To accomplish long-duration and complex orbit flight missions, next-generation spacecrafts need to carry large flexible structures and high-capacity liquid fuel tanks. The nonlinear coupling problems between rigid body motion, liquid sloshing, and flexible structure vibrations become particularly significant during spacecraft maneuvering and control processes. A dynamic model for rigid-liquid-flexible coupling systems was presented, to first calculate the vibration of the flexible structure with the Kirchhoff-Love plate theory and the finite element methods. Then the flow theory was employed to model liquid fuel sloshing, and finally the overall dynamic model for the coupling system was derived with the Lagrange method. The study reveals the coupling dynamic interactions between rigid body motion, liquid sloshing, and flexible structure vibrations. The proposed modeling approach for rigid-liquid-flexible coupling spacecrafts was validated by comparison with published experimental and analytical results. The coupling analysis of complex, liquid-filled spacecrafts with large, flexible structures shows that, the finite element method can accurately capture the dynamic responses of high-frequency modes of the flexible structures. Additionally, due to the low-frequency characteristics of these large and complex space structures, the coupling effects with liquid fuel sloshing become even more pronounced.
Yan et al. (2026) studied this question.