带多充液圆柱贮箱航天器刚-液耦合动力学研究

文中以在低重环境下带多充液圆柱贮箱刚性航天器中刚-液耦合方程的建立和求解为主要研究目的。推导航天器中充液圆柱贮箱内任意点的牵连运动方程，根据壁面边界条件给出了贮箱内液体牵连晃动势的表达式；利用第二类边界条件下的傅立叶-贝塞尔级数展开法对低重力环境下的弯曲自由液面处的复杂动力学边界条件进行处理，建立以液体相对晃动势的模态坐标和晃动波高的模态坐标为状态向量的液体耦合晃动力学方程，通过积分分别得到了耦合晃动力和耦合晃动力矩的解析式；运用准坐标系下的拉格朗日方程建立以航天器主刚体姿态坐标和轨道坐标为状态向量的刚体耦合运动动力学方程，进一步联立上述耦合方程得到航天器整体系统的刚-液耦合动力学状态方程；最后，编制出适用于带多充液圆柱贮箱航天器内刚-液耦合动力学计算的模块化计算程序，通过计算实例验证所编程序的准确性的同时，研究了携带多充液箱航天器系统贮箱布局、外激励方式对航天器刚-液耦合系统动力学特性的影响。

Study on the Rigid Liquid Coupled Dynamics for Spacecraft with Multiple Partially Liquid filled Cylindrical Tanks

In this paper, the solution and model of rigid-liquid coupled dynamics state equations of spacecraft with multiple liquid-filled cylindrical tanks in low-gravity environment are mainly studied. Firstly, the carrier motions equations of a representative point in liquid-filled cylindrical tank in spacecraft are deduced, and the carrier potential function equations of liquid in the tank are given according to wall boundary conditions. The complex dynamic boundaries conditions on curved free-surface under low-gravity environment are transformed to general simple differential equations by means of Fourier-Bessel series expansion method. The dynamic state equations for coupled rigid-liquid spacecraft system are presented, in which, the state vectors of equations consist of the modal coordinates of relative potential function and the modal coordinates of wave height. The formulas of coupled sloshing forces and coupled sloshing moments are obtained by integrating. Then the dynamic state equations of coupled motion of main body are deduced using the Lagrange’s equations in terms of general quasi-coordinates. Correspondingly, the rigid-liquid coupled dynamics state equations of whole systems of spacecraft are obtained. Lastly, a modularized calculation code based on the present method is programmed. The influences of layouts of multi-tanks and driving mode on the dynamics performance of coupled rigid-liquid system are studied. Consequently, the validity of the presented methods and the computer program are verified.