An approach is proposed to obtain the global analytical modes (GAMs) and establish discrete dynamic model with low degree-of-freedom for a three-axis attitude stabilized spacecraft installed with a pair of solar arrays. The flexible spacecraft is simplified as a hub–plate system which is a typical rigid-flexible coupling system. The governing equations of motion and the corresponding boundary conditions are derived by using the Hamiltonian principle. Describing the rigid motion and elastic vibration of all the system components with a uniform set of generalized coordinates, the system GAMs are solved from those dynamic equations and boundary conditions, which are used to discretize the equations of motion. For comparison, another discrete model is also derived using assumed mode method (AMM). Using ansys software, a finite element model is established to verify the GAM and AMM models. Subsequently, the system global modes are investigated using the GAM approach. Further, the performance of GAM model in dynamic analysis and cooperative control for attitude motion and solar panel vibration is assessed by comparing with AMM model. The discrete dynamic model based on GAMs has the capability to carry out spacecraft dynamic analysis in the same accuracy as a high-dimensional AMM model. The controller based on GAM model can suppress the oscillation of solar panels and make the control torque stable in much shorter time.

A novel nonlinear dynamic modeling approach is proposed for the T-shaped beam structures widely used in the field of aerospace. All of the geometrical nonlinearities including the terms in the deformation of the beams, the terms at the connections, and the free ends of beams are considered in the dynamic modeling process. The global mode method is employed to determine the natural frequencies and global mode shapes of the linearized system. The validity and accuracy of the derived model are verified by comparing the natural frequencies obtained with those calculated from FEM. Adopting the Galerkin truncation procedure, a set of reduced-order nonlinear ODEs is obtained for the structure. A study on the variation of dynamic responses taking the different numbers of global modes into account is performed to determine the number of modes taken in nonlinear vibration analysis. A comparison between the responses of the system with linear or nonlinear matching and boundary conditions is given to evaluate the importance of neglecting and reserving the nonlinear terms in matching and boundary conditions. It is shown that ignoring the nonlinear terms in both matching and boundary conditions may significantly alter the responses while developing the discretized governing ODEs of the structure.