Torsional Magnetoelastic Waves in a Circular Cylinder

Abstract

In this paper the effect of an electromagnetic field on the propagation of a pure torsional elastic wave in a conducting circular cylinder is investigated. The general field equations and boundary conditions are linearized and the equations of motion for an infinitely long circular rod are obtained for the particular electromagnetic field configurations considered. The torsional motion of a solid rod in a steady axial magnetic field with and without a steady electric field is considered. In the first case it is found that a pure torsional mode will not propagate. In the second case a pure torsional mode will propagate and its frequency equation is obtained. The results for a perfect conductor are compared to a real material. The torsional motion of a hollow rod in a steady tangential magnetic field with and without a steady axial electric field is considered. Without the electric field the equations are completely uncoupled and the solution is the standard elastic one. The electric field introduces coupling via the induced magnetic field. The equations of motion are obtained, however the actual solutions are not obtained due to the mathematical complexity involved.