Nonlinear analysis of energy harvesting systems with fractional order physical properties

An electromechanical energy harvesting system with a fractional order current-voltage relationship for the electrical circuit and fractional power law in the restoring force of its mechanical part is considered to act as an energy harvester. Our results showthat, under a single-well potential configuration, for a small amplitude of the perturbation, as the order of derivative increases, the resonant amplitude of mechanical vibration decreases while the bending degree (hardening case) remains fairly constant. For a large amplitude of the perturbation, the output power is increased due to the hardening effects. Under a double-well configuration, the fractional power stiffness a strongly affects the crossing well dynamics (large amplitude motion) and consequently the output electrical power. The harvested electric power appears to be maximal for deterministic and random excitation for small a. High-level noise intensity is found to reduce the output power in the region of resonance and surprisingly increases the output in other regions of a. For sufficiently large amplitude of harmonic excitation, this effect is realized in a stochastic resonance.