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Journal of Vibration Testing and System Dynamics 1(1) (2017) 73--91 | DOI:10.5890/JVTSD.2017.03.006

Albert C.J. Luo; Siyuan Xing

Department of Mechanical and Industrial Engineering Southern Illinois University Edwardsville Edwardsville, IL 62026-1805, USA

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Abstract

In this paper, time-delay effects on periodic motions in a periodi- cally forced, time-delayed, hardening Duffing oscillator are discussed. One often considers the time-delay interval is very small compared to the oscillation period. In engineering application, the time-delay interval is often very large. Bifurcation trees of periodic motions to chaos varying with time-delay are presented for such a time-delayed, Duffing oscillator. Using the nite discrete Fourier series, harmonic amplitude varying with time-delay for stable and unstable solutions of period-1 to period-4 motions are developed. From the analytical prediction, numerical results of periodic motions in the time-delayed, hardening Duffing oscillator are completed. Through the numerical illustrations, time-delay effects on period-1 motions to chaos in non- linear dynamical systems are strongly dependent on the distributions and quantity levels of harmonic amplitudes.

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