Abstract
Two dynamical problems of the propagation of oscillations in an anisotropic medium generated by a point harmonic force are considered. In the first problem steady harmonic oscillations in an anisotropic plane are investigated. The solution can be reduced to solving a system of second-order elliptic equations for the steady part of the displacements. As the second problem, within the framework of the basic physical model [1], the dynamical contact problem for an anisotropic half-plane reinforced along its boundary by an infinite ellastic coating in the form of a thin cover is considered. The generating point force is harmonic. The solution of each of the two problems is constructed by the method of Fourier transforms. Using Lighthill's method [2] and the method of stationary phase [3], asymptotic formulae are obtained for the strains and stresses, in which surface, quasilongitudinal and quasitransverse wave!; can be distinguished explicitly.
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