用多维模态理论分析航天器贮箱液体有限幅晃动力

首次将多维模态理论应用到求解航天工程中常见的圆柱贮箱液体非线性晃动问题中。针对贮箱作水平横向运动，根据Narirrmnov-Moiseev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5维渐近模态系统。在模态系统基础之上，推导出了液体作用于贮箱壁的力的简洁表达式。数值仿真结果表明，相对于线性晃动理论结果，有限幅晃动液体将对贮箱壁产生更大的横向作用力，同时对贮箱底部还作用有明显的纵向力。可将此公式应用于工程实际问题中部分充液贮箱液体有限幅晃动力的估算。

Calculation of Liquid Finite Amplitude Sloshing Force on Spacecraft Tank by Multidimensional Modal Theory

The muhidimensional modal theory is applied to solve liquid nonlinear sloshing in right circular cylindrical tank for the first time. After selecting the leading modes and fixing their order of magnitudes according to Narimanov - Moiseev third order asymptotic hypothesis, the general infinite dimensional modal system is reduced to a five dimensional asymptotic modal system for translational excited tank. Based on the modal system, the compact formula of liquid force on the tank is derived. The numerical simulations indicate that the finite amplitude sloshing liquid produces larger translational force on the tank and it produces axial force on the tank bottom at the same time in contrast to linear sloshing theory. The compact formula can be used in the approximate calculation of liquid finite amplitude sloshing force on partially filled tank in engineering practice.