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

Abstract

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.

Nonlinear Dynamic Response of Galfenol Cantilever Energy Harvester Considering Geometric Nonlinear with a Nonlinear Energy Sink

“…The magnetostrictive vibration energy harvester has attracted growing attention thanks to its peculiar properties. For instance, high magnetostriction, high permeability, small brittleness, high tensile strength, and a wide working temperature range are reported in the previous works [2,15]. Through the inverse effect (Virari effect) of magnetostrictive materials, including Terfenol-D and Galfenol material, the vibration energy can be effectively transferred into electric energy by the magnetostrictive vibration energy harvester [16][17][18].…”

“…Assuming that the stress and strain of the structural layer follow Hooke's law and the stress-strain of the Galfenol layer follows a linear constitutive equation [15], the potential energy V of the coupling system can be given by…”

“…is the moment due to the electrical effect [15]. It should be pointed out that in the derivation of M ele , the magnetic field in the Galfenol layer is presumed to be uniformly distributed along the axial and lateral directions of the cantilever structure.…”

“…The motion characteristics and the induction voltage of the Galfenol device were analyzed by theoretical derivation analysis, the ANSYS Workbench, as well as experimental tests. Wang et al [15] established the electromechanically coupled model of the Galfenol-based cantilever energy harvester. In their work, the explicit analytical formulations of the output performances for the proposed energy harvesting model were obtained by the Galerkin decomposition method and electro-mechanical decoupling method.…”

“…In our previous work, the research focus was more on introducing geometric nonlinearity into piezoelectric energy harvesters [51][52][53][54]. In 2023, based on Galfenol materials, we proposed a magneto-electric energy harvester without taking into account the cantilever structure's geometric nonlinearity [15]. To the best of the authors' knowledge, there have been no reports on the simultaneous introduction of NES and geometric nonlinearity into the Galfenol energy harvester.…”