Dynamic stability of conducting beam-plates in transverse magnetic fields

The dynamic stability of electrically conducting beam-plates in transverse magnetic fields is considered in this paper. A concise theory of flexural vibration of magnetoelastic plates immersed in transverse magnetic fields is presented first. The dynamic stability of a beam-plate is then examined without making a priori assumptions about its magnetic property. In contrast to the writer's earlier work, where a beam plate is subjected to an external axial load in the presence of a longitudinal magnetic field, an axial force arises naturally from the magnetoelastic interaction in the form of surface traction. The magnetic damping due to the induced eddy current is also included in the analysis. Two nondimensional parameters are introduced and the stability of a simply supported beam-plate is examined as a function of these parameters. It is shown that three stability regions exist. Critical fields are obtained explicitly and discussed in some detail.