Bifurcation analysis for vibrations of a turbine blade excited by air flows

作     者：WANG Dan CHEN YuShu HAO ZhiFeng CAO QingJie 

作者机构：School of Astronautics Harbin Institute of Technology Harbin 150001 China 

出 版 物：《Science China(Technological Sciences)》 (中国科学（技术科学英文版）)

年 卷 期：2016年第59卷第8期

页      面：1217-1231页

核心收录：

学科分类：080704[工学-流体机械及工程] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 0801[工学-力学（可授工学、理学学位）] 

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

主　　题：fluid-structure interaction (FSI) internal resonance two-parameter bifurcation diagram saddle-node bifurcation Hopf bifurcation direct numerical simulation 

摘      要：A reduced three-degree-of-freedom model simulating the fluid-structure interactions （FSI） of the turbine blades and the on- coming air flows is proposed. The equations of motions consist of the coupling of bending and torsion of a blade as well as a van der Pol oscillation which represents the time-varying of the fluid. The 1：1 internal resonance of the system is analyzed with the multiple scale method, and the modulation equations are derived. The two-parameter bifurcation diagrams are computed. The effects of the system parameters, including the detuning parameter and the reduced frequency, on responses of the struc- ture and fluid are investigated. Bifurcation curves are computed and the stability is determined by examining the eigenvalues of the Jacobian matrix. The results indicate that rich dynamic phenomena of the steady-state solutions including the sad- dle-node and Hopf bifurcations can occur under certain parameter conditions. The parameter region where the unstable solu- tions occur should be avoided to keep the safe operation of the blades. The analytical solutions are verified by the direct nu- merical simulations.