Abstract: To investigate the thermally induced vibration problem of solar sail in tandem caused by the alternating thermal environments during the period of entering and exiting the Earth’s shadow, a rigid-flexible-thermal coupling dynamic modeling method is proposed. Firstly, the dynamic variational equations and heat conduction equations of the flexible solar plate are derived, and then the multi-physics coupling dynamic model of solar sail in tandem is established based on forward recursive formulation, considering the influences of the attitude angles of central rigid-body and solar plates, elastic deformations, and the Earth’s shadow on the solar radiation heat flux. The use of the joint relative coordinates and the modal coordinates can reduce the system degrees of freedom, such that the computational efficiency is improved a lot. Simulation results indicate that when the spacecraft enters and leaves the Earth’s shadow, significant vibrations of the central rigid-body angular velocity and the solar plate deflection are induced, and that the vibration amplitude decreases with the increase of the convective heat transfer coefficient. The stable temperature after the attenuation of the vibration approaches the environment temperature. The proposed method reveals the influence of multi-source coupled vibration on the stability of system motion, which lays a foundation for the attitude control of solar sail in tandem in variable temperature environment.

Key words: solar sail in tandem, entering and exiting the Earth's shadow, rigid-flexible-thermal coupling, dynamics, forward recursive formulation