Dynamic stability of a cantilever conductive plate in transverse impulsive magnetic field

When a conductive plate is in an applied impulsive magnetic field, it will be subjected to a kind of electromagnetic forces arising from an interaction between the eddy current induced in the plate and the magnetic fields included the applied one and one induced by the eddy current in the plate. Some in-plane components of the electromagnetic force exerted on the plate are usually neglected in existing researches on some mechanical behavior, such as bending and vibrating, of the plate. In this paper, a cantilever conductive thin plate in an applied transverse impulsive magnetic field is taken as an example, in which there only exist in-plane components of the electromagnetic force, to show the effect of these components on bending and vibrating of the plate. The numerical results demonstrate that the plate will be dynamic instability for some kinds of applied transverse impulsive magnetic field. The critical values B0cr of applied magnetic field are searched out. The effects of the conductivity r and the length–thickness ratio a/h of the plate as well as the impulse parameter s of applied impulsive magnetic field on the critical value B0cr of applied magnetic field are also discussed in detail.