含板类柔性附件的充液航天器动力学研究

对含有板类柔性附件和曲壁轴对称充液储腔的复杂航天器系统进行动力学建模和耦合机理研究。首先，采用Kirchhoff-Love薄板理论对航天器的板类柔性附件进行研究，通过D’Alembert原理得到柔性附件的振动方程，运用模态假设法将混合方程转换为常微分方程。其次，通过推导充液航天器储腔内任意点的运动，得到储腔液体的牵连速度势函数，采用Gauss超几何级数得到液体相对速度势函数的解析形式，通过Hamilton变分原理推导液体晃动的运动方程，以及液体速度势函数模态系数的控制方程。最后采用准坐标Lagrange方程得到耦合航天器系统的状态方程，通过数值仿真校验系统动力学模型的有效性。研究结果表明，刚性平台、液体、柔性附件的相互耦合效应使得航天器系统存在复杂动力学行为，在复杂航天器系统动力学建模过程中需要充分考虑液体晃动和柔性附件振动的影响，柔性附件的安装位置对于耦合航天器系统的动力学行为也有着重要影响。

Research on Dynamics of Liquid Filled Spacecraft Carrying Plate Type Flexible Appendages

The dynamic behavior and rigid-liquid-flex coupling effect of the complex spacecraft system carrying plate-type flexible appendages and liquid-filled arbitrary axisymmetrical tanks with curved wall are investigated in this paper. The plate-type flexible appendages attached to spacecraft are discussed by the Kirchhoff-Love plate theory, and the coupled vibration equations of the flexible appendage are drawn from the D’Alembert principle. By the spatial discretization and truncation, the differential equations reduce to the nonlinear discretized state equations, which are convenient for numerical calculations. The carrier velocity potential function of the liquid is obtained by the motion equation of a representative point in the tank, while the relative velocity potential function can be expressed by the Gauss hypergeometric series. By using the Hamilton’s variational principle, the governing equations of the liquid sloshing coupled with the spacecraft motion and modal coefficients of the relative velocity potential function can be derived. The motion equations of the coupled spacecraft system are deduced by using the Lagrange’s equations in terms of general quasi-coordinates. The efficiency of the dynamical model of the coupled spacecraft system is examined through numerical simulations. The results indicate that the rigid-liquid-flex coupled effect of the spacecraft system exhibits complex dynamical behaviors, the effects of the fuel sloshing and the flexible appendage vibration should be fully considered in the process of dynamic modeling and analysis of complex spacecraft system. The installation position of the flexible appendage has great influence on the dynamic behavior