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

作     者：Dan WANG Yushu CHEN M.WIERCIGROCH Qingjie CAO 无

作者机构：School of Astronautics Harbin Institute of Technology Centre for Applied Dynamics Research School of Engineering University of AberdeenKing's College 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2016年第37卷第9期

页      面：1251-1274页

核心收录：

学科分类：08[工学] 080101[工学-一般力学与力学基础] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Project supported by the National Basic Research Program of China(973 Program)(No.2015CB057405) the National Natural Science Foundation of China(No.11372082) the State Scholarship Fund of China Scholarship Council(CSC)(2014) 

主　　题：vortex-induced vibration van der Pol oscillator dynamic response tran-sition set singularity theory bifurcation phenomenon 

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 hystere- sis 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 va- lidity 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.