ELASTIC VIBRATIONS OF SOLIDS CONTAINING D ISCLINATIONS

The method commonly used in elastic continuum mechanics to describe lo w-amplitude waves in non-uniformly strained medium is generalized to a n elastic isotropic medium containing Volterra disclinations for which distortion is a non-unique function of the spatial coordinates. The M urnagan law of slate is used to find the equation of elastic energy de nsity and obtain dynamic equations describing small vibrations of the medium strained with elastic disclination fields. The particular probl em of normal vibrations of an extended cylinder with a wedge disclinat ion whose line is along the cylinder axis is studied. The disclination effect on the family of axis-symmetrical torsional oscillation modes of the cylinder is studied thoroughly. A theory of small-parameter (di mensionless disclination strength) perturbation has been developed and used to find analytical expressions for the law of dispersion and osc illatory states.