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ISSN: 2475-4811 (print)
ISSN: 2475-482X (online)
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn

Bifurcation Dynamics of Periodic Motions in a Duffing Oscillator under Multiple Periodic Excitations

Journal of Vibration Testing and System Dynamics 10(2) (2026) 191--207 | DOI:10.5890/JVTSD.2026.06.007

Yuzhou Zhu, Albert C. J. Luo

Department of Mechanical and Mechatronics Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026, USA

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Abstract

In this paper, periodic motions in a Duffing oscillator under two external periodic forces are obtained through the corresponding discrete implicit maps. Using specific mapping structure, the bifurcation trees of periodic motions to chaos are developed semi-analytically, and the corresponding stability and bifurcation analysis of periodic motions are carried out through the corresponding eigenvalue analysis. From discrete nodes on periodic motions, the frequency-amplitude characteristics of periodic motions are computed through the discrete Fourier series, and the bifurcation trees of periodic motions are also presented through frequency-amplitude curves. For a better understanding of periodic motions in nonlinear systems under multiple excitations, numerical illustrations of period-2 and period-4 motions are presented.

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