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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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Abstract

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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