On the Magnetic Field Effect in Electroconductive Plates Under Nonconservative Loading

This work investigates the behavior of an electroconductive plate under the action of a nonconservative load and subjected to a transversal magnetic field. The governing equation of the bending vibrations of an electroconductive plate, subjected to a transverse magnetic field and a follower type force at one edge, is presented. The assumption of an elongated plate leads to a simplified equation, which is conveniently written in dimensionless terms. For a cantilevered configuration, the characteristic equation relative to the magnetoelastic modes of vibration of the system is derived. Approximate solutions based on Galerkin method and an adjoint formulation are also presented and compared with the semi-analytical results. Root loci plots are computed as a function of the proper dimensionless parameters. The behavior of the system is very similar to the one exhibited by other structures subjected to nonconservative loads when damping is present. A relaxed definition of stability is used to regain continuity in the instability envelope.