Dynamic Analysis of Vibration Reduction and Energy Harvesting Using a Composite Cantilever Beam with Galfenol and a Nonlinear Energy Sink

Abstract

This paper explores a new method for vibration control and energy harvesting by coupling a nonlinear energy sink (NES) with a cantilever beam containing giant magnetostrictive material. A mathematical model of the principal linear system under the action of an external harmonic force is established, and the dynamic equation of the system is derived using Newton’s second law, Hamilton’s principle, and nonlinear boundary conditions. The displacement responses of the system as functions of time and of frequency are obtained by using the Runge–Kutta method and harmonic balance method. The analytic results are found to be consistent with the numerical solution, confirming the accuracy and reliability of the calculated results. The frequency response and time response of the system with and without NES coupling, and with other parameters unchanged, were compared. The results show that the proposed structure can achieve excellent vibration suppression. The energy harvesting effect of the system as a function of time is also analyzed by the Runge–Kutta method, comparing results for different values of parameters such as NES mass, nonlinear spring stiffness, and damping coefficient. The results indicate that the proposed structure can achieve the desired effects of vibration reduction and energy harvesting, and that results can be optimized by adjusting the relevant parameters.