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Periodic solution and bifurcation of a suspension vibration system by incremental harmonic balance and continuation method

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Abstract

A compressed air generator hang under vehicle is simplified as a suspension mass connected to a vertical spring and two horizontal springs. It is configured generally as a geometrical negative stiffness to reduce dynamic stiffness. The periodic motion, chaotic motion and bifurcation of the compressed air generator model are investigated using the incremental harmonic balance method in combination with arc length continuation technique. The stability and bifurcation route are also distinguished with Floquet theory. The system exhibits a period doubling bifurcation route to chaos in different regions of excitation frequency. The stiffness ratio of the vertical spring and the horizontal spring has a significant influence on the dynamic response. When the vertical stiffness is close to the stiffness at horizontal direction, resonance occurs with the emergence of the chaotic motion. The dynamic response of the vibration system can be improved by reducing the stiffness in the horizontal direction to increase the stiffness ratio.

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Acknowledgments

The authors gratefully acknowledge the support of the National Science Foundation of China (NSFC) through Grants Nos. 51305462 and 51275530.

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Authors and Affiliations

  1. Key Lab of Disaster Forecast and Control in Engineering, Ministry of Education of the People’s Republic of China (Jinan University), Guangzhou, 510632, China

    Li Yuanping

  2. Department of Mechanics and Civil Engineering, Jinan University, Guangzhou, 510632, China

    Li Yuanping

  3. State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha, 410083, Hunan, China

    Chen Siyu

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  1. Li Yuanping
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  2. Chen Siyu
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Correspondence to Chen Siyu.

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The authors declare that they have no conflict of interest. This article does not contain any studies with human participants or animals performed by any of the authors. Informed consent was obtained from all individual participants included in the study.

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Yuanping, L., Siyu, C. Periodic solution and bifurcation of a suspension vibration system by incremental harmonic balance and continuation method. Nonlinear Dyn 83, 941–950 (2016). https://doi.org/10.1007/s11071-015-2378-5

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  • DOI: https://doi.org/10.1007/s11071-015-2378-5

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