On the Nonlinear Dynamics of an Energy Harvesting Device Based on Magnetostriction

Abstract

In this paper, a magnetostrictive material (MSM)-based energy harvesting device is proposed. The device is made up of a steel beam laminated with Metglas 2605sc as the magnetostrictive material; the device undergoes mechanical strain due to the external base excitation. The mechanical strain yields in a magnetic field around the beam. A pickup coil is surrounded around the beam which converts the magnetic field into electrical current. The equation of motion is derived based on the nonlinear Euler-Bernoulli beam theory to account for large deflections. Kirchhoff and Faraday's laws are also benefited to couple the mechanical, magnetic and electrical fields. The equation is discretized based on the Galerkin method and numerically integrated over time. Energy conservation is examined and the response in the frequency domain is obtained. In the case of initial displacement, in the absence of mechanical damping, vibration amplitude attenuates as the electrical current induces in the pickup coil; this was attributed to the attenuation of the total mechanical energy of the beam as it was harvested from the pickup coil. The temporal response was fitted to that of a single degree of freedom mass-spring-damped and the equivalent damping ratio was determined. The attenuation rate was studied with different values of resistance and the number of turns in the pickup coil and the relation between these two factors was obtained to maximize the output electrical power.