Numerical Solution of the Problems of Magnetoelasticity of Plates

Abstract

When a conducting body moves in a magnetic field or when the magnetic field changes with time, induced currents and the ponderomotive Lorentz forces caused by them arise in the body, which, in turn, is accompanied by deformation of the medium and the appearance of stress waves. The motion of an elastic medium in a magnetic field is described by a joint system of equations of electrodynamics of a slowly moving medium and equations of the dynamic theory of elasticity, taking into account ponderomotive forces. This system of equations is non-linear due to the non-linearity of the relations of the generalized Ohm's law and expressions for ponderomotive forces. The work mathematically simulates the magnetoelastic vibrations of non-ferromagnetic annular plates under the influence of non-stationary electromagnetic forces and mechanical loads, taking into account electric currents. Numerical results are obtained and an analysis is made of the electromagnetic effects of the stress-strain state of non-ferromagnetic annular plates.