液体晃动动力学中的若干问题讨论
A Discussion on Several Problems in Dynamics of Liquid Sloshing
摘要: 本文简要讨论了液体晃动动力学中的三大问题：1) 液体晃动等效力学模型；2) 液体晃动阻尼问题；3) 参数晃动问题。本文指出经典的等效力学模型理论存在建模方法错误，因而经典理论不能给出完全正确的解答，这一问题亟需进一步澄清；讨论了液体晃动阻尼的理论与试验识别方法，一般情况下，液体晃动阻尼需要由试验来确定；讨论了参数晃动稳定性分析的一个新方法—能量增长指数与系数，采用能量增长指数与系数可给出彩色的参数晃动不稳定图，得到的不稳定边界与传统理论解精确吻合，能量增长指数与系数可更全面地描述参数晃动的不稳定性质，讨论了液体参数晃动的极限环运动非线性阻尼及各模态之间的相互耦合作用。
Abstract: This paper briefly discusses three issues on dynamics of liquid sloshing: 1) the equivalent mechanical model of liquid sloshing; 2) liquid sloshing damping; 3) parametric sloshing. This paper points out that there are modeling mistakes in the classical theory of equivalent mechanical model. Thus the complete correct solutions cannot be derived by the classical theory. This issue should be further clarified. The theoretical and experimental identification methods are discussed for fluid sloshing damping. The sloshing damping should be generally determined by the experiment. A new method (energy growth exponent and coefficient, EGE/EGC) is applied to discuss the unstable properties of parametric sloshing. A colorful instability diagram can be obtained with the EGE/EGC. The instability boundaries by EGE/EGC agree accurately with the traditional solutions. The unstable characteristics of parametric sloshing can be comprehensively described by using EGE/EGC. The nonlinear damping and mode interaction of limit cycle motion of parametric sloshing are discussed in this paper.
文章引用：李遇春, 欧亿鹏. 液体晃动动力学中的若干问题讨论[J]. 应用物理, 2018, 8(4): 171-177. https://doi.org/10.12677/APP.2018.84021

参考文献

[1] Abramson, H.N. (1966) The Dynamic Behavior of Liquids in Moving Containers. NASA SP-1 06, National Aeronautics and Space Administration, Washington DC.
[2] Dodge, F.T. (2000) The New “Dynamic Behavior of Liquids in Moving Con-tainers”. Southwest Research Institute, San Antonio.
[3] Moiseev, H.N. and Petrov, A.A. (1966) The Calculation of Free Oscillations of a Liquid in a Motionless Container. Advances in Applied Mechanics, 9, 91-154. [Google Scholar] [CrossRef] 
[4] Moiseev, H.N. and Rumjantsev, V.V. (1968) Dynamic Stability of Bodies Containing Fluid. Edited by Abramson, H.N., Springer-Verlag, New York. [Google Scholar] [CrossRef] 
[5] Ibrahim, R.A. (2005) Liquid Sloshing Dynamics: Theory and Applica-tions. Cambridge University Press, Cambridge. [Google Scholar] [CrossRef] 
[6] Faltinsen, O.M. and Timokha, A.N. (2009) Sloshing. Cambridge University Press, Cambridge.
[7] 王照林，刘延柱. 充液系统动力学[M]. 北京: 科学出版社, 2002.
[8] 居荣初，曾心传. 弹性结构与液体的耦联振动理论[M]. 北京: 地震出版社, 1983.
[9] 李遇春. 液体晃动动力学基础[M]. 北京: 科学出版社, 2017.
[10] Graham, E.W. and Rodriguez, A.M. (1952) Characteris-tics of Fuel Motion Which Affect Airplane Dynamics. Journal of Applied Mechanics, 19, 381-388.
[11] Housner, G.W. (1957) Dynamic Pressure on Accelerated Fluid Containers. Bulletin of the Seismological Society of America, 47, 15-35.
[12] Li, Y. and Wang, J. (2012) A Supplementary, Exact Solution of an Equivalent Mechanical Model for a Sloshing Fluid in a Rectangu-lar Tank. Journal of Fluids and Structures, 31, 147-151. [Google Scholar] [CrossRef] 
[13] 李遇春, 来明. 矩形容器中流体晃动等效模型的建议公式[J]. 地震工程与工程震动, 2103, 33(1): 111-114.
[14] Li, Y., Di, Q. and Gong, Y. (2012) Equivalent Mechanical Models of Sloshing Fluid in Arbitrary-Section Aqueducts. Earthquake Engineering and Structural Dynamics, 41, 1069-1087. [Google Scholar] [CrossRef] 
[15] 水电工程水工建筑物抗震设计规范[S]. NB 35047-2015.
[16] Li, Y. and Wang, Z. (2016) Unstable Characteristics of Two-Dimensional Parametric Sloshing in Various Shape Tanks: Theoretical and Experi-mental Analyses. Journal of Vibration and Control, 22, 4025-4046. [Google Scholar] [CrossRef] 
[17] 王立时, 李遇春, 张皓. 二维晃动自然频率与阻尼比系数的试验识别[J]. 振动与冲击, 2016, 35(8): 173-176.
[18] Li, Y., Wang, L. and Yu, Y. (2016) Stability Analysis of Parametrically Ex-cited Systems using the Energy-Growth Exponent/Coefficient. International Journal of Structural Stability and Dynamics, 16, Article ID: 1750018.
[19] 王庄. 任意截面水槽液体二维参数晃动研究[D]: [博士学位论文]. 上海: 同济大学, 2014.

为你推荐