Complicated nonlinear oscillations caused by maneuvering of a flexible spacecraft equipped with hinged solar arrays

We present a general methodology for the nonlinear dynamical modeling of a three-axis stabilized spacecraft equipped with flexible solar arrays. The large-span multi-panel solar arrays are modeled as flexible thin plates that are connected to the rigid central body of the spacecraft by means of nonlinear flexible hinges. We construct a low-dimensional yet accurate dynamical model by using a Galerkin expansion in terms of global modes of the system that we compute first by using the Rayleigh–Ritz method. The hinged connections between the rigid and flexible parts of the system are imposed employing Lagrange multipliers. The model is used to study the spacecraft response triggered by various maneuvering scenarios. We in particular focus on the coupling between vibrations of the flexible components and the rigid motion of the spacecraft induced by hinge nonlinearities during these orbital and attitude maneuvering operations. In all cases considered, it is found that four global modes are sufficient to accurately compute the system’s response. We also observe other complicated nonlinear dynamical phenomena, such as hysteresis and superharmonic resonance that may be of concern in spacecraft design. Our modeling approach can be applied to other multibody systems directly.