Abstract
Abstract In this paper a mathematical model was found, and numerical results obtained for the pendulum behavior when coupled to a DC generator. A simple pendulum is vertically excited on its support and consequently exhibiting oscillations and rotations. The motion of the pendulum spins the axis of a DC generator and inducing a current. The dynamic model involving the generator and the pendulum dynamics is developed and analyzed in this article. Bifurcation diagrams demonstrate doubling-period and saddle-node bifurcations with the chaos. The presence of chaos is verified by the Lyapunov exponents applied on the time series of the pendulum speed and position. Nonideal interactions of a DC motor with a pendulum by a crank-shaft-slider mechanism is analyzed and compared with an ideal excitation of the pendulum.
Highlights
The main aim in this paper is the analysis of types of motion of the parametric pendulum coupled to a DC generator
A clear analysis of rotating orbits of the classic parametric pendulum is presented in Xu et al (2005), at that moment the study of the parametric pendulum dynamics was already justified with the possibility of energy harvesting from sea waves
3.1 Bifurcation diagrams and results for the pendulum coupled to the DC generator
Summary
The main aim in this paper is the analysis of types of motion of the parametric pendulum coupled to a DC generator. A new wave energy converter based on the parametrically excited pendulum was presented in Yurchenko and Alevras (2018) This mechanism reduces the influence of the gravity force and achieves a dominant rotational motion without any active control. Horton et al (2008) considered for small oscillations dry friction becomes prevalent and neglect this could lead to out of phase motions when comparing experimental and numerical results. These assumptions allowed to reduce errors and better predict amplitude oscillations when the pendulum approaches to the resting position.
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