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

doi:10.1007/s10483-016-2128-6

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (9): 1251-1274.doi: https://doi.org/10.1007/s10483-016-2128-6

• 论文 • 上一篇

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

Dan WANG¹, Yushu CHEN¹, M. WIERCIGROCH², Qingjie CAO¹

1. School of Astronautics, Harbin Institute of Technology, Harbin 150001, China;
2. Centre for Applied Dynamics Research, School of Engineering, University of Aberdeen, King's College, Aberdeen AB24 3 UE, Scotland, U. K

收稿日期:2015-12-23 修回日期:2016-04-25 出版日期:2016-09-01 发布日期:2016-09-01
通讯作者: Dan WANG E-mail:danwang2014518@hotmail.com
基金资助:
Project supported by the National Basic Research Program of China (973 Program) (No. 2015CB057405), the National Natural Science Foundation of China (No. 11372082), and the State Scholarship Fund of China Scholarship Council (CSC) (2014)

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

Dan WANG¹, Yushu CHEN¹, M. WIERCIGROCH², Qingjie CAO¹

1. School of Astronautics, Harbin Institute of Technology, Harbin 150001, China;
2. Centre for Applied Dynamics Research, School of Engineering, University of Aberdeen, King's College, Aberdeen AB24 3 UE, Scotland, U. K

Received:2015-12-23 Revised:2016-04-25 Online:2016-09-01 Published:2016-09-01
Contact: Dan WANG E-mail:danwang2014518@hotmail.com
Supported by:
Project supported by the National Basic Research Program of China (973 Program) (No. 2015CB057405), the National Natural Science Foundation of China (No. 11372082), and the State Scholarship Fund of China Scholarship Council (CSC) (2014)

摘要/Abstract

摘要：

A reduced model is proposed and analyzed for the simulation of vortexinduced vibrations (VIVs) for turbine blades. A rotating blade is modelled 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 the equations of motion for the blade to simulate the fluid-structure interaction. The action for the structural motion on the fluid is considered as a linear inertia coupling. The 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 set and the hysteresis set is constructed by the singularity theory and the effects of the system parameters, such as the van der Pol damping. The coupling parameter on the equilibrium solutions is analyzed. The frequency-response curves are obtained, and the stabilities are determined by 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 is useful in explaining the rich dynamic response characteristics such as possible bifurcation phenomena in the VIVs.

关键词: vortex-induced vibration, bifurcation phenomenon, transition set, singularity theory, van der Pol oscillator, dynamic response

Abstract:

Key words: singularity theory, dynamic response, transition set, vortex-induced vibration, van der Pol oscillator, bifurcation phenomenon

中图分类号:

70K30
70K50

Dan WANG, Yushu CHEN, M. WIERCIGROCH, Qingjie CAO. Bifurcation and dynamic response analysis of rotating blade excited by upstream vortices[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(9): 1251-1274.

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

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

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