On 2D Approximations for Magnetoelastic Non-Magnetizable Plates

Abstract

The coupled equations governing the out-of-plane vibrations of magnetoelastic plates of both finite and infinite conductivity are compared theoretically. The 2D non-iterative approximations due to the method of hypotheses corresponding to the classical Kirchhoff theory are recalled. The slightly modified simplest form of the plausible assumptions regarding the variation of the in-plane magnetic induction in the thickness direction is utilized for the case of real conduction. All the final equations are appropriately reduced in view of the "thinness" of the plate. Several further successive approximations involving the specific conductivity are introduced. An approach based on the simplified Ohm's law is also taken into account. The terms due to the transverse magnetic field are not found to be negligible in the equation of motion unless the specific conductivity is small enough.