We realise magnetic levitation utilizing two static magnets to suspend a middle floating magnet. The latter is free to oscillate in the proximity of a coil of inductive wire. Vibrations of the housing structure are essentially translated to response vibrations of the middle magnet that are inducing voltage to the coil.

**Figure 13. Oscillating magnet suspended by magnetic levitation**

From a dynamics point of view, the master concept is equivalent to a magnetic mass suspended from a linear and a cubic spring. The second elastic component introduces broadness to the frequency response of the oscillator. We position the master concept on a rotating disc, with the main axis extending radially from the disc’s centre of rotation.

**Figure 14. Concept implementing magnetic levitation nonlinearity for harvesting torsional vibration energy**

The devised rotational concept exhibits a rich dynamical behaviour, which promises significant potential for broadband vibration energy harvesting in rotor applications. In particular, the oscillator possesses two main regions regarding its stability properties: for low speeds (blue shaded region) it behaves as a regular mono-stable nonlinear oscillator, whereas higher rotating speeds (orange shading) lead to bi-stable vibrations due to the action of the centrifugal force. The combined response effectively introduces multiple resonant zones over separate frequency domains.

**Figure 15. Velocity response of the harvester to increasing frequency ramp with 2 ^{nd} shaft order vibrations**

Further to the stability properties, the system experiences a combination of direct forcing (blue region) and parametric forcing (orange region). The first corresponds to base excitation applied directly onto the magnetic mass, giving rise to the first two peaks of the frequency response (blue shading). The second leads to periodic variations of the system’s stiffness that are responsible for the high frequency peaks (orange shading). These multifaceted response properties are superimposed to each other, effectively leading to broadband energy harvesting.

**Figure 16: Average power delivered to a common electrical load**