Analysis of the Motion of Conducting Sheets in Magnetic Fields

Solution of the equation of motion for conductors in external magnetic fields requires the knowledge of the magnetic forces due to the induced eddy currents that, in turn, can be determined if the position and the velocity of the bodies are known. An iterative technique is adopted, where, at each time step, an initial value of the magnetic force is used to determine the position and the velocity of the body at the end of the time step and, then, the value of the force is corrected. To reduce the computational effort in the case of thin metallic sheets, it is proposed to use the surface integral equation of the induced eddy currents, with a supplementary term added to account for the motion. A sinusoidal with time variation of the excitation field is considered and a phasor representation of various physical quantities is employed. An average magnetic force over each period is used to solve the equation of motion.