Study On Nonlinear Dynamics Of A Liquid-filled Spacecraft With Flexible Appendages

Modern large spacecraft is a typical'rigid-liquid-flexible-control'complex coupling system. The coupling dynamics is a necessary problem for the course correction and the attitude maneuver, and it can also cause the nonlinear sloshing of propellant. However, these effects can influence the controllability of the spacecraft. Considering the nonlinear sloshing of liquid, the coupling dynamics of the'rigid-liquid-flexible'system is studied systematically in this dissertation.The nonlinear dynamics equations of liquid-filled rectangular tank with flexible appendages subjected to horizontal and pitch excitation are deduced by H-O principle. At the same time, the nonlinear boundary condition of liquid is considered. The wave height function is applied and the potential function is introduced, here the stocks potential function is utilized to describe the coupled moving boundary when the rigid tank is forced in pitch. Then Galerkin's method is used to discrete the dynamics equations into ordinary differential equations.The study on the nonlinear dynamics of the rigid-liquid coupling system with the liquid in a rectangular tank under horizontal excitation has been carried out. Given the movement or the motivation of rigid, the natural frequencies are formulated, and the primary resonances of the rigid-liquid coupling system are studied analytically. As the height of filled liquid increases, the amplitude-frequency response changes from soft character to hard character. Further investigation reveals that the critical height is determined by the spacecraft initial wet-dry ration. Comparison with the numerical simulation validates the analytical solutions.The nonlinear dynamics of a liquid-filled rectangular tank with flexible appendages subjected to pitch excitation is studied. Given the exciting torque, the natural frequencies of'rigid-liquid-flexible'coupling system are formulated that vary with the position of liquid fuel and the gravity acceleration. Afterwards, the primary resonances of the rigid-liquid-flexible coupling system are studied analytically, the amplitude-frequency response changes with the torque and the position of fuel. It is found that the amplitude-frequency response changes from soft character to hard character with the height of filled liquid increasing. Further investigation reveals that the critical height is determined by the spacecraft initial wet-dry ration, the fuel position and the ratio of solid to liquid moment of inertia. Analytical solutions are verified by numerical simulations.When the attitude of spacecraft is controlled, the coupling dynamics of the pitching of spacecraft, the sloshing of liquid fuel and the vibration of flexible appendages are investigated. The natural frequencies are analyzed and the 1:1:1 internal resonance of the'rigid-liquid-flexible'coupling system is studied analytically. It is found that the resonance of rigid and flexible appendages is similar to the 1:1 internal resonance of'rigid-flexible'coupling system, and the coupling of liquid is complicated that is determined by the character of liquid fuel. Comparison with the numerical simulation validates the analytical solutions.The static bifurcation analysis is given by singularity theory. The hysteresis bifurcation is found in the coupling system, which is represented by the amplitude-frequency response switches between soft and hard characters at the critical height of liquid fuel. Finally, the dynamic bifurcation is investigated briefly.