The problem of diffraction of a plane elastic wave by a gradient transversely isotropic layer is considered. Using the method of overdetermined boundary value problem in combination with the Fourier transform method, the system of ordinary differential equations of the second order with boundary conditions of the third type is obtained which is solved by the grid method. Results of calculations obtained using the above-mentioned technique for the case of piecewise linear profiles for the Young modulus of the layer are given. 1. Introduction In nature, many of the geological formations form layered structures with elastic properties differing in various directions. Of all the formations and media, the special interest is often given to transversely isotropic media in which elastic modula of the media are the same in the plane normal to the axis of symmetry but differ from those of the direction along the axis of symmetry. Studies show that many sedimentary rocks indeed are transversely isotropic [1–3]. Besides, a thin-layered packet of parallel beds each of which is isotropic but properties of which differ from properties of the other beds within the packet behaves as a transversely isotropic medium at presence of deformations. Furthermore, transversely isotropic structures are normally used at production of composites. If fibers packed in parallel are used as a reinforcing agent, then the composite possesses a unidirectional structure and is treated as a transversely isotropic material in the planes normal to the direction of reinforcement [4]. Most often sheet metals are not isotropic and possess normal anisotropy (transversely isotropic). Ferroconcrete containing cracks is considered a transversely isotropic material with the plane of isotropy parallel to the plane of the crack [5]. Transversely isotropic structures also occur at production of laminated wood [6]. A number of works have been dedicated to studying processes of propagation of sound waves through anisotropic elastic layers. For example, in [7, 8], an elastic layer was considered as uniform and anisotropic whereas [9] dealt with the problem of propagation of the sound wave through a transversely isotropic nonuniform layer. A simpler case of the problem was considered by the authors of present paper earlier [10]. In the present work considered is the problem of diffraction of an elastic wave by a nonuniform transversely isotropic plate with constant elasticity characteristics along the axis of the layer and a continuous distribution of elasticity parameters in the section. Differential
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