The problem of small vibrations in an isotropic elastic continuum was studied, within the framework of a gauge approach, against the background of a static distortion that was due to a linear defect. The equations of motion for an isotropic elastic continuum with a topological defect were obtained using an approximation which was linear in the dynamic displacements. An analysis of the vibrational spectrum was presented for elastic materials with a screw dislocation, a wedge disclination and a disclination monopole. Known results of classical defect theory were reproduced in the case of a screw dislocation. Only minor changes in the spectrum were found to appear for a wedge disclination with a small non-integer Frank index. It was shown that the situation changed markedly for topologically stable disclinations. The character of the vibrations differed essentially from that for topologically unstable defects.

Vibrational Properties of an Elastic Continuum with Dislocations and Disclinations: a Gauge Approach. V.A.Osipov: Journal of Physics - Condensed Matter, 1995, 7[1], 89-99