开放式内嵌流体柔性悬臂梁振颤失稳分析  

Investigation on fluttering destabilization for a flexible cantilever opening beam with interior inlay fluid

作　　者：王建伟[1] 徐晖[1] 马宁[1] 

机构地区：[1]西安交通大学,西安710049

出　　处：《应用力学学报》2010年第2期258-263,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(10372076)

摘　　要：针对开放式内嵌流体柔性悬臂梁流固耦合系统,在对流体运动和梁的振动作一定假设的前提下,综合考虑阻尼以及振动变形引起的梁轴向伸长等因素,建立了系统的耦合非线性动力学控制方程,导出了系统的状态空间方程和线性化扰动方程。运用代数判据求得了Hopf分岔临界流速须满足的条件,并采用经典Runge-Kutta法求解了系统的状态方程。研究结果表明:当流速大于临界流速时,系统的相空间将发生Hopf分岔,产生稳定的极限环;此时梁水平平衡位置的稳定性遭到破坏,在外界扰动的作用下,系统发生振颤失稳,梁以水平位置为中心作周期性振动。Under certain assumptions of fluid movements and beam vibrations,considering the damping and axial elongation caused by vibration deformations,coupling nonlinear dynamic controlling equations are established for a flexible cantilever opening beam with interior inlay fluid,then the state-space equations and the corresponding linearized perturbation equations are derived.According to the Hopf bifurcation theory,the characteristic polynomial of the Jacobi matrix of perturbation equations and its roots,the algebraic criteria,which the critical velocity must satisfy,are derived.The typical 4th-order Runge-Kutta method is utilized to solve state-space equations.The results show that when the fluid velocity exceeds the critical velocity,the Hopf bifurcation occurs,and the limit cycle appears in the phase-space.In this case,the stability of the beam in the horizontal position is destroyed,the fluttering destabilization happens in this system,and the beam periodically vibrates around the horizontal position.

关 键 词：流固耦合 HOPF分岔 临界流速 极限环 振颤失稳 

分 类 号：O325[理学—一般力学与力学基础] TB123[理学—力学]