变截面柔性杆与流体的耦合运动特性研究
Study on Interaction between Moving Fluid and Flexible Rod with Variable Cross-Section
DOI: 10.12677/IJM.2021.101003, PDF,    国家自然科学基金支持
作者: 席小峰, 韩明君：兰州理工大学，理学院，甘肃 兰州
关键词: 柔性体；流固耦合；变截面；运动特性；Flexible Sheet； Fluid-Structure Interaction； Variable Cross-Section； Motion Characteristics
摘要: 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。
Abstract: 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.
文章引用：席小峰, 韩明君. 变截面柔性杆与流体的耦合运动特性研究[J]. 力学研究, 2021, 10(1): 19-28. https://doi.org/10.12677/IJM.2021.101003

参考文献

[1] Liao, J.C., Beal, D.N., Lauder, G.V., et al. (2003) Fish Exploiting Vortices Decrease Muscle Activity. Science, 302, 1566-1569. [Google Scholar] [CrossRef] [PubMed]
[2] Muller, U.K. (2003) Physiology. Fish ‘n Flag. Science, 302, 1511-1512. [Google Scholar] [CrossRef] [PubMed]
[3] Lighthill, M.J. (2006) Note on the Swimming of Slender Fish. Journal of Fluid Mechanics, 9, 305-317. [Google Scholar] [CrossRef] 
[4] 陆夕云, 杨基明, 尹协振, 等. 飞行和游动的生物运动力学和仿生技术研究[J]. 中国科学技术大学学报, 2007, 37(10): 1159-1163.
[5] 董帝渤. 仿生柔性结构与流固耦合系统的数值方法及运动机理研究[D]: [博士学位论文]. 哈尔滨: 哈尔滨工业大学, 2016.
[6] Huang, L. (1995) Flut-ter of Cantilevered Plates in Axial Flow. Journal of Fluids and Structures, 9, 127-147. [Google Scholar] [CrossRef] 
[7] Balint, T.S. and Lucey, A.D. (2005) Instability of a Cantilevered Flexible Plate in Viscous Channel Flow. Journal of Fluids and Structures, 20, 893-912. [Google Scholar] [CrossRef] 
[8] Lim, W.L., Chew, Y.T., Low, H.T., et al. (2003) Cavitation Phenomena in Mechanical Heart Valves: The Role of Squeeze Flow Velocity and Contact Area on Cavitation Initiation between Two Impinging Rods. Journal of Biomechanics, 36, 1269-1280. [Google Scholar] [CrossRef] 
[9] Gerbeau, J.F., Vidrascu, M. and Frey, P. (2005) Flu-id-Structure Interaction in Blood Flows on Geometries Based on Medical Imaging. Computers & Structures, 83, 155-165. [Google Scholar] [CrossRef] 
[10] Watanabe, Y., Isogai, K., Suzuki, S., et al. (2002) A Theoretical Study of Paper Flutter. Journal of Fluids and Structures, 16, 543-560. [Google Scholar] [CrossRef] 
[11] 张成瑶. 单个或多个柔性体自主推进的流固耦合数值研究[D]: [博士学位论文]. 合肥: 中国科学技术大学, 2020.
[12] Jia, P., Andreotti, B. and Claudin, P. (2015) Paper Waves in the Wind. Physics of Fluids, 27, Article ID: 104101. [Google Scholar] [CrossRef] 
[13] Taneda, S. (1968) Waving Motions of Flags. Journal of the Physical So-ciety of Japan, 24, 392-401. [Google Scholar] [CrossRef] 
[14] Datta, S.K. and Gottenberg, W.G. (1975) Instability of an Elastic Strip Hanging in an Airstream. Journal of Applied Mechanics, 42, 195-198. [Google Scholar] [CrossRef] 
[15] Lemaitre, C., Hemon, P. and de Langre, E. (2005) Instability of a Long Ribbon Hanging in Axial Air Flow. Journal of Fluids and Structures, 20, 913-925. [Google Scholar] [CrossRef] 
[16] Yamaguchi, N., Sekiguchi, T., Yokota, K., et al. (2000) Flutter Limits and Behavior of a Flexible Thin Sheet in High-Speed Flow II: Experimental Results and Predicted Be-haviors for Low Mass Ratios. Journal of Fluids Engineering, 122, 74-83. [Google Scholar] [CrossRef] 
[17] Argentina, M. and Mahadevan, L. (2005) Fluid-Flow-Induced Flutter of a Flag. Proceedings of the National Academy of Sciences of the United States of America, 102, 1829-1834. [Google Scholar] [CrossRef] [PubMed]
[18] Eloy, C., Kofman, N. and Schouveiler, L. (2011) The Origin of Hysteresis in the Flag Instability. Journal of Fluid Mechanics, 691, 583-593. [Google Scholar] [CrossRef] 
[19] 孙传宝, 贾来兵, 李发尧, 等. 单个柔性旗帜在均匀流中摆动的测力实验[J]. 实验力学, 2011, 25(2): 1-6.
[20] 王思莹, 孙传宝, 尹协振. 均匀来流条件下并行排列旗帜耦合运动模式的实验[J]. 实验力学, 2010, 25(4): 401-407.
[21] Kim, D., Cossé, J., Huertas, C.C., et al. (2013) Flapping Dynam-ics of an Inverted Flag. Journal of Fluid Mechanics, 736, R1-R7. [Google Scholar] [CrossRef] 
[22] Cisonni, J., Lucey, A.D. and Elliott, N.S.J. (2019) Flutter of Structurally in Homogenous Cantilevers in Laminar Channel Flow. Journal of Fluids and Structures, 90, 177-189. [Google Scholar] [CrossRef] 
[23] 郭日修. 弹性力学与张量分析[M]. 北京: 高等教育出版社, 2003: 177-179.
[24] 原渭兰. 气体动力学[M]. 北京: 科学出版社, 2013: 55-56.
[25] Yang, T. and Mason, M.S. (2019) Aerodynamic Characteristics of Rectangular Cylinders in Steady and Accelerating Wind Flow. Journal of Fluids and Structures, 90, 246-262. [Google Scholar] [CrossRef] 
[26] 高云, 邹丽, 宗智. 两端铰接的细长柔性体圆柱体涡激振动响应特征数值研究[J]. 力学学报, 2018, 50(1): 9-20.

为你推荐