Bifurcation and dynamic response analysis of rotating blade excited by upstream vortices

Dan Wang, Yushu Chen, Marian Wiercigroch, Qingjie Cao

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23 Citations (Scopus)
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A reduced model simulating vortex-induced vibrations (VIVs) for turbine blades is proposed and analyzed. The rotating blade is modeled as a uniform cantilever beam while a van der Pol oscillator is used to represent the time-varying characteristics of the vortex shedding, which interacts with equations of motion for a blade to simulate the fluid-structure interaction. The action for the structural motion on the fluid is considered as a linear inertia coupling. Nonlinear characteristics for the dynamic responses are investigated with the multiple scale method and the modulation equations are derived. The transition set consisting of the bifurcation and hysteresis sets is constructed by using the singularity theory and the effects of system parameters including the van der Pol damping and the coupling parameter on the equilibrium solutions are analyzed. Frequency-response curves are obtained and the stabilities are determined by using the Routh-Hurwitz criterion. The phenomena including the saddle-node and Hopf bifurcations are found to occur under certain parameter values. A direct numerical method is used to analyze the dynamic characteristics for the original system and verify the validity of the multiple scale method. The results indicate that the new coupled model can be useful to explain the rich dynamic response characteristics including possible bifurcation phenomena in the VIVs.
Original languageEnglish
Pages (from-to)1251-1274
Number of pages24
JournalApplied Mathematics and Mechanics
Issue number9
Early online date28 Jul 2016
Publication statusPublished - Sept 2016

Bibliographical note

Acknowledgements The authors acknowledge the projects supported by the National Basic Research Program of China (973 Project)(No. 2015CB057405) and the National Natural Science Foundation of China (No. 11372082) and the State Scholarship Fund of CSC. DW thanks for the hospitality of the University of Aberdeen.


  • vortex-induced vibration
  • van der Pol oscillator
  • dynamic responses
  • transition set
  • singularity theory
  • bifurcation phenomenon


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