轴向流作用下柔性简支梁静态与动态稳定性分析

王建伟;徐晖;马宁

振动与冲击 ›› 2011, Vol. 30 ›› Issue (7) : 59-62.

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PDF(1163 KB)
振动与冲击 ›› 2011, Vol. 30 ›› Issue (7) : 59-62.
论文

轴向流作用下柔性简支梁静态与动态稳定性分析

  • 王建伟; 徐晖; 马宁
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Investigation on Static and Dynamic Stability for Simply Supported Flexible Beam with Axial Flow

  • WANG Jian-wei; XU Hui; MA Ning
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摘要

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Jacobi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。

Abstract

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

关键词

柔性简支梁 / 状态空间方程 / 静态分岔 / 临界流速 / 动态Hopf分岔 / 振颤失稳

Key words

simply supported flexible beam / state-space equations / static bifurcation / critical flow velocity / Hopf bifurcation / flutter destabilization

引用本文

导出引用
王建伟;徐晖;马宁. 轴向流作用下柔性简支梁静态与动态稳定性分析[J]. 振动与冲击, 2011, 30(7): 59-62
WANG Jian-wei; XU Hui;MA Ning. Investigation on Static and Dynamic Stability for Simply Supported Flexible Beam with Axial Flow [J]. Journal of Vibration and Shock, 2011, 30(7): 59-62

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