In recent decades, nonlinear time-delay systems were often applied in controlling nonlinear systems, and the stability of such time-delay systems was very actively discussed. Recently, one was very interested in periodic motions in nonlinear time-delay systems. Especially, the semi-analytical solutions of periodic motions in time-delay systems are of great interest. From the semi-analytical solutions, the nonlinearity and complexity of periodic motions in the time-delay systems can be discussed. In this paper, time-delay effects on periodic motions of a periodically forced, damped, hardening, Duffing oscillator are analytically discussed through a semi-analytical method. The semi-analytical method is based on discretization of the differential equation of such a Duffing oscillator to obtain the corresponding implicit discrete mappings. Through such implicit mappings and mapping structures of periodic motions, period-1 motions varying with time-delay are discussed, and the corresponding stability and bifurcation analysis of periodic motions are carried out through eigenvalue analysis. Numerical results of periodic motions are illustrated to verify analytical predictions. The corresponding harmonic amplitude spectrums and harmonic phases are presented for a better understanding of periodic motions in such a nonlinear oscillator.
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ASME 2016 International Mechanical Engineering Congress and Exposition
November 11–17, 2016
Phoenix, Arizona, USA
Conference Sponsors:
- ASME
ISBN:
978-0-7918-5055-8
PROCEEDINGS PAPER
On Time-Delay Effects on Period-1 Motions in a Periodically Forced, Time-Delayed, Duffing Oscillator
Albert C. J. Luo,
Albert C. J. Luo
Southern Illinois University Edwardsville, Edwardsville, IL
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Siyuan Xing
Siyuan Xing
Southern Illinois University Edwardsville, Edwardsville, IL
Search for other works by this author on:
Albert C. J. Luo
Southern Illinois University Edwardsville, Edwardsville, IL
Siyuan Xing
Southern Illinois University Edwardsville, Edwardsville, IL
Paper No:
IMECE2016-66198, V04BT05A020; 7 pages
Published Online:
February 8, 2017
Citation
Luo, ACJ, & Xing, S. "On Time-Delay Effects on Period-1 Motions in a Periodically Forced, Time-Delayed, Duffing Oscillator." Proceedings of the ASME 2016 International Mechanical Engineering Congress and Exposition. Volume 4B: Dynamics, Vibration, and Control. Phoenix, Arizona, USA. November 11–17, 2016. V04BT05A020. ASME. https://doi.org/10.1115/IMECE2016-66198
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