Electromagnetically conducting elastic plates in a magnetic field: modeling and dynamic implications

The basic field equations and boundary conditions necessary for the dynamic approach of electromagnetically conducting flat plates subjected to an external magnetic field are derived.Whereas the structural equations include the geometrical non-linearities of elastic isotropic plates, the electromagnetic equations are used in a linearized form that is obtained from their non-linear counterpart by applying the small disturbance concept. In this context, it was shown that the governing equations involve the bending-stretching coupling arising from both the geometrical non-linear approach of the problem and the inclusion of the Lorentz ponderomotive forces that are reduced to a 2-D plate counterpart.A number of special cases are considered, implications of the external magnetic field on non-linear/linear eigenfrequencies are highlighted, and pertinent conclusions are outlined.