RADIAL EIGENFUNCTIONS FOR THE ELASTIC CIRCULAR CYLINDER

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Abstract
Boundary-value problems for semi-infinite circular cylindrical bodies are treated via eigenfunction expansions. An orthogonality relation is derived between two sets of three-dimensional vector eigenfunctions associated with any admissible homogeneous boundary conditions on the curved surfaces of the hollow cylinder. These eigenfunctions satisfy adjoint differential equations which are derived from the Navier equations for displacements. All admissible combinations of stress and displacement boundary conditions on the flat end of the cylinder may be prescribed with full generality, provided they are such as to induce a solution that decays away from the end. Conditions which ensure decaying solutions are easily found from the analysis and are explicitly derived for all the axisymmetric problems. It is required that non-axisymmetric boundary conditions should admit a Fourier series expansion in the angular coordinate.

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