Enhanced stochastic, subharmonic, and ultraharmonic energy harvesting

Abstract

Nonlinear bistable systems have been shown to provide improved efficiency for harvesting energy from random and broadband vibration sources. This article explores the distinct frequency response in the broadened spectrum of a particular nonlinear energy harvester, a piezoelectric cantilever with magnetic coupling. The cantilever response evolves dynamically with frequency around the main cantilever resonance. Both stochastic and multifrequency vibration responses are observed and account for some of the improved efficiency. In addition, subharmonics and ultraharmonics of the main resonance, along with various combinations of these, appear. An analytical model of the bistable dynamics produces results consistent with those observed experimentally. Overall, four distinct types of efficiency improvements appear, in which the signal is amplified above the noncoupled cantilever response: (a) ultraharmonic amplification below resonance frequency, (b) stochastic amplifications in multifrequency and multiamplitude oscillations, (c) ultrasubharmonic amplification, and (d) subharmonic amplification. Taken together, the stochastic, subharmonic, and ultraharmonic responses produce an average of threefold to fivefold increase in voltage production.

Forced oscillations with linear and nonlinear damping

“…Forced oscillatory motion occurs in a broad variety of engineering applications, [1][2][3][4] and such a system can give rise to resonance, among other phenomena. Adding different kinds of damping forces to a forced oscillation provides an experimental realization to many real applications.…”

Non-Linear Energy Harvesting with Random Noise and Multiple Harmonics

“…The second part of this chapter provides an in-depth study of the response of a magnetically coupled cantilever at different frequencies [22][23]. It is our observation that amplification of the cantilever output occurs not only under stochastic motion but also due to subharmonic and ultraharmonic resonance in the vicinity of the main resonant frequency.…”

Piezoelectric bistable buckled beam energy harvester.

“…The experimental data is shown in the left image as compared to the theoretical prediction, shown in the right image. [12] As one can clearly see, the nonlinear system produces a significant response amplitude over a much wider (roughly 5 to 7 times) bandwidth than the linear cantilever case. Although this is a promising result, it should be noted that this specific device does not lie within the MEMS regime; the cantilever and proof mass have a combined mass of 3.2 g, while the cantilever itself is 4.4 cm in length.…”

“…FIGURE 5: Piezoelectric response voltage of the cantilever beam system described in [12] for the nonlinear case (with the opposing magnet, solid line) as opposed to the linear case (without the opposing magnet, dashed line). The experimental data is shown in the left image as compared to the theoretical prediction, shown in the right image.…”

“…A nonlinear harvester adapted from a simple cantilever beam which utilizies magnetic coupling to enhance response voltage amplitude over a larger bandwidth [12]. One such nonlinear adaptation to the cantilever beam harvester is illustrated inFigure 4; this design[12] utilizes magnetic repulsion between permanent magnets located at the end of the beam and directly across from the beam equilibrium point. This magnetic coupling, responsible for the system's nonlinearity, enhances the beam's response and sensitivity over a wider range of frequencies by increasing the amplitude of the beam deflection via the added repulsion.…”