Broadband and Low Frequency Vibration-based Energy Harvesting Improvement through Magnetically Induced Frequency Up- Conversion

In order to extract as much energy as possible from ambient vibrations, many vibration-based energy harvesters (VEHs) are designed to resonate at a specific base excitation frequency. Unfortunately, many vibration energy sources are low frequency (0.5 Hz-100 Hz), intermittent, and broadband. Thus, resonant VEHs would not be excited continuously and would require a large mass or size to tune to such a low frequency. This work presents the modeling, analysis, and experimental application of a nonlinear, magnetically excited energy harvester that exhibits efficient broadband, frequencyindependent performance. This design utilizes a passive auxiliary structure that remains stationary relative to the base motion of the VEH. This device is especially effective for driving frequencies well below its fundamental frequency, thus enabling a more compact design compared to traditional resonant topologies. A mechanical model based on EulerBernoulli beam theory is coupled to a linear circuit and a model of the nonlinear, magnetic interaction to produce a distributed parameter magneto-electromechanical system. The results of both harmonic and broadband, stochastic simulations demonstrate multiple-order-of-magnitude power harvesting performance improvement at low driving frequencies and an insensitivity to time-varying base excitation frequency content. Furthermore, the proposed system is shown to enable more practical designs than a resonant energy harvester for the specific example of harvesting energy from walking motion. INTRODUCTION In the last decade, vibration-based energy harvesting has received significant attention due to the ubiquity of untapped vibrational energy available in or around most manmade systems [1]. In order to maximize harvested power, vibrationbased generators are designed to match one of their natural frequencies – typically the fundamental frequency – to the base excitation frequency. Additionally, it has been shown that minimizing the mechanical damping in the system enhances the power harvesting performance [2–4]. Unfortunately, lightly damped systems, while exhibiting the greatest peak power, also have the least bandwidth. In many applications for which energy harvesting could be utilized, vibrations are intermittent, time-varying, and stochastic, rendering standard energy harvester designs ineffective. Indeed, Halvorsen [5] has shown large qualitative differences in the behavior of vibration-based energy harvesters under stochastic excitation. Hence, a means of making these devices less constrained to a single operating regime is desirable. If a single magnet is placed in the vicinity of the magnetized tip mass of the beam, a “hardening spring” effect can occur. This effect can increase the mechanical response of the beam over a wider range of excitation frequencies; however, this setup suffers from hysteresis and can perform worse than the baseline system if it is operating in the non-resonant branch of the response [6]. Lin et al. [7] place a magnet in the vicinity of the tip and note an increase in voltage generated in a wider bandwidth around the resonant peak compared to the baseline system. This phenomenon is magnified when the nearby magnet is attached to the end of another cantilevered beam; however, no energy is harvested from the secondary beam in that study, thereby reducing the power density of the device. Nonlinear stiffness can also be created structurally, as in [8], in which the tip mass of the beam is attached to a prebuckled plate. This auxiliary structure produces greater damping at high base excitation amplitudes, which may be considered a safety feature to prevent excessive strain in the device. In this paper, a design consisting of a permanent magnet attached to the tip of a cantilevered, piezoelectric beam structure is presented. As the beam vibrates due to base excitation, the tip passes through the wells of attraction of Proceedings of the ASME 2010 Conference on Smart Materials, Adaptive Structures and Intelligent Systems SMASIS2010 September 28 October 1, 2010, Philadelphia, Pennsylvania, USA