in Russian]. |
5. | R. D. Gauthier and W. E. Jahsman,
"A Quest for Micropolar Elastic Constants,"
Trans. ASME: J. Appl. Mech.
42 (2), 369-374 (1975). |
6. | V. I. Erofeev,
Wave Processes in Solids with Microstructure
(Isz-vo MGU, Moscow, 1999)
[in Russian]. |
7. | R. S. Lakes,
"Experimental Methods for Study of Cosserat Elastic Solids and Other
Generalized Continua,"
in Continuum Models for Materials with Micro-Structure,
Ed. by H. Muhlhaus
(Wiley, New York, 1995),
Chap. 1, pp. 1-22. |
8. | R. D. Gauthier and W. E. Jahsman,
"A Quest for Micropolar Elastic Constants, Pt 2,"
Arch. Mech.
33 (5), 717-737 (1981). |
9. | I. A. Viktorov,
Acoustic Surface Waves in Solids
(Nauka, Moscow, 1981)
[in Russian]. |
10. | S. V. Biryukov, Yu. V. Gulyaev, V. V. Krylov, and V. P. Plesskii,
Surface Acoustic Waves in Inhomogeneous Media
(Nauka, Moscow, 1991)
[in Russian]. |
11. | G. Adomeit,
Ausbreitung elastischer Wellen und Bestimmung von Materialkonstanten
im Cosserat-Kontinuum
(Techn. Hochschule, Aachen, 1967)
[in German]. |
12. | A. E. Lyalin, V. A. Pirozhkov, and R. D. Stepanov,
"On Surface Wave Propagation in a Cosserat Medium,"
Akust. Zh.
28 (6), 838-840 (1982). |
13. | P. Bhatnagar,
Nonlinear Waves in One-Dimensional Dispersive Systems
(Clarendon Press, Oxford, 1979; Mir, Moscow, 1983). |
14. | J. Whitham,
Linear and Nonlinear Waves
(Wiley, New York, 1974; Mir, Moscow, 1977)
[in Russian]. |
15. | J. D. Achenbach,
Wave Propagation in Elastic Solids
(North-Holland, Amsterdam-London, 1973). |
16. | R. M. Rene, J. L. Fitter, P. M. Forsyth, et al.,
"Multicomponent Seismic Studies Using Complex Trace Analysis,"
Geophysics
51 (6), 1235-1251 (1986). |
17. | Y. Nakamura, "A Method for Dynamical Characteristics Estimation of
Subsurfaces Using Microtremor on the Ground Surface," Quart.
Report Railway Techn. Research Inst. 30 (1), 25-33 (1989). |
18. | A. L. Levshin, T. B. Yanovskaya, A. V. Lander, et al.,
Surface Seismic Waves in Horizontally Inhomogeneous Earth
(Nauka, Moscow, 1986)
[in Russian]. |
19. | M. Holschneider,
Wavelets: An Analysis Tool
(Clarendon Press, Oxford, 1995). |
20. | N. M. Astaf'eva, "Wavelet Analysis: Theoretical Backgrounds
and Application Examples," Usp. Fiz. Nauk 166 (11),
1145-1170 (1996). |
21. | A. I. Lurie,
Theory of Elasticity
(Nauka, Moscow, 1970)
[in Russian]. |
22. | G. A. Korn and T. M. Korn, Mathematical Handbook for
Scientists and Engineers (McGraw-Hill, New York, 1968; Nauka,
Moscow, 1973). |
23. | M. A. Kulesh, V. P. Matveenko, and I. N. Shardakov,
"Construction of Analytic Solutions of Some Two-Dimensional Problems
of the Moment Theory of Elasticity,"
Izv. akad. Nauk. Mekh. Tverd. Tela,
No. 5, 69-82 (2002)
[Mech. Solids (Engl. Transl.)]. |
24. | J. S. Bendat and A. G. Piersol,
Random Date: Analysis and Measurement Procedures
(Wiley, New York, 1971; Mir, Moscow, 1989). |
25. | D. G. Ghiglia and L. A. Romero,
"Robust Two-Dimensional Weighted and Unweighted Phase Unwrapping That Uses
Fast Transforms and Iterative Methods,"
J. Opt. Soc. America A
11 (1), 107-117 (1994). |
26. | M. Kulesh, M. Holschneider, M. S. Diallo, et al.,
"Modeling of Wave Dispersion Using Continuous Wavelet Transforms,"
Pure and Appl. Geophys.
162 (5), 843-855 (2005). |
|
Received |
15 September 2004 |
Link to Fulltext |
|
<< Previous article | Volume 42, Issue 4 / 2007 | Next article >> |
|
If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|