An Influence of Homogeneity of Magnetic Field on Stability of a Rectangular Plate

Abstract

The main objective of presented work is a rectangular plate subjected to dynamic in-plane load generated by magnetic field. The plate is made of polyethylene (PE). There are two pockets on each of the two opposite edges of the plate. These pockets with porous structure are filled in with ferrofluid. The coil system consists of two magnetic field coil subsystems. These systems are built of Helmholtz (MC) and Golay coils (GC) and generate nonhomogeneous magnetic field. If the magnetic field is more homogeneous, the compression load is induced. In other cases, local tensile load occurs (compression load dominates). For presented coil systems, the intensity of load was examined for two variants. For the first of them, the intensity of load was dependent on the radius of Golay coil arcs. The change of the radius of saddle coils also influences on the strength of the gradient of the magnetic field. The second one describes the intensity of load which depends on the change of GC radius without changing the strength of magnetic field (the strength of magnetic field is compensated with changing the current flowing through the coils wires or with changing the number of wires). In this paper, the analytical model of the plate is presented. The model of the plate was formulated with the use of classical Kirchhoff–Love hypothesis. Elastic strain energy, kinetic energy as well as work of load were formulated. The equation of motion was derived based on the Hamilton’s principle. The numerical studies were related to the analysis of the intensity of load distribution.