The Duffing oscillator is well-known models of nonlinear system, with applications in many fields of applied sciences and engineering. In this paper, a response integration algorithm is proposed to analyze high-order harmonic and chaotic motions in this oscillator for modeling rotor excitations. This method numerically integrates the distance between state trajectory and the origin in the phase plane during a specific period and predicted intervals with excitation periods. It provides a quantitative characterization of system responses and can replace the role of the traditional stroboscopic technique (Poincare´ section method) to observe bifurcations and chaos of the nonlinear oscillators. Due to the signal response contamination of system, thus it is difficult to identify the high-order responses of the subharmonic motion because of the sampling points on Poincare´ map too near each other. Even the system responses will be made misjudgments. Combining the capability of precisely identifying period and constructing bifurcation diagrams, the advantages of the proposed response integration method are shown by case studies. Applying this method, the effects of the change in the stiffness and the damping coefficients on the vibration features of a Duffing oscillator are investigated in this paper. From simulation results, it is concluded that the stiffness and damping of the system can effectively suppress chaotic vibration and reduce vibration amplitude.
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ASME Turbo Expo 2007: Power for Land, Sea, and Air
May 14–17, 2007
Montreal, Canada
Conference Sponsors:
- International Gas Turbine Institute
ISBN:
0-7918-4794-2
PROCEEDINGS PAPER
Characteristics in Response Integration and Bifurcation of a Forced Duffing Oscillator Available to Purchase
Jang-Der Jeng,
Jang-Der Jeng
National United University, Taiwan
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Yuan Kang,
Yuan Kang
Chung Yuan Christian University, Chung Li, Taiwan
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Yeon-Pun Chang,
Yeon-Pun Chang
Chung Yuan Christian University, Chung Li, Taiwan
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Shyh-Shyong Shyr
Shyh-Shyong Shyr
Chung Shan Institute of Science and Technology, Taiwan
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Jang-Der Jeng
National United University, Taiwan
Yuan Kang
Chung Yuan Christian University, Chung Li, Taiwan
Yeon-Pun Chang
Chung Yuan Christian University, Chung Li, Taiwan
Shyh-Shyong Shyr
Chung Shan Institute of Science and Technology, Taiwan
Paper No:
GT2007-28118, pp. 239-246; 8 pages
Published Online:
March 10, 2009
Citation
Jeng, J, Kang, Y, Chang, Y, & Shyr, S. "Characteristics in Response Integration and Bifurcation of a Forced Duffing Oscillator." Proceedings of the ASME Turbo Expo 2007: Power for Land, Sea, and Air. Volume 5: Turbo Expo 2007. Montreal, Canada. May 14–17, 2007. pp. 239-246. ASME. https://doi.org/10.1115/GT2007-28118
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