Mechanical Response of Solid Cylindrical Conductors to Axial Electrical Currents

Abstract

An analytical investigation has been made of the behavior of long cylindrical conductors which are subjected to the thermal and magnetic stresses arising from the passage of axial, time‐dependent, electrical currents. The motion of the medium is assumed to be small, and it is also assumed that the electrical, mechanical, and thermodynamic properties of the medium are constant. Solutions have been obtained to the equations of linear thermoelasticity describing the radial motion induced by stresses of electromagnetic origin both for a medium of finite electrical conductivity and for the limiting case of a perfect conductor. The wavelengths of the axial waves produced by the radial motion are given as solutions of the Pochhammer‐Chree equation. Results of the calculations of the axial wavelengths for a Poisson's ratio of ⅓, corresponding to the value for copper and aluminum, are presented.