No abstract

No abstract

No abstract

No abstract

Reflection and transmission of acoustic waves through a planar inhomogeneous elastic layer was studied by Prikhod'ko and Tyutekin [1]. The elastic layer was assumed to be isotropic. The transmission of sound through an anisotropic layer was examined by Lonkevich [2] and Shenderov [3]. A homogeneous transversely isotropic elastic layer was considered in these papers. Skobel'tsyn and Tolokonnikov [4] considered transmission of acoustic waves through a transversely isotropic inhomogeneous elastic layer. In the present paper, the problem of transmission of a planar monochromatic acoustic wave through a planar inhomogeneous elastic layer whose material possesses general-type anisotropy is solved.1. We consider an anisotropic inhomogeneous planar layer of thickness 2h. The modulus of elasticity and the density of the material of this layer are described by continuous differentiable functions of the coordinate x3. The system of rectangular coordinates xl, x2, x3 is chosen so that the xl axis lies in the middle plane of the layer and the x3 axis is directed downward, normal to the layer surface. We assume that the upper and lower surfaces of the layer are interfaces with ideal homogeneous liquids with densities pl and p2 and speeds of sound cl and c2, respectively.Let a planar acoustic wave be incident onto an elastic layer from the half-space x3 < -h. The velocity potential in this wave iswhere kll = kl sin01 and kla = kl cos 01 are the projections of the wave vector kl onto the coordinate axes Xl and x3, respectively, kl = w/cl is the wavenumber in the upper half-space, w is the angular frequency, and 01 is the angle of incidence of the planar wave. In what follows, we omit the time factor exp (-iwt). We find the waves reflected from the layer and transmitted through the layer, and the displacement field inside the elastic layer.2. Propagation of elastic waves in an inhomogeneous anisotropic layer is described by the general equations of an elastic medium [5] Oo'ii i = 1, 2, 3, (2.1) piii = Oxj ' where p = p(x3) is the density of the material of the layer, ui is the projection of the displacement vector u onto the xi axis, and O'ij are the components of the stress tensor, which are related to the components of the