Nonlinear Dynamics

, Volume 83, Issue 1–2, pp 941–950 | Cite as

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

  • Li Yuanping
  • Chen SiyuEmail author
Original Paper


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.


Nonlinear vibration Suspension Bifurcation Continuation Stability 



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

Compliance with ethical standards

Conflict of interest

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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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Key Lab of Disaster Forecast and Control in EngineeringMinistry of Education of the People’s Republic of China (Jinan University)GuangzhouChina
  2. 2.Department of Mechanics and Civil EngineeringJinan UniversityGuangzhouChina
  3. 3.State Key Laboratory of High Performance Complex ManufacturingCentral South UniversityChangshaChina

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