The propagation of waves in an elastic half-space containing a cylindrical cavity

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Abstract
The problem of the propagation of time harmonic waves in an isotropic elastic half-space containing a submerged cylindrical cavity is solved analytically. Linear plane strain conditions are assumed. Using an expansion theorem proved in a previous paper (Gregory (3)), the elastic potentials are expanded in a series form which automatically satisfies the governing equations, the conditions of zero stress on the flat surface, and the radiation conditions at infinity. The conditions of prescribed normal and tangential stresses on the cavity walls are shown to lead to an infinite system of equations for the expansion coefficients. This system of equations is shown to be a regular L2-system of the second kind and from its unique l2-solution, the solution to the problem is constructed. The fundamental questions of existence and uniqueness are fully treated and methods are described for constructing the solution.Three applications of the general theory are presented dealing respectively with the production, amplification and reflexion of Rayleigh waves.

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