The paper presents a theoretical model of a passive magnetic suspension based on rare-earth permanent magnets; the aim is to minimize the dependence of the natural frequency of a single degree of freedom system on mass.
In order to estimate magnetic interactions, the gradient of magnetic induction is evaluated by using a magnetic model based on the analogy of the equivalent currents method in a quasi-static open-circuit-type configuration. Therefore magneto-elastic forces between permanent magnets can be determined and compared with empirical formulas, applied in practical uses, and with experimental static tests.
For a single degree of freedom system with variable mass, static configuration and dynamic behavior are evaluated for classic linear elastic systems, for purely magnetic suspensions and for a combination of the two.
In particular the dynamics of the magneto-mechanic interaction by use of nonlinear and linearized models are investigated for non-zero initial conditions, in order to underline the influences of nonlinearities on the system response.
Finally, the single degree of freedom system frequency response is presented for different values of the geometrical and inertial properties of the system, thus demonstrating the insensibility of resonance with respect to mass.
The paper presents a comparison between the theoretical dynamic model of systems made of structures of paramagnetic or diamagnetic conductible materials interacting with rare-earth passive magnetic elements and the relative experimental outcomes. The magnetic effects are characterized by a viscous-type damping, and by an interesting dynamic effect of stiffening of the structure called phantom effect, modeled adding an imaginary term in the damping coefficient of a single degree of freedom system. The theoretical model finds a proper application in case of a uniform cantilever clamped-free beam of different kinds of paramagnetic or diamagnetic conductible materials, whose frequency response is modified by the presence of a pair of concordant or discordant magnets settled at the free end. Through the comparison between theoretical and experimental results, the paper demonstrates the validity of the model; besides, the model points out the above mentioned effect of dynamic stiffening of the structure and, finally, the considerable localized damping properties in paramagnetic or diamagnetic materials with low electric resistivity, when interacting with permanent magnets of high residual induction.
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