A finite strain beam formulation. The three-dimensional dynamic problem. Part I

Ultra-kilometre and super-flexible spacecraft are the important development trends in the future. Classical multi-body dynamics and structural dynamics analysis theory have some limitations in dynamic modelling and solution of large deformation structures. In this paper, an improved dynamic stiffness method (DSM) is proposed to deal with the dynamical modelling and solution of ultra-kilometre spacecraft. The method retains the high accuracy and efficiency of the original DSM in dealing with continuous dynamical systems and breaks through the limitations of the original method in dealing with large deformation structures by introducing equivalent linearization techniques. Results show that the modal frequencies and mode shapes in this paper agree well with finite element solutions, and the maximum deviation is less than 1%; Besides, with the increase of spacecraft length, the structure has entered the nonlinear stage from the linear stage, the fundamental frequency of the structure will be lower than 0.001Hz, and the influence of structure length, density, and the mass of additional cabins on natural frequencies is less significant than that in linear stage. The proposed dynamic analysis framework can be further employed in the dynamic response and vibration control problems of super large spacecraft.