An experimental validation of complex damping and fractional derivative models on vibrating structures under magnetic effects

The paper presents a comparison between dynamic models with complex viscous-type damping coefficients and dynamic models with fractional derivative damping terms in order to describe the behaviour of vibrating paramagnetic or diamagnetic conductible structures interacting with rare-earth permanent magnets. A complex viscous damping model is derived from a magnetic theoretical model, which predicts both a viscous damping effect and an interesting dynamic stiffening due to eddy currents. The complex viscous damping model is then compared and related to a fractional derivative model, suitable to extend the analysis in transients. Finally, theoretical and experimental results are compared for a uniform cantilever clamped-free beam, whose frequency response is modified by the presence of a pair of discordant magnets settled at the free end