Numerical Investigation of a Reluctance Force Shunt Damping System

In this chapter, an electromagnetic energy transducer for vibration damping is investigated. The device consists of a magnetic circuit, a flux linking coil, and a variable air gap between a fixed horseshoe type magnet with a moving magnetic core. Due to the magnetic effect caused by the reluctance forces in the air gap, the horseshoe magnet and its counterpart attract each other. The corresponding force–displacement behavior is strongly nonlinear and can be characterized as negative stiffness. We now introduce passive shunts of the coil to create a phase shift in the reluctance force dynamics. This way, the resulting hysteresis between reluctance force and air gap causes damping of an oscillating motion of the moving magnetic core. The nonlinear state equation is solved by applying the harmonic balance method to obtain the magnetic flux for a given harmonic input signal. For harmonic air gap oscillation, resistive as well as resonant shunts are considered at different frequencies. In contrast to a simple energy dissipation, the resonant shunt leads to an amplification of the damping effect as the electric circuit is capable of vibration itself. Furthermore, additional resonance effects can occur if the oscillation frequency is close to, for example, half or one-third of the electrical resonance frequency. This is due to the strong nonlinear characteristic of the system activating the electric resonance with the oscillation’s higher harmonics.