Nonlinear Dynamics

, Volume 95, Issue 2, pp 1435–1456 | Cite as

Nonlinear vibration control of a cantilevered fluid-conveying pipe using the idea of nonlinear energy sink

  • K. Zhou
  • F. R. Xiong
  • N. B. Jiang
  • H. L. DaiEmail author
  • H. Yan
  • L. Wang
  • Q. Ni
Original Paper


Different from the both-end supported pipe conveying fluid as a conservative system, the cantilevered fluid-transporting pipe is a non-conservative system and its dynamic behavior is more complex with flutter instabilities when the flow velocity is beyond the critical value. Indeed, controlling such a flutter system is always challenging in engineering applications. This study presents nonlinear vibrations of cantilevered pipe conveying fluid passively controlled via a nonlinear energy sink (NES). Based on the Hamilton principle, the nonlinear dynamic equations coupling with the NES are derived and discretized using high-order Galerkin method. It is indicated that increasing the mass and damping of NES results in an increase in critical flow velocity. Importantly, the optimal placed position of NES where the critical flow velocity is highest has a strong relationship with the pipe’s flutter mode. In the following, the nonlinear analysis shows the dynamic controlling effect on vibration amplitude of the pipe can be classified to three suppression regions with increasing the flow velocity. Varying the mass, damping and stiffness of NES is followed by variations of the suppression regions which are associated with controlling effects and dynamic behaviors of the pipe system.


Pipe conveying fluid Nonlinear energy sink Flutter Chaotic Nonlinear dynamics 



The authors acknowledge the support provided by Science and Technology on Reactor System Design Technology Laboratory, Fundamental Research Funds for the Central Universities, HUST (2017KFYXJJ135), Natural Science Foundation of Hubei Province (2017CFB429) and National Natural Science Foundation of China (Nos. 11602090, 11672115 and 11872060).

Compliance with ethical standards

Conflict of interest

They have no conflict of interest.

Ethical standard

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards.

Human and animal rights

This article does not contain any studies with animals performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • K. Zhou
    • 1
    • 2
  • F. R. Xiong
    • 3
  • N. B. Jiang
    • 3
  • H. L. Dai
    • 1
    • 2
    Email author
  • H. Yan
    • 1
    • 2
  • L. Wang
    • 1
    • 2
  • Q. Ni
    • 1
    • 2
  1. 1.Department of MechanicsHuazhong University of Science and TechnologyWuhanChina
  2. 2.Hubei Key Laboratory for Engineering Structural Analysis and Safety AssessmentWuhanChina
  3. 3.Science and Technology on Reactor System Design Technology LaboratoryNuclear Power Institute of ChinaChengduChina

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