Abstract
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 language | English |
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Pages (from-to) | 1251-1274 |
Number of pages | 24 |
Journal | Applied Mathematics and Mechanics |
Volume | 37 |
Issue number | 9 |
Early online date | 28 Jul 2016 |
DOIs | |
Publication status | Published - 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.Keywords
- vortex-induced vibration
- van der Pol oscillator
- dynamic responses
- transition set
- singularity theory
- bifurcation phenomenon