Gravity-Gradient-Induced Vibration of a Large Spacecraft with Axially Deployable Appendages

Purpose: Large sun-facing deployable appendages are widely used in ultra-large spacecrafts. The effects of gravity gradient on the dynamic characteristics are always neglected due to the small size of traditional spacecrafts. Therefore, the dynamics of an axially deployable large flexible sun-facing spacecraft under gravity gradient are studied in this paper. Methods: Firstly, the extended Hamilton’s principle is utilized to derive the transverse vibration equations of the deployable appendages under a floating coordinate frame. Two kinds of deployment strategies including constant-speed deployment and practical deployment are considered. Then, the assumed mode method and Galerkin’s method are adopted to solve the governing equations. Finally, the numerical results of transverse vibration are obtained by using the symplectic Runge–Kutta method. Results: With the decrease of deploying time, the amplitude of flexible vibration decreases in the deploying process but increases in the long-time evolution for the two deploying strategies. Meanwhile, the higher orbital altitude leads to a lower vibration amplitude. In addition, the practical deploying strategy will lead to larger displacement than the constant deploying strategy even though it can avoid speed residual automatically. Conclusions: The results show that the gravity gradient force has a significant influence on the transverse vibration both in the deployment process and the long-time evolution. The results will provide constructive guidance for vibration control.