Transversal vibrations of elastic rod in magnetic field under simultaneous kinematic and force action

Abstract

A model problem of transversal vibrations of an elastic conducting rod in the magnetic field is studied. Vibrations in the rod are excited due to kinematic and force factors. A partial differential equation of motion containing the integral term for the electromagnetic force was constructed. After applying the Fourier procedure, the problem is reduced to a set of ODEs. The condition for passive stabilization of the main vibrational mode’s amplitude is derived. A method of active electromagnetic suppression of certain vibrational modes is proposed.