A HORIZONTAL ELASTIC CYLINDRICAL INCLUSION
M. G. Seleznev, T.N. Selezneva · 1984
We present a method for the rigorous analysis of wave fields excited in an elastic halfspace containing a horizontal elastic cylindrical inclusion by a distributed harmonic surface load. For simplicity we illustrate the application of the method by investigating a model problem of antiplane oscillations of the composite elastic medium. We derive asymptotic representations of the solutions when the inclusion is rigidly bonded, which permit a rather simple analysis of the wave field in the medium. The proposed method can be applied without changes to similar problems in two and three dimensions. In doing this only the awkwardness of the derived relations is increased significantly. 1. We consider steady-state antiplane oscillations of an elastic half-space X>~0 with a density p and a shear modulus ~, containing an elastic cylindrical inclusion with a shear modulus DI and a density Pl in the region R = /(X -- h) = + YZ-~a (a < h). The inclusion is rigidly bonded to the half-space. Shear oscillations are oriented along the generatrix of the cylinder (parallel to the Z axis). The motion of the medium is described by the elasticity theory dynamical equations in displacements (the Lam~ equations), which for antiplane oscillations have the form [I] ~AW(X, Y, t) = p~2W(X, Y, t)/~t 2, where W(X, Y, t) is the displacement of a point of the medium along the Z axis, and A = ~2/~X2 + ~2/~y2 is the Laplacian operator. We seek the solution of the latter equation for steady-state oscillations in the form W(X, Y, t) = w(x, y) exp (--i~t). In this case the equation for the amplitude of the displacement takes the form