Dynamic analysis of large–scale flexible systems for free—free space structures

Based on the theory of modified constrained modal methods, in which the constraints can be defined on arbitrary points of the system or subsystems, a simplified method for free–free modal analysis is presented in this paper. Using this method, the rigid–body motion of structures can be eliminated by an arbitrary selection of the constraints. The constrained structures then become either statically determinate or indeterminate. Therefore, the inverse of the stiffness matrix of the constrained system exists. The modelling of the finite–element method can be verified or corrected via numerical or experimental results involving statically constrained and normal modes of the constrained system. Hence, the modal analysis of the free–free system can be easily performed using modal information from numerical or experimental results. The traditional modal experimental method of hanging with flexible strings can be changed, and the effective experimental methods can be chosen in accordance with the real condition of the test structure and site. To verify the effectiveness of this approach, several examples of a free–free rocket are presented. From the results, it can be clearly seen that the presented method is practical for modal analysis. Additionally, it is suitable for large space structures, especially those involving the assemblage of large flexible space structures. For such a system, generally, the components can be tested on–ground but the assemblage cannot, as it can only be deployed in space.