ELASTIC WAVE SCATTERING ON A SYSTEM OF ROD-LIKE INCLUSIONS

Scattering of elastic wave on two collinear cylindrical inclusions is considered. Analysis is restricted by the case of normal incidence. Inclusions are thin; the aspect ratio is small. The length of the incident wave is comparable with the length of inclusion, and the distance between them. Inclusions and the surrounding medium are homogeneous, isotropic, and linearly elastic. They differ only in the mass density. Direct numerical analysis (such as FEM, BEM, FDM, etc.) of scattering on thin deformable inclusions is connected with the principal difficulty caused by degeneration of the domain occupied by inclusions into a set of segments. A two-dimensional (2-D) approach, where the length is assumed to be infinite, is inefficient at low frequencies. An engineering approach based on beam theory equations (for inclusions) would lead to considerable errors. An original asymptotic approach is proposed. The integral equation of stationary motion of an inhomogeneous elastic medium is derived and then asymptotically simplified. The original 3-D dynamic problem is decomposed to the combination of two problems of reduced dimension. The first one is governed by the integral equation over the mid-line contour. The second one is a 2-D quasi-static problem for the cross-section of inclusion. In such a way the separation of variables is made. The averaged (over the cross-section) displacement of inclusions is calculated numerically. Results obtained are compared with the corresponding ones for the single inclusion. Displacement and stress fields inside inclusions are to be determined through solving a quasi-static 3-D (2-D at the points of middle region of the inclusion) problem.