Investigating threshold escape behavior for the gimballed horizontal pendulum system

Abstract

This paper examines a gimballed horizontal pendulum for use as an energy harvester. It can be designed for threshold escape behavior rather than the conventional method of matching frequencies. A nonlinear electromechanical model is developed to study the system's equilibrium states as a function of tilt angle. Bifurcation diagrams and basins of attraction are generated to illustrate these equilibria and their associated stability. A static bifurcation point is solved for analytically and the implications for an energy harvester, one that can be designed to jump across stable attractors based on forcing amplitudes, are discussed. Amplitude sweeps are conducted showing a dynamic bifurcation point that varies as a function of frequency and effective damping. Experiments are run to validate computational results and the applications for energy harvesters are discussed.