Dissertation/Thesis Abstract

Periodic Motions and Bifurcation Trees in a Periodically Excited Duffing Oscillator with Time-delay
by Xing, Siyuan, M.S., Southern Illinois University at Edwardsville, 2016, 109; 10147051
Abstract (Summary)

In this paper, bifurcation trees of periodic motions in a periodically forced, time-delayed, hardening Duffing oscillator are analytically predicted by a semi-analytical method. Such a semi-analytical method is based on the differential equation discretization of the time-delayed, non-linear dynamical system. Bifurcation trees for the stable and unstable solutions of periodic motions to chaos in such a time-delayed, Duffing oscillator are achieved analytically. From the finite discrete Fourier series, harmonic frequency-amplitude curves for stable and unstable solutions of period-1 to period-4 motions are developed for a better understanding of quantity levels, singularity and catastrophes of harmonic amplitudes in the frequency domain. From the analytical prediction, numerical results of periodic motions in the time-delayed, hardening Duffing oscillator are completed. Through the numerical illustrations, the complexity and asymmetry of period-1 motions to chaos in nonlinear dynamical systems are strongly dependent on the distributions and quantity levels of harmonic amplitudes. With the quantity level increases of specific harmonic amplitudes, effects of the corresponding harmonics on the periodic motions become strong, and the certain complexity and asymmetry of periodic motion and chaos can be identified through harmonic amplitudes with higher quantity levels.

Indexing (document details)
Advisor: Luo, Albert c.j.
Commitee: Chen, Xin, Wang, Fengxia
School: Southern Illinois University at Edwardsville
Department: Mechanical and Industrial Engineering
School Location: United States -- Illinois
Source: MAI 56/01M(E), Masters Abstracts International
Source Type: DISSERTATION
Subjects: Mechanical engineering
Keywords:
Publication Number: 10147051
ISBN: 9781369023473
Copyright © 2019 ProQuest LLC. All rights reserved. Terms and Conditions Privacy Policy Cookie Policy
ProQuest