Bending of a Thin Plate Subjected to Strong Uniform Magnetic Field

Abstract

The problem of an elastic plate, originally unmagnetized, in a uniform magnetic field is considered in the paper. The magnetic forces are of two kinds: the force of the magnetic field on conducting currents in the material, induced by its motion in the static field and the force between the magnetic field and the magnetized material (independent of the motion).The general equations are linearized by assuming linear constitutive equations and that all electromagnetic variables in the deformed body may be divided into two parts: a rigid body state and a perturbation state. Maxwell’s stress is calculated and involved in differential equation related to bending. Obtained equation is solved in analytical form using the integral-transformation technique (Double Fourier finite-sine transformation and Laplace transformation). Discussion of the obtained solution is done using Kirchhoff’s hypothesis.