Analytical solutions of periodic motions in a periodically excited, Duffing oscillator with a time-delayed displacement are developed through the Fourier series, and the stability and bifurcation of such periodic motions are discussed through eigenvalue analysis. The analytical bifurcation trees of period-1 motions to chaos in the time-delayed Duffing oscillator is presented through asymmetric period-1 to period-4 motions. Four independent symmetric period-3 motions were obtained. Two independent symmetric period-3 motions are not relative to chaos, while the other two includes bifurcation trees of period-3 motion to chaos, which are presented through period-3 to period-6 motions. Stable periodic motions are illustrated from numerical and analytical solutions. The appropriate initial history functions for periodic motions are analytically computed from the analytical solutions of periodic motions. Without the appropriate initial history functions, such a time-delayed system cannot yield periodic motions directly.
|Advisor:||Luo, Albert C. J.|
|Commitee:||Kweon, Soondo, Lu, Chunqing|
|School:||Southern Illinois University at Edwardsville|
|Department:||Mechanical and Industrial Engineering|
|School Location:||United States -- Illinois|
|Source:||MAI 53/06M(E), Masters Abstracts International|
|Keywords:||Analytical solution, Bifurcation, Chaos, Duffing oscillator, Periodic motion, Time-delay|
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