圆柱贮箱液体非线性晃动的多维模态分析方法  

Multidimensional Modal Analysis of Liquid Nonlinear Sloshing in Right Circular Cylindrical Tank

作　　者：余延生[1] 马兴瑞 王本利[1] 

机构地区：[1]哈尔滨工业大学卫星技术研究所,哈尔滨150001 [2](2.中国航天科技集团,北京100830

出　　处：《应用数学和力学》2007年第8期901-911,共11页Applied Mathematics and Mechanics

基　　金：国防十五预研资助项目(41320020301)

摘　　要：将Faltinsen等提出的多维模态理论应用到求解圆柱贮箱液体非线性晃动问题中.根据Narimanov-Moiseiev的三阶渐近假设关系,通过选取主导模态以及确定它们的阶次关系,将一般形式的无穷维模态系统降为五维渐近模态系统,即描述自由液面波高的广义坐标之间相互耦合的二阶非线性常微分方程组.通过对这个模态系统的数值积分,得到了与以前的理论分析和实验结果相吻合的非线性现象.研究结果表明,多维模态方法是用来求解液体非线性晃动动力学的一个很好的工具.在我们的下一步工作中,将继续发展这种方法,用来研究更为复杂的晃动问题.The multidimensional modal theory proposed by Faltinsen, et al （2000） was applied to solve liquid nonlinear free sloshing in right circular cylindrical tank. After selecting the leading modes and fixing the order of magnitudes based on the Narimanov-Moiseiev third order asymptotic hypothesis, the general infinite dimensional modal system was reduced to a five dimensional asymptotic modal system （the system of second order nonlinear ordinary differential equations coupling the generalized time dependent coordinates of free surface wave elevation）. The numerical integrations of this modal system discover most important nonlinear phenomena, which agree well with both pervious analytic theories and experimental observations. The results indicate that the multidimensional modal method is a very good tool for solving liquid nonlinear sloshing dynamics and will be developed to investigate more complex sloshing problem in our following work.

关 键 词：圆柱贮箱 非线性自由晃动 多维模态方法 渐近模态系统 耗散效应 

分 类 号：O353.1[理学—流体力学]