Gravity-gradient-induced transverse deformations and vibrations of a sun-facing beam

Ultralarge sun-facing structures are adopted in many large spacecraft, such as solar power satellites. The in-plane transverse steady deformations and vibrations of a large sun-facing beam induced by the gravity gradient are studied considering geometric nonlinearity. First, the problem is divided into a static problem when the beam maintains a constant pitch attitude angle, and a dynamic problem when the beam maintains a sun-facing attitude. For the static problem, three static models are established to study the gravity-gradient-induced steady deformations. An analytical solution is obtained in small deformation cases, which reveals the influences of the parameters of the orbit and the beam on the steady deformations. The influence mechanism of the geometric nonlinearity in large deformation cases is studied using geometrically exact beam theory and absolute nodal coordinate formulation. For the dynamic problem, four dynamic models are built to investigate the gravity-gradient-induced vibrations. According to the numerical results, a novel resonance is induced by the gravity gradient and the geometric nonlinearity when the lowest natural frequency of the beam is approximately four times the orbital frequency in circular orbit, which is found for the first time. The resonance must be considered seriously in structural design of large sun-facing structures.