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Master's Dissertation
DOI
10.11606/D.18.2016.tde-26022016-144941
Document
Author
Full name
Vinícius Santos Andrade
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2003
Supervisor
Committee
Oliveira, Vilma Alves de (President)
Balthazar, José Manoel
Tsuchida, Masayoshi
Title in Portuguese
Análise da dinâmica caótica de pêndulos com excitação paramétrica no suporte
Keywords in Portuguese
Bifurcações
Caos
Equação de Lagrange
Expoentes de Lyapunov
Mapa e seção de Poincaré
Multiplicadores de Floquet
Pêndulos
Abstract in Portuguese
Este trabalho apresenta a modelagem de um problema representado por um pêndulo elástico com excitação paramétrica vertical do suporte e a análise de estabilidade do sistema pendular que se obtém desconsiderando a elasticidade do pêndulo. A modelagem dos pêndulos e a obtenção das equações do movimento são feitas a partir da equação de Lagrange, utilizando as leis de Newton e para a análise de estabilidade do sistema pendular são apresentados os diagramas de bifurcações, multiplicadores de Floquet, mapas e seções de Poincaré e expoentes de Lyapunov. O comportamento do sistema pendular com excitação paramétrica vertical do suporte é investigado através de simulação computacional e apresentam-se resultados para diferentes faixas de valores da amplitude de excitação externa.
Title in English
Analysis of chaotic dynamics of pendulums with parametric excitation of the support
Keywords in English
Bifurcations
Chaos
Floquet's multipliers
Lagrange's equation
Lyapunov exponents
Pendulums
Poincaré maps and sections
Abstract in English
This work presents the modeling of an elastic pendulum with parametric excitation of the support and the analysis of the stability of the pendulum that one obtains disregarding the elasticity of the pendulum. The modeling of the pendulum and the equation of motions are obtained from the Lagrange's equations, using Newton's law. The concepts of bifurcation, Floquet's multipliers, Poincaré maps and sections and Lyapunov exponent are presented for the analysis of stability. The behavior of the pendulum with parametric excitation of the suport is investigated through computational simulation and results for different intervals of values of the external excitation amplitude are presented.
 
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Publishing Date
2016-02-26
 
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