Analytical solution and optimal design for the output performance of Galfenol cantilever energy harvester considering electromechanical coupling effect.

The theoretical model of a Galfenol cantilever energy harvester is investigated for vibration energy harvesting. Compared with the numerical solution, the analytical solution can better capture the intrinsic effects of the physical parameters on the performance of the harvester. In this work, an electromechanical coupled distributed-parameter model of the Galfenol cantilever energy harvester is established based on Hamilton's principle, linear constitutive equations of magnetostrictive material, and Faraday's law of electromagnetic induction. The definitions and expressions of the electric damping and modified frequency are proposed due to the electromechanical coupling. The explicit analytical expressions of the average harvested power across the load resistance and tip vibration displacement of the Galfenol energy harvesting model are derived using the methods of Galliakin decomposition and electromechanical decoupling. The accuracy of the derived analytical results is verified by the experimental data and numerical solutions. The vibration response and energy harvesting performance of the Galfenol energy harvesting model are investigated by varying the excitation frequency, external resistance, and excitation acceleration amplitude. The analytical results show that, with the increase of the external load resistance and excitation frequency, the harvested power increases first and then decreases, indicating the existence of the optimal resistance and excitation frequency. From the explicit analytical expressions of the average harvested power, the optimal external load resistance or excitation frequency could be easily found to achieve the maximum harvested power for any fixed excitation frequency or external load resistance. The concept of proposing the electric damping and modified frequency for the Galfenol cantilever energy harvester simplifies the solution process for the output performances benefiting from the exact relationship between the output performances and the electromechanical coupling parameter derived in this work.