Energy harvesting in the super-harmonic frequency region of a twin-well oscillator

Nonlinear dynamical systems exhibit super-harmonic resonances that can activate large-amplitude motions at fraction integers of the fundamental frequency of the system. Such resonances offer a unique and untapped opportunity for harnessing vibratory energy from excitation sources with low-frequency components. To that end, this paper exploits the super-harmonic frequency bands of a nonlinear twin-well (bi-stable) oscillator for harvesting energy from low-frequency excitations. Theoretical and experimental studies are performed on an axially loaded clamped-clamped piezoelectric beam harvester with bi-stable potential characteristics. Voltage- and power-frequency bifurcation maps are generated near the super-harmonic resonance of order two. It is shown that, for certain base acceleration levels, the harvester can exhibit responses that are favorable for energy harvesting. These include a unique branch of large-orbit periodic inter-well oscillations, coexisting branches of large-orbit solutions, and a bandwidth of frequencies where a unique chaotic attractor exists. In these frequency regions, the harvester can produce power levels at half its fundamental frequency that are comparable to those obtained near the fundamental frequency. (C) 2012 American Institute of Physics. [doi: 10.1063/1.3684579]