Abstract
The elastodynamics of a halfspace with a cylindrical hole belongs to a class of problems which involve solving the elastic wave equation in a geometry that is bounded by nonparallel surfaces. Integral transform techniques are not very suitable for the solution of such problems because the transform approach yields solutions in terms of wavefronts (or rays). For a nonparallel geometry one may need a large collection of such terms and this may be an inconvenient description. So, we have taken an approach to construct the eigenmodes (normal modes) for this geometry for a given set of boundary conditions. A set of linearly independent solutions, without any reference to sources or receivers, is developed and completeness of this set is verified explicitly. Using this complete set of eigenmodes the displacement field for any source problem in this geometry can be expressed following standard mathematical procedures.
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