Coupling dynamic analysis on T-shaped spatial rigid-flexible combination structure

T-shaped rigid-flexible combination structure is one of the most common space structure forms. Modeling and analyzing on T-shaped spatial rigid-flexible combination structure are challenging due to two types of coupling effects: one is the orbit-attitude-flexible vibration coupling and another is the rigid-flexible structural coupling. In this paper, the strong coupling dynamic problem involved in the on-orbit operation of the T-shaped spatial structure is considered, which is formulated as an orbit-attitude-flexible vibration coupling dynamic model based on the Hamiltonian variational principle firstly. Inspired by the merit of the symplectic Runge-Kutta method in precisely preserving the global conservation quantities of the system’s planar motion and the advantage of the generalized multi-symplectic method in excellently reproducing the local dissipative characteristics of the flexible component, a structure-preserving iteration method is developed to investigate the coupling dynamic behaviors of the T-shaped spatial structure. Using the structure-preserving iteration method, the influences of damping coefficients and initial conditions (including the initial attitude angle and the initial orbital radial velocity) on the dynamic behavior of the model are investigated in detail. From the numerical results, it can be found that, compared to the damping effect, the initial orbital radial velocity has a more significant impact on the evolutions of the orbital radius and of the attitude angle. According to Kepler’s second law, to further verify the validity of the iteration method, the areas swept by the orbital radius corresponding to the geometric center and the fixed point of the T-shaped structure per unit time are presented in the numerical simulation respectively. It can be found that the areas swept by the orbital radius corresponding to the geometric center (or the fixed point) of the T-shaped structure per unit time are almost invariable, which verifies the validity of the numerical iteration method developed in this paper indirectly. The tiny variations of swept areas result from the influence of the gravitational gradient on the orbit-attitude-vibration coupling dynamic behaviors of the large-scale spatial structure. The main contribution of this work is providing an effective numerical iteration method to reveal the coupling dynamic behaviors of large spatial combination structures, which is expected to provide real-time dynamic response results for the real-time feedback control of large spatial structures.