基于多尺度方法的平动圆柱贮箱航天器刚——液耦合动力学研究

以充液航天器为工程背景,借助多尺度方法研究刚--液耦合动力学系统非线性动力学特性.利用多维模态方法,将描述横向外激励下圆柱贮箱中液体非线性晃动的自由边界问题转换为液体模态系数相互耦合的有限维非线性常微分方程组.推导液体晃动产生的作用于贮箱壁的晃动力和晃动力矩的解析表达式,进而建立航天器刚体部分平动和液体晃动耦合的非线性动力学方程组.应用多尺度方法对刚--液耦合系统的动力学特性进行解析分析,通过固有频率的特征方程求解耦合系统固有频率,推导外激励频率接近耦合系统第一阶固有频率时液体晃动稳态解的幅值频率响应方程.结合数值方法,研究了液体晃动稳态解的幅值频率响应曲线和激励--幅值响应曲线.结果表明, 随充液比变化,液体晃动稳态解的幅值频率响应曲线会发生软、硬弹簧特性转换现象和"跳跃"现象;幅值频率响应曲线的软、硬弹簧特性转换点受重力加速度和弹簧刚度系数影响;以上所得研究结果表明,考虑非线性效应时的刚--液耦合系统动力学特性与传统的线性系统模型所显示的动力学特性具有本质区别.本文的研究工作对进一步分析充液航天器刚--液耦合非线性动力学特性具有重要参考价值. 

STUDY ON THE RIGID-LIQUID COUPLING DYNAMICS OF A CYLINDRICAL-TANK SPACECRAFT IN TRANSLATION BASED ON MUTI-SCALE METHOD1)

Based on the engineering background of liquid-filled spacecraft, the nonlinear dynamic characteristics of rigid-liquid coupling dynamic system are studied by means of multi-scale method. By using the multi-dimensional modal method, the free boundary problem describing the nonlinear sloshing of the liquid in a cylindrical tank under horizontal excitation is transformed into a finite dimensional nonlinear ordinary differential equation system in which the coupled liquid sloshing modal coefficients are assumed as state variables. The analytical expressions of sloshing force and sloshing moment acting on the tank wall caused by liquid sloshing are derived, and then the coupled dynamic equations for the spacecraft translation and liquid fuel sloshing are obtained. The dynamic characteristics, especially the first-order primary resonance, of rigid-liquid coupling system are analyzed by multi-scale method. The natural frequency of rigid-liquid coupling system is solved by the characteristic equation of natural frequency, and the amplitude-frequency response equation of liquid steady-state solution is derived when the external excitation frequency is close to the first natural frequency of coupling system. Combined with the numerical method, the amplitude-frequency response curve and excitation-amplitude response curve of liquid steady state solution are studied. The results show that with the change of liquid filling ratio, the amplitude frequency response curve of liquid steady state solution will exhibit soft, hard spring features conversion phenomenon. In addition to that, a `jump' phenomenon was also observed during this kind of soft-hard spring feature conversion. Furthermore, it is shown that the soft and hard spring characteristic conversion point of amplitude frequency response curve will be affected by gravity acceleration and spring stiffness coefficient. The above results show that the dynamic characteristics of the rigid-liquid coupling system considering the nonlinear effect are essentially different from those shown by the traditional linear system model. The investigations presented have important reference value for further analysis of rigid-liquid coupling nonlinear dynamic characteristics of liquid-filled spacecraft.