VIBRATIONAL PROPERTIES OF AN ELASTIC CONTINUUM WITH DISLOCATIONS AND DISCLINATIONS - A GAUGE APPROACH

We study, in the framework of a gauge approach, the problem of small vibrations in an isotropic elastic continuum against the background of a static distortion due to a linear defect. In the approximation, which is linear in the dynamical displacements, the equations of motion for an isotropic elastic continuum with a topological defect are obtained. An analysis of the vibrational spectrum is presented for elastic materials with a screw dislocation, a wedge disclination and a disclination monopole. In the case of a screw dislocation the known results of classic defect theory are reproduced. For a wedge disclination, with a small non-integer Frank index, only minor changes of the spectrum are found to appear. It is shown that the situation is changed remarkably for topologically stable disclinations. In this case we deal with another topological sector, and the character of the vibrations differs essentially from that for topologically unstable defects.