HR: 0800h
AN: U21B-0808    [Abstracts]
TI: Surface Waves Properties in Cosserat Continuum: Construction of Solution and Analysis Using Wavelet Transform
AU: * Kulesh, M
EM: mkulesh@math.uni-potsdam.de
AF: University of Potsdam, Applied and Industrial Mathematics, Am Neuen Palais 10, Potsdam, 14469 Germany
AU: Holschneider, M
EM: hols@math.uni-potsdam.de
AF: University of Potsdam, Applied and Industrial Mathematics, Am Neuen Palais 10, Potsdam, 14469 Germany
AU: Shardakov, I
EM: shardakov@icmm.ru
AF: Ural Branch of RAS, Institute of Continua Media Mechanics, Academic Korolev street, 1, Perm, 614013 Russian Federation
AB: The problem of the surface elastic wave propagation in the half-space 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. The main result of presented work consist in fact, that within the framework of the Cosserat continuum in half-space besides elliptical Rayleigh wave can be in existence the surface 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 surface 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. As a second result of presented work the method of the displacement seismogram inversion has been proposed. This method is based on continues wavelet transform and allows to restore the wave number, phase and group velocities. These results can be effectively used in possible experiments which are aimed at the detection of couple-stress effects in medium and further at the identification of material constants of nonsymmetrical elasticity theory. This work was supported by Russian Foundation of Fundamental Research under project 03-01-00561 and by the Deutsche Forschungsgemeinschaft (DFG) within the framework of the priority program SPP 1114, ®Mathematical methods for time series analysis and digital image processing¯.
DE: 3280 Wavelet transform (3255, 4455)
DE: 3285 Wave propagation (0689, 2487, 4275, 4455, 6934)
DE: 5102 Acoustic properties
DE: 5112 Microstructure
DE: 7255 Surface waves and free oscillations
SC: Union [U]
MN: Fall Meeting 2005