This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Similar articles in Web of Science Alert me to new issues of the journal Add to Saved Citations Download to citation manager Request Permissions Request Reprints Add to My Marked Citations Citing Articles Citing Articles via Google Scholar Citing Articles via Scopus Google Scholar Articles by Dassios, G. Articles by Kathreptas, N. Search for Related Content Social Bookmarking                         What's this?

On the Low-Frequency Interaction Between a Central Dyadic Wave and a Spherical Cavity

Katerina Karveli

Department of Chemical Engineering, University of Patras and ICEHT/FORTH, Greece

Spilios E. Kattis

Department of Mechanical Engineering, University of Patras and ICEHT/FORTH, Greece

Nikolaos Kathreptas

Technological and Educational Institute of Patras, Greece

The dyadic fundamental solution of the linearized theory of elasticity in a homogeneous and isotropic medium is considered as a point-generated incident dyadic field. This central field is disturbed by a small spherical cavity within the medium of propagation. This two-center interaction problem provides a general dyadic scattering problem which includes the classical elasticity problems as a special case, obtained via contractions with specific directions. An analytic solution of the low-frequency approximations can be obtained via a generalization from the vector displacement field to a dyadic displacement field. Using this generalization the zerothand the first-order approximation of the near field are obtained explicitly In the far field the leading nonvanishing approximation for the radial and the tangential scattering amplitudes as well as that for the scattering cross-section are also evaluated. The analytic results obtained are then compared against relative results in classical elasticity obtained via the boundary element method and an amazing coincidence is observed when the radius of the sphere is small with respect to the wavelengh of the central incident field.

Key Words: dyadic scattering • low-frequency • point sources • traction free boundaries

Mathematics and Mechanics of Solids, Vol. 9, No. 2, 141-165 (2004)
DOI: 10.1177/1081286504033007


CiteULike    Complore    Connotea    Del.icio.us    Digg    Reddit    Technorati    Twitter    What's this?