The problem of propagation of an acoustic surface wave is considered within the framework of the asymmetric theory of elasticity (Cosserat medium). A new analytical solution of the problem in displacements is obtained. These solutions are compared with the corresponding solution for the classical elastic medium. Within the framework of the Cosserat continuum in half-space besides elliptical Rayleigh wave can be in existence the shear wave with only transversal component. Thus, in Cosserat medium the new wave mode is found out, and there is no analogue of it in classical elasticity theory.

The problem of the shear elastic wave propagation within the framework of the Cosserat continuum has been considered. Medium deformation in this model is described not only by the displacement vector, but also by kinematically independent rotation vector. This model can be used for the description of the media with microstructure, for example concrete, sand, sandy-gravel mixture etc.

At the same time the applications of these models almost do not exist in praxis, since there are no reliable data about the material properties in nonsymmetrical elasticity theory and in fact there are no experiments which can demonstrate the effects of couple-stress behavior in solid under deformation.

Main models of elastic waves propagation in medium with microstructure have been proposed in 50-60th. At that time many significant theoretical results have been obtained, for example the fact of Rayleigh waves dispersion. But the classical elasticity theory does not describe this effect.

1) We have considered the problem of a propagation of elastic surface waves in half-space in the Cosserat medium [1-4].

Within the framework of the Cosserat continuum in half-space besides elliptical Rayleigh wave can be in existence the shear wave with only transversal component. Geometrically such wave is equal to Love wave, but in classical elasticity theory existence of the Love wave as shear elastic wave is defined by presence of a layer on a half-space, and while a layer thickness vanishing the Love wave proceeds to a plane wave. Thus, in Cosserat medium the new wave mode is found out, and there is no analogue of it in classical elasticity theory.

2) The problem of propagation of a Lamb elastic wave in a thin plate is considered using the Cosserat continuum model [5]. Solutions of the equations of motion are sought in the form of wave packets specified by a Fourier spectrum of an arbitrary shape for three components of the displacement vector and three components of the rotation vector which depend on time, depth, and the longitudinal coordinate. The initial system of equations is split into two systems, one of which describes a Lamb wave and the second corresponds to a transverse wave whose amplitude depends on depth. Analytical solutions in displacements are obtained for the waves of both types. Unlike the solution for Lamb waves, the solution obtained for the transverse wave has no analogs in classical elasticity theory.

3) We have also considered the reduced Cosserat medium where the couple stress is zero, while the rotation vector is independent of the translational displacement. In this model, the stress depends on the rotation of a particle relatively to the background continuum of mass centers, but it does not depend on the relative rotation of two neighboring particles. This model seems to be adequate for the description of granular media, consolidated soils, and rocks with inhomogeneous microstructure. We have obtained and analyzed theoretical solutions for this model describing the propagation of body waves and surface waves [6]. We have shown both the dispersive character of these waves in elastic space and half space, and the existence of forbidden frequency zones.

These results can be used for the preparation, execution, and interpretation of seismic experiments, which would allow one to determine whether (and in which situations) polar theories are important in rock mechanics, and to help with the identification of material parameters of the reduced Cosserat continuum.

