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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


C. Steve Suh (editor)

Texas A&M University, USA


Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China


Bifurcation Trees of Period-1 to Period-2 Motions in a Periodically Excited Nonlinear Spring Pendulum

Journal of Vcibration Testing and System Dynamics 4(3) (2020) 201--248 | DOI:10.5890/JVTSD.2020.09.001

Albert C.J. Luo, Yaoguang Yuan

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

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The spring-pendulum system has been of greet interest for a long time, and one tried to use the perturbation analysis to understand such a system. Until now, one cannot provide a satisfied result to explain the dynamics of the spring-pendulum system. In this paper, bifurcation trees of period-1 to period-2 motions in a periodically forced, nonlinear spring pendulum system are obtained through the discrete mapping method. The corresponding harmonic frequency-amplitude characteristics of period-1 to period-2 motions are presented, and the stability and bifurcations of period-1 to period-2 motions on the bifurcation trees are presented as well. From the analytical prediction, numerical illustrations of period-1 and period-2 motions are completed for comparison of numerical and analytical solutions. The results presented in this paper are totally different from the traditional perturbation analysis.


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