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In present article we consider the problems of concentrated point force which is moving with constant velocity and oscillating with cyclic frequency in unbounded homogeneous anisotropic elastic two-dimensional medium. The properties of plane waves and their phase, slowness and ray or group velocity curves for 2D problem in moving coordinate system are described. By using the Fourier integral transform techniques and established the properties of the plane waves, the explicit representation of the elastodynamic Green's tensor is obtained for all types of source motion as a sum of the integrals over the finite interval. The dynamic components of the Green's tensor are extracted. The stationary phase method is applied to derive an asymptotic approximation of the far wave field. The simple formulae for Poynting energy flux vectors for moving and fixed observers are presented too. It is noted that in the far zones the cylindrical waves are separated under kinematics and energy. It is shown that the motion bring some differences in the far field properties. They are modification of the wave propagation zones and their number, fast and slow waves appearance under trans- and superseismic motion and so on., Comment: 19 pages, Proceeding of the Conference "Advanced Problems in Mechanics", Russia, St.Petersburg (Repino), June 22-July 2, 2003

The paper deals with classical problem for cracks dislocated in a certain very specific porous elastic material, described by a Cowin-Nunziato model. We propose a method based upon a reducing of stress concentration problem for cracks to some integral equations. By applying Fourier integral transforms the problem is reduced to some integral equations. For the plane-strain problem we operate with a direct numerical treatment of a hypersingular integral equation. In the axially symmetric case, for the penny-shaped crack, the problem is reduced to a regular Fredholm integral equation of the second kind. In the both cases we study stress-concentration factor, and investigate its behavior versus porosity of the material. More in particular the stress concentration factor in the medium with voids is always higher, under the same conditions, than in the classical elastic medium made of material of the skeleton. Further, as can be seen, the influence of the porosity becomes more significant for larger cracks; that is also quite natural from a physical point of view., Comment: 24 pages, 4 figures, accepted by International Journal of Engineering Science

In this paper a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions, is presented. The main goal of the present work is the development of an efficient direct numerical collocation method. The second part of the work is devoted to the application of the method to the porous elastic materials. This part deals with classical problem for cracks dislocated in a certain very specific porous elastic material, described by a Cowin-Nunziato model. By applying Fourier integral transform the problem is reduced to some integral equations. For the plane-strain problem we operate with a direct numerical treatment of a hypersingular integral equation. We also study stress-concentration factor, and investigate its behaviour versus porosity of the material. At the end we investigate the possibility to extend the results in the thermoelastic case., Comment: 4 Pages, Proceedings Of Thermal Stress 2003

In this paper we study the spatial and temporal behaviour of the dynamic processes in porous elastic mixtures. For the spatial behaviour we use the time-weighted surface power function method in order to obtain a more precisely determination of the domain of influence and we establish spatial decay estimates of Saint-Venant type with time-independent decay rate for the inside of the domain of influence. For the asymptotic temporal behaviour we use the Cesaro means associated with the kinetic and strain energies and establish the asymptotic equipartition of the total energy. A uniqueness theorem is proved for finite and infinite bodies and we note that it is free of any kind of a priori assumptions of the solutions at infinity., Comment: 25pages, accepted by Ukcrainian Mat.Jour