Diamagnetic levitation for nonlinear vibration energy harvesting: Theoretical modeling and analysis

This paper provides theoretical modeling and analysis of applying diamagnetic levitation for nonlinear vibration energy harvesting in detail by first identifying potential merits as well as limitations. Based on a magnetic dipole model, analytical analysis is conducted by providing simplified analytical expressions of restoring forces and electromagnetic damping which are then transformed into a hardening spring model and results in a Duffing equation with strong nonlinearity. In addition, constraints on physical geometry are discussed and derived in the view of practical energy harvester design. More importantly, the derivation and discussion extended to multi-well potential suggest that diamagnetic levitation may enable designing an energy harvester that subject to cross-well chaos with a compact volume and wideband responses. Without mechanical damping in any form, diamagnetic levitation may be considered as a promising mechanism for developing vibration energy harvesters with great performance, and the paper provides a technology push on the possibility.