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变截面柔性杆与流体的耦合运动特性研究
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Abstract:
为了研究变截面柔性杆与流体的耦合运动特性，建立了在轴向风力作用下两端夹紧的变截面柔性杆模型。先通过理想流体假设和Euler-Bernoulli梁假设，给出变截面柔性杆与风场之间的流固耦合方程，再通过线性稳定性分析得到该柔性杆的扰动时间增长率和特征函数的表达式，由此研究柔性杆的长波不稳定性和失稳机制，并讨论了频率与扰动时间增长率的变化规律。结果表明：柔性杆的截面变化系数与位置函数对频率和扰动时间增长率的影响较为显著；弹性模量对扰动时间增长率影响较大，对频率的影响可忽略不计。推导得出了耦合运动最不稳定时的波数和频率的表达式，并得到最不稳定时的频率与风速成线性关系。
In order to study the interaction between moving fluid and flexible rod with variable cross-section, a model of flexible rod with variable cross-section clamped at both ends under the action of axial wind is established. Based on the ideal fluid assumption and the Euler Bernoulli beam assumption, it establishes the basic equation of the interaction between flexible rod with variable cross-section and the wind field. Then through the linear stability analysis, the expression of the temporal growth rate of the perturbation and the characteristic function of the flexible rod is obtained. From this, the long-wave instability and instability mechanism of the flexible rod are studied, and the change law of the growth rate of the frequency and the temporal growth rate of the perturbation is discussed. The results show that the section variation coefficient and position function of flexible rod have a significant influence on the value of the frequency and the temporal growth rate of the perturbation; the modulus of elasticity has a greater influence on the temporal growth rate of the perturbation, and the influence on the frequency is negligible. It derives the expressions of the wave number and frequency when the coupled motion is the most unstable, and the frequency at the most unstable time is linearly related to the wind velocity.
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