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27-10-2015

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

Authors: Rafael Henrique Avanço, Hélio Aparecido Navarro, Reyolando M. L. R. F. Brasil, José Manoel Balthazar, Átila Madureira Bueno, Angelo Marcelo Tusset

Published in: Meccanica | Issue 6/2016

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Abstract

The nonlinear dynamics behavior analyzed, in this paper, consists in a pendulum vertically excited on the support by a crank-shaft-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 crank-shaft-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 crank-shaft-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.

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Title: Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism
Authors: Rafael Henrique Avanço
Hélio Aparecido Navarro
Reyolando M. L. R. F. Brasil
José Manoel Balthazar
Átila Madureira Bueno
Angelo Marcelo Tusset
Publication date: 27-10-2015
Publisher: Springer Netherlands
Published in: Meccanica / Issue 6/2016
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI: https://doi.org/10.1007/s11012-015-0310-1

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