Computation of the Motion of Conducting Bodies Using the Eddy-Current Integral Equation *

The analysis of the motion of a system of solid conductors in the presence of magnetic fields is performed by solving the classical mechanics equation of motion under the action of magnetic forces. Application of the eddy-current integral equation and the usage of the local coordinates attached to the bodies in motion allow the determination of electromagnetic field without being necessary to reconstruct the discretization grid at each new position of the conducting bodies. Only the submatrices associated with the coupling between the bodies in relative motion are modified in the global system matrix. A time-domain method of solution is first presented for the .electromagnetic field problem, coupled with the equation of motion, which can be efficiently applied at high frequencies when the time steps are small. The eddy-current integral equation for the derivative of current density contains a term that takes into account the relative motion of the bodies. Since the electromagnetic quantities vary much more rapidly than the mechanical quantities, a second method is also proposed in this paper, where the eddy-current integral equation is solved in the frequency domain by assuming that the bodies are motionless, but by adding supplementary terms due to the actual motion of the bodies. Thus, only the average force over a period of time is now computed. This method is extremely efficient especially at higher frequencies when the time steps are very small.