Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism

Abstract

The nonlinear dynamics behavior analyzed, in this paper, consists in a pendulum vertically excited on the support by a crankshaft -slider mechanism. The novelty is the obtainment and analysis of a mathematical model for the pendulum dynamics, under an excitation of a crank-slider, which is based on an extension of the mathematical model of the classical parametric pendulums. Through the modeling, it was verified that the nonlinear dynamics of the pendulum, excited by the crankshaft -slider mechanism approaches to that of harmonic excitation, when one considered the length of the shaft is sufficient larger than the radius of the crank. The nonlinear dynamic analyses focused on observation of different kinds of motion for different values of dimensionless parameters of the adopted mathematical model. These parameters, includes the frequency of excitation, the amplitude and the geometry of the crankshaft -slider mechanism. The adopted method of analyses used tools, such as, Lyapunov exponents, parameter space plots, basins of attractions, bifurcation diagrams, phase portraits, time histories and Poincaré sections. The kinds of motion include results on fixed point, oscillations, rotations, oscillations-rotations and chaotic motions.

Nonlinear Dynamics in Semiconductor Quantum Dot Laser Subject to Double Delayed Feedback: Numerical Analysis

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Parametric pendulum based wave energy converter

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On nonlinear dynamics behavior of an electro-mechanical pendulum excited by a nonideal motor and a chaos control taking into account parametric errors

“…A dynamic analysis of a pendulum vertically excited by a crank-shaft-slider mechanism was performed in Avanço et al [4]. In the current literature, the motion of the slider is commonly approached to a harmonic displacement as it was carried out in Krasnopolskaya and Shvets [5], where the chaotic behavior of a nonlinear system was verified.…”

“…In the current literature, the motion of the slider is commonly approached to a harmonic displacement as it was carried out in Krasnopolskaya and Shvets [5], where the chaotic behavior of a nonlinear system was verified. The dynamic equation in Avanço et al [4] considered, in the modeling, the complexity of the crank-shaft-slider in the motion on the pivot of support of the pendulum. The geometry of the mechanism was applied like a perturbation in the equation correspondent of the classical parametric pendulum of Leven and Koch [2].…”