摘要:
以微重环境下部分充液圆柱贮箱受横向简谐激励作用时液面小幅晃问题为研究背景，利用一阶Bessel函数构造了满足该问题中存在的Laplace方程和边界条件的速度势和波高函数。由于微重下的自由静液面呈复杂的“弯月形”，这使得要求速度势和波高函数精确满足自由液面处的边界条件存在一定的困难。在前人研究的基础上，运用第二类边界条件下的Bessel函数展开法，对微重下的自由液面条件进行精确处理，得到晃动速度势和波高函数的一种半解析法。进一步推导了晃动力和晃动力矩的求解式，并基于等效准则建立了液体自由晃动的弹簧-振子等效力学模型。通过数值计算和对比，验证了文中方法的准确性，并研究了等效力学模型中的参数与Bond数之间的变化规律。
Abstract:
The present study is based on the problem of liquid sloshing with small amplitude in a partial filling cylindrical cavity under harmonic excitation and low-gravity environment. Liquid sloshing velocity potential and wave height function, which are the problems belongs to Laplace equation and boundary conditions, were formulated using Bessel expansion method in this paper. Since the phenomenon o “crescent” of free surface due to low-gravity, the solving process of velocity potential and wave height become more difficult. And the study of characters of liquid sloshing with small amplitude in a cylindrical cavity in low-gravity condition was presented. Based on the consideration of surface tension and the foundation of the predecessor studies, the analytical solution of Laplace equation was calculated after the liquid velocity potential and wave height function were formulated firstly. Then the liquid sloshing force and sloshing moment ware given, and frequency of liquid free sloshing and velocity potential were computed. The equivalent mechanical model of mass-spring was established by mechanical equivalent principle. The present method was certified by comparison between numerical numerical solution and analytical solution. The relationship between parameters of the equivalent mechanical models and Bond number were revealed.