求旋转椭球形贮箱内液体小幅晃动基频的一种新方法  

SOLVING THE FIRST EIGENFREQUENCY OF LIQUID SLOSHING IN ELLIPSOIDAL TANKS USING ANALYTICAL METHOD

作　　者：杨旦旦[1] 岳宝增[1] 

机构地区：[1]北京理工大学宇航学院力学系,北京100081

出　　处：《动力学与控制学报》2011年第3期249-252,共4页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11072030)~~

摘　　要：针对旋转椭球形贮箱内液体小幅晃动,建立了原点位于与箱于箱内静液面接触线处相切的圆锥的顶点的球坐标系,用高斯超几何级数解析表达速度势和波高的模态函数,通过伽辽金方法把变分方程转变为一个标准的特征值问题形式的频率方程,求解了不同尺寸比例的椭球形贮箱在不同的充液比和不同的Bond数情况下液体小幅晃动的基频,把所求结果和已有的理论和实验结果进行对照.A spherical coordinates was built, whose origin is at the top of the cone tangent to the container at the contact line of the meniscus with the container wall. The velocity potential and the liquid surface displacement were determined analytically in terms of the Gauss hypergeometric series. The variational principle was transformed into a frequency equation in the form of a standard eigenvalue problem by the Galerkin method. The first eigenfrequency solved by this method was compared with that from other theoretical and experimental methods. Large calculations prove that this method is effective in solving the small amplitude sloshing eigenfrequency of liquid.

关 键 词：变分原理 高斯超几何级数 晃动基频 

分 类 号：V414.1[航空宇航科学与技术—航空宇航推进理论与工程]