充液挠性航天器俯仰运动 1:1:1 内共振动力学分析

采用已推导的俯仰运动矩形贮箱受控刚-液-弹耦合系统在外力矩作用下的耦合动力 学模型，在刚体上加入控制项，详细分析了系统固有频率的精确解与近似解. 应用多尺 度法对耦合系统1:1:1内共振进行解析分析，与数值解比较验证解析解的正确性. 通过近 似解析分析得到刚-液-弹之间的耦合作用机理：1) 液深影响整个系统的软硬特性，当液体发 生软硬特性转化时，处于液体原多值频率区域的刚体和弹性体幅频曲线分支峰值会减弱，且 具有相同的特性转化趋势；处于液体新多值频率区域的刚体和弹性体幅频曲线分支峰值会增 强，且具有相反的特性转化趋势. 2) 刚体和弹性体幅频曲线的峰值均在以受控刚体和弹性体 为主的耦合系统固有频率处，以液体为主固有频率激励，刚体和弹性体振幅较小.

ANALYTIC STUDY ON 1:1:1 INTERNAL RESONANCE NONLINEAR DYNAMICS OF A LIQUID-FILLED SPACECRAFT WITH ELASTIC APPENDAGES

The coupling dynamics of the pitching of spacecraft, the sloshing of liquid fuel and the vibration of elastic appendages are investigated. The coupling dynamics equations deduced by using H-O principle are adopted. The attitude of spacecraft is controlled. The multiple scale method is proposed to analyze the 1:1:1 internal resonance of the rigid-liquid-elastic coupling system. The effect mechanism of the coupling dynamics are obtained by the analytic study. The amplitude-frequency response switches between soft and hard spring type with liquid depth. The resonances of the spacecraft and elastic appendages occur at both of the natural frequencies of spacecraft and elastic appendages.