Dynamic Design of a Quad-Stable Piezoelectric Energy Harvester via Bifurcation Theory

Abstract

The parameter tuning of a multi-stable energy harvester is crucial to enhancing harvesting efficiency. In this paper, the bifurcation theory is applied to quantitatively reveal the effects of structural parameters on the statics and dynamics of a quad-stable energy harvester (QEH). Firstly, a novel QEH system utilizing the geometric nonlinearity of springs is proposed. Static bifurcation analysis is carried out to design quad-stable working conditions. To investigate the cross-well and high-energy vibration, the complex dynamic frequency (CDF) method, suitable for both weakly and strongly nonlinear dynamic problems, is then applied to deduce the primary response solution. By using the unfolding analysis in singularity theory, four steady-state properties and dozens of primary resonance modes are demonstrated. Based on the transition set, the effective bandwidth for energy harvesting can be customized to adapt well to various vibration environments by parametric adjustment. Finally, the experimental tests verify that the output power can reach up to 1 mW. The proposed QEH and its mechanics optimization can guide energy supply for next-generation wireless systems and low-power sensors under magnetic forbidding environments.

A Circuit Theory Perspective on the Modeling and Analysis of Vibration Energy Harvesting Systems: A Review

“…The idea to exploit multi-stability was further developed and generalized, introducing tri-stable [77][78][79] and, more generally, multi-stable energy harvesters [80][81][82][83][84][85]. In [77] it was shown that a tri-stable arrangement passes easily through potential wells, generating higher energy output over a wider range of frequency with respect to a bi-stable setup with a deeper potential well.…”

“…It was shown that such a solution not only reduced the potential energy barrier and the threshold of snapthrough, but also broadened the bandwidth of inter-well motion. In [80], an ingenious setup, where the inertial mass on the top of a cantilever beam is connected to a support through three springs, was proposed. The resulting structure exhibits four steady state responses and dozens of primary resonance modes.…”

Comparisons for Global Dynamics of a Geometrically Nonlinear Oscillator among Single-, Double- and Quadruple-Well Configurations

“…For VEHs, the geometric configuration of linear springs in the oscillators can be effective in broadening the frequency band of the resonance, thereby showing effective qualities in improving the performance of VEHs [8][9][10]. The most commonly used oscillator is the smooth and discontinuous (SD) oscillator [11,12]. It consists of a lumped mass and a pair of symmetrically inclined springs, as can be seen in the primary structure of the VEH in Figure 1a.…”