机翼颤振的Hopf分岔分析与控制  

Hopf Bifurcation Analysis and Control of Aerodynamic Flutter for an Airfoil

作　　者：李鹏松[1] 盛桂全[1] 孟永永 刘琦[1] 

机构地区：[1]东北电力大学理学院,吉林吉林132012

出　　处：《吉林大学学报（理学版）》2015年第4期647-654,共8页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11072085);吉林省科技发展计划项目(批准号:20130101065JC)

摘　　要：考虑二元非线性机翼颤振系统,利用多尺度法研究系统的Hopf分岔类型和周期解的稳定性.设计非线性时滞控制器抑制Hopf分岔引起的颤振,将原系统的亚临界Hopf分岔变为超临界Hopf分岔,将原系统的超临界Hopf分岔控制为稳定.理论分析和数值模拟结果验证了所给控制方法的有效性.We considered a two-variable nonlinear system,namely,the flutter of airfoil.The type of Hopf bifurcation and the stability of periodic solution were analyzed with the method of multiple scales.The nonlinear time delay controller was designed to restrain the flutter caused by Hopf bifurcation.Thus the nonlinear control gain can be determined to transform subcritical Hopf bifurcation into supercritical one and transform supercritical Hopf bifurcation into steady points.The results of the theory analysis and numerical simulation show that the designed controller is valid.

关 键 词：亚临界Hopf分岔 超临界Hopf分岔 非线性控制 多尺度法 

分 类 号：O193[理学—数学]