Computational Methods Of Non-proportionally Damped Structures With Applications To Satellite Design

With dynamic problems associated with the damped steructure design in morden spacecraft as a background, aiming at the multiple contents of structural dynamic characteristics design of spacecraft from launch to flight in orbit, and the characteristics of high local damping of modern spacecraft structure, this dissertation systematically studies the computational methods of damped structural systems and their applications to the design of spacecraft structure. Considering the current research status of the computational methods of damped structural systems, the dissertation focuses on the methods of frequency response analysis, transient response analysis, component mode synthesis, and dynamic modeling and model reduction of flexible spacecraft. Some new or improved methods are proposed, which can be more effective in the application to the design of spacecraft structures. Main contents of this are as the following.Aiming at the need for design of vibration attenuation/isolation structure for spacecraft during launch, the method of frequency response is studied. For the design of whole-spacecraft vibration attenuation/isolation structure, the simplified equivalent equation for vibration of adapter is firstly established by using the concepts of modal participation factor and modal effective mass. The equation is computational efficient and is emphasized on the design parameters of the structure when it is used to analyse the dynamic characteristics of the structure near its main resonance. Meanwhile, the limitation of the simplified equivalent equation is pointed out. For the frequency response analysis of general damped structures, iterative methods are studied. Based on the Jacobi method and the error analysis of iteration process, the variably preconditioned iterative method is proposed and the convergence speed is accelerated