Abstract:

 A global modal dynamic model is proposed for a spacecraft with a small center rigid body and a single large flexible structure. The global rigid body motion and the global flexible deformation are described in a unified form. Based on the Hamilton principle, the global modal dynamics equations are derived, and the calculation method of the unconstrained modal frequencies and modal shapes is derived by the Rayleigh-Ritz method. The accuracy of the global modal dynamics model is verified by the simulation and experiments. Compared with the finite element model, the variation of the unconstrained modal frequency along with the mass and the inertia ratios is analyzed. The results show that the global modal dynamic model describes the unconstrained modal frequency more accurately. The maximum error of the first modal frequency is 0.003 Hz. The dynamic response is accurately described with the maximum error of 2.6%. The experimental system is constructed, and the measured unconstrained modal frequencies are consistent with the theoretical analysis and the finite element simulation results. It shows that the theoretical model accurately describes the variation of the unconstrained modal frequency with the rigid-flexible coupling characteristics.

Key words: Global modal dynamic model, Global modal shapes, Unconstrained modal frequencies, Rayleigh-Ritz method