Oscillatory Motion of Permanent Magnets Above a Conducting Slab

This paper provides the 3-D time-dependent analytical solution of the electromagnetic fields and forces emerging if a coil or a permanent magnet moves with a sinusoidal velocity profile relative to a conducting slab of finite thickness. The results can be readily used in application scenarios related to electromagnetic damping, eddy current braking, energy harvesting, or nondestructive testing in order to efficiently analyze diffusion and advection processes in case of harmonic motion. This paper is performed for rectangular and circular coils as well as for cuboidal and cylindrical permanent magnets. The back reaction of the conductor and therewith associated inductive effects are considered. The solutions of the governing equations and the integral expressions for the time-dependent drag and lift force are provided. The analytical results are verified by a comparison with numerical simulations obtained by the finite-element method. The relative difference between the analytically and numerically evaluated force profiles was <;0.1%. Exemplary calculations show that the waveforms of both force components strongly depend on the level of constant nominal velocity $v_{0}$ , the magnitude of the velocity oscillation amplitude $v_{1}$ , and the underlying oscillation frequency $f_{v}$ .