We consider the initial-boundary-value problem for an infinite linearly elastic cylinder. Of interest are the question of solvability and the issue of constructing approximate solutions. Because the body is infinite in extent, standard existence theorems for linear elasticity cannot be applied unless additional assumptions are made. We begin by constructing the solution formally. We look at the Fourier-transformed displacements in eigenfunction expansions. Existence of the eigenfunctions is established after a Korn-type inequality is derived. It is then shown that the inverse Fourier transform, which returns the transformed displacements to physical displacements, is convergent under appropriate hypotheses. We end with a discussion on the use of this formal solution method in finding the approximate transient response of infinite cylinders to body-force excitations, and in particular, to point excitations.
|Original language||English (US)|
|Number of pages||23|
|Journal||Quarterly Journal of Mechanics and Applied Mathematics|
|State||Published - Aug 1 1989|