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Title:Coupled oscillators near resonance
Author(s):Arsenault, Lance Eric
Doctoral Committee Chair(s):Jackson, E. A.
Department / Program:Physics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Engineering, Mechanical
Abstract:We study the dynamics of two conservative librating oscillators with perturbations from a linear displacement coupling and non-Hamiltonian forces such as damping. We examine the dynamics of these systems when they are near a resonance using secular perturbation theory. We show that near resonance a large class of driven oscillators and two coupled oscillators can be transformed to the same ordinary differential equations (ODEs). We consider two types of resonances: accidental and intrinsic. For an accidental resonance, we find that the dynamics near a resonance is a generalization of the standard Hamiltonian dynamics of two coupled conservative oscillators, which we call the standard equation. For an intrinsic resonance, we show that a primary resonance island can fill all of the available phase space. We derive expressions for the parameters in these ODEs. From a fixed-point analysis of these ODEs, we show that hard oscillators lock in-phase and soft oscillators lock out-of-phase. We develop a novel method for calculating accurate response curves for driven strongly nonlinear oscillators, where no existing method can give accurate results. We present a method for finding the steady state frequency of two coupled oscillators. We compare our theoretical predictions with computer simulations of many examples including: a sinusoidally driven highly nonlinear Duffing oscillator, and two coupled van der Pol oscillators with a highly nonlinear Duffing force.
Issue Date:1996
Rights Information:Copyright 1996 Arsenault, Lance Eric
Date Available in IDEALS:2011-05-07
Identifier in Online Catalog:AAI9702450
OCLC Identifier:(UMI)AAI9702450

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