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Stable Rotational Orbits of Base-Excited Pendula System

Abstract:

The dynamics of a harmonically base-excited two pendula system, is investigated for the practical application of energy harvesting from rotatory motions [1, 2]. The central aim of this study is to identify system parameter ranges for which pendulum rotations exist. The external harmonic excitation amplitude and frequency, and the difference in pendulums lengths are the system parameters which have been varied thresholds. Bifurcation analysis has been performed for the identification of values beyond which rotations exist, and the study of corresponding bifurcation points has been conducted with computational tool ABESPOL, developed at the Centre for Applied Dynamics Research (CADR) of the University of Aberdeen [3]. Direct simulations and one-parameter continuation analysis were performed with ABESPOL and some results were corroborated with direct numerical integration in Matlab, based on a Runge-Kutta algorithm. One parameter continuation results showed complex bifurcation scenarios for antiphase rotatory motions, presenting evidence of existence and form of representation. Further results showed that pendulum rotations, in phase and antiphase, co-exist with oscillatory motions. Therefore, the basins of attraction have been computed, enabling attractors to be targeted so as to enable antiphase rotatory motion.