[1]	M.A. Kulesh, V.P. Matveenko and I.N. Shardakov Construction and analysis of an analytical solution for the surface Rayleigh wave within the framework of the Cosserat continuum // Journal of Applied Mechanics and Technical Physics. V. 46. No. 4. P. 556-563 (2005). Full text (pdf, eng, 184Kb); Abstract (html, rus); About the journal
[2]	M.A. Kulesh, V.P. Matveenko and I.N. Shardakov On the propagation of elastic surface waves in the Cosserat medium // Doklady Physics. V. 50. No. 11. P. 601 - 604 (2005). Abstract (html, eng); About the journal
[3]	M.A. Kulesh, V.P. Matveenko and I.N. Shardakov Propagation of surface elastic waves in the Cosserat medium // Acoustical Physics. V. 52. No. 2. P. 186-193 (2006). Full text (pdf, eng, 243Kb); About the journal
[4]	M.A. Kulesh, V.P. Matveenko and I.N. Shardakov Dispersion and polarization of surface Rayleigh waves within the framework of the Cosserat continuum (in Russian) // Proceedings of RAS, Solid State Mechanics. No. 4, in press (2007). Full text (pdf, rus, 508Kb)
[5]	M.A. Kulesh, V.P. Matveenko and I.N. Shardakov Constructing an analytical solution for Lamb waves using the cosserat continuum approach // Journal of Applied Mechanics and Technical Physics. V. 48. No. 1. P. 119-125 (2007). Full text (pdf, eng, 188Kb); Abstract (html, eng); About the journal
[6]	M.A. Kulesh and E.F. Grekova Rayleigh-type waves for the isotropic elastic reduced Cosserat half-space. Application in rocks and soils // Proceedings of the EAGE International Conference & Exhibition (16-19 October, 2006, Saint Petersburg, Russia). Full text (pdf, eng, 350Kb); Presentation (pdf, eng, 1810Kb); About the conference
[7]	Kulesh M.A., Ulitin M.V., Shardakov I.N. Analysis of solutions of Cosserat elastokinetics equations for plane volumetrical waves (in Russian) // Proceedings of 15th Winter School on Continuous Media Mechanics, Ekaterinburg, UrO RAS. V. 2. P. 273-275 (2007). Full text (pdf, rus, 671Kb)

[1]	Shardakov I.N. and Kulesh M.A Analysis of analytical solutions some static and dynamic problems of the couple-stress elasticity theory (in Russian) // Book of abstracts of II All-Russian Scientific Conference "Actual Problems of Applied Mathematics and Mechanical Engineers" (8-11 September 2004, Abrau-Dyurso). P. 113-114. Full text (pdf, rus, 111Kb); About the conference
[2]	Shardakov I.N. and Kulesh M.A Characterization of the shallow Rayleigh waves analysis for Cosserat-continuum (in Russian) // Book of abstracts of International Scientific-Technical Conference "Mechanics of inhomogeneous medium: methods, models, solutions" (1-8 October 2004, Sevastopol). P. 69-70. Full text (pdf, rus, 1112Kb); About the conference
[3]	M.A.Kulesh, M.Holschneider and I.N.Shardakov Surface waves properties in cosserat continuum: construction of solution and analysis using wavelet transform // Eos Trans. AGU, 86(52), Fall Meet. Suppl., Abstract U21B-0808 (2005). Full text (html, eng); Presentation (pdf, eng, 723Kb); About the conference
[4]	Kulesh M.A. and Shardakov I.N About the propagation of surface elastic waves in Cosserat continuum (in Russian) // Book of abstracts of 14th All-Russian Conference of Young Scientists and Students "Mathematical simulation in natural sciences" (5-7 October 2005, Perm). P. 40-41. Full text (pdf, rus, 845Kb)
[5]	M.A.Kulesh, M.Holschneider, I.N.Shardakov Surface waves propagation in Cosserat continuum: construction of solution and analysis using wavelet transform // Book of abstracts of International Summer School-Conference "Advanced Problems in Mechanics" (June 25 - July 1, 2006, St.Petersburg, Russia). P. 54. Full text (pdf, eng, 1242Kb); Presentation (pdf, eng, 1364Kb); About the conference
[6]	M.A.Kulesh, E.F.Grekova, I.N.Shardakov Rayleigh wave in the isotropic and linear, reduced Cosserat continuum // Book of abstracts of International Summer School-Conference "Advanced Problems in Mechanics" (June 25 - July 1, 2006, St.Petersburg, Russia). P. 53-54. Full text (pdf, eng, 1242Kb); Presentation (pdf, eng, 1720Kb); About the conference
[7]	M.V. Ulitin, M.A. Kulesh, I.N. Shardakov About the propagation of Stonley wave in the Cosserat medium (in Russian) // Book of abstracts of 15th All-Russian School-conference of young scientists "Mathematical simulation in natural sciences" (4-7 October 2006, Perm, Russia). P. 91-92. Full text (pdf, rus, 525Kb); About the conference
[8]	E. Grekova, M. Kulesh, G. Herman and I. Shardakov Modeling of the Propagation of Seismic Waves in Non-Classical Media: Reduced Cosserat Continuum // Eos Trans. AGU, 87(52), Fall Meet. Suppl., Abstract S23B-0151 (2006). Full text (html, eng); Presentation (pdf, eng, 1606Kb); About the conference