低重环境下旋转轴对称贮箱内液体晃动研究

针对低重环境下旋转轴对称贮箱自由晃动和受侧向、纵向激励时的箱内液体晃动，用变分原理推导了基于低重环境下静液面形状的液体晃动的积分形式的动力学控制方程，由拉普拉斯方程得到用高斯超几何级数解析表达的速度势和波高，进而得到液体晃动的模态运动方程。分析了球形贮箱和Cassini贮箱内液体自由晃动基频，贮箱受侧向激励时液体晃动波高振幅、晃动对贮箱产生的晃动力和力矩、晃动的等效力学模型，以及贮箱受纵向激励时的晃动波高振幅、可能出现的参激共振问题。

Research on Sloshing in Axisymmetrical Containers Under Low Gravity

For free sloshing and forced sloshing excited in lateral and axial direction in axisymmetrical container under low gravity, the variational principle is applied to derive the dynamics equation of the sloshing liquid in integral form based on shapes of hydrostatic surface. Analytical expressions of velocity and surface displacement are obtained by Laplace equation, and then modal equation is obtained. For both spherical container and Cassini container, when the container is under lateral force, the basic frequency of sloshing, amplitude of liquid surface displacement, slosh force and slosh moment of the sloshing liquid exerted to the container, equivalent mechanical model of the sloshing are analyzed. When the container is under axial force, amplitude of liquid surface displacement and possible parametric resonance problem are also analyzed.