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 1989|
Bibliographical noteFunding Information:
Acknowledgments I am grateful to Professor Y. H. Pao for suggesting the investigation of this problem, and for maintaining continued dialogue on the work that proved invaluable. I am indebted to Professor L. E. Payne for having taught me so much and for making helpful suggestions on this research. Finally I should like to thank Professors Rakesh, Paul Sacks, Bill Symes, and Dick Weinacht for useful conversations about this work. This work was supported in part by the Office of Naval Research under an SRO-III grant to Cornell University, and ONR contract N-000-14-85-K0725.