轴向流作用下柔性简支梁静态与动态稳定性分析

Static and dynamic stabilities of a simply supported flexible beam with an axial flow

对于一个轴向流作用下的柔性简支梁流固耦合模型,基于一定的假设,建立了系统的流固耦合非线性动力学方程,并运用参数无量纲化、假设模态、高阶模态截断等方法导出了有限自由度无量纲状态空间方程。根据静态分岔理论,对系统线性化扰动方程的Jacob i系数矩阵特征多项式进行了分析,理论上求得系统发生静态分岔时的临界流速。数值计算结果表明当流速大于临界流速时,系统发生静态失稳,在外界扰动作用下,梁随机地向上或向下弯曲。基于动态Hopf分岔理论与相关的实系数多项式特征根代数判据,证明了系统不会出现振颤失稳。

The liquid-solid coupled dynamic equation was established for a simply supported flexible beam with an axial flow under certain assumptions,and the dimensionless state equation with finite degrees of freedom was derived by introducing dimensionless variables,assumed modes and truncating higher order modes.On the basis of the static bifurcation theory,the Jacobi matrix of the perturbation equation of the system was analyzed,and the static bifurcation critical flow velocity was obtained theoretically.Numerical calculations showed that if the flow velocity exceeds the critical velocity,the system is statically destabilized,and the flexible beam bends upward or downward randomly under the external minimal disturbance.Utilizing the dynamic Hopf bifurcation theory and the relative algebraic criterion for roots of real-coefficient polynomials,it is proved that the flutter destabilization can＇t take place in this system.