Homogeneity of magnetic field influence on buckling of three layer polyethylene plate

The paper describes buckling of rectangular plate made of polyethylene. The plate is built of three layers. External faces are solid and the core is porous. The plate is described with broken line hypothesis. On the two opposite ends of the plate are pockets with porous structure as well. Each pocket is filled in with ferrofluid. Magnetic field is generated by coils systems and acts on ferrofluid in pockets. System of magnetic field coils consists of two subsystems. First of the subsystems is a Helmholtz coil, which has high homogeneity of magnetic field. The bigger radius of Helmholtz coil, the bigger volume of homogeneous magnetic field. The second subsystem is Golay coil, that generate transverse gradient magnetic field. Homogeneity of gradient magnetic field for Golay coil is much worse that for Helmholtz coil. Such systems of coils generate magnetic field changing in space. Changing dimensions of coils the homogeneity of magnetic field is changing as well. It causes that induced force in the pockets is also changed. In the paper critical states are obtained for static load and equation of motion are solved for equilibrium paths for example plates.