Passive effects of rare-earth permanent magnets on flexible conductive structures

The paper presents a theoretical and experimental study of vibrating structures where paramagnetic or diamagnetic sys- tems interact with rare-earth passive magnets. The theoretical model of the system is focused on the damping properties of permanent magnets and on their interac- tions with the dynamic behaviour of an Euler–Bernoulli beam. In particular, the magnetic model is based on the analogy of the equivalent currents method in a quasi-static open-circuit-type configuration and it is used to determine the influence of eddy currents on the dynamic behaviour of conducting material structures. The magnetic effects are characterised by a vis- cous-type damping and by a stiffening dynamic effect of the structure, called ‘‘phantom effect’’. The authors present the experimental outcomes for uniform cantilever clamped-free beams of different kinds of para- magnetic or diamagnetic conducting materials. It appears that the system frequency response can be modified by the pres- ence of a pair of concordant or discordant permanent magnets of high residual induction settled at the free end. Through the comparison between theoretical and experimental results, the paper demonstrates the validity of the model, that is able to describe both the above mentioned effect of dynamic stiffening of the structure and the considerable localised damping properties in paramagnetic or diamagnetic materials having low electric resistivity.