Orthogonality Relations for the "End Problem" for Transversely Isotropic Cylinders
The differential equations governing the "end problem" in tranversely isotropic cylinders are rewritten as a pair of vector adjoint equations. An orthgonality relation is derived which simplifies the computation of the coefficients in eigenfunction expansions of solutions which decay with distance from the end. Admissible combinations of stress and displacement boundary conditions on the end of the cylinder may be prescribed provided that they lead to solutions which decay away from the end. Conditions which ensure decaying solutions are derived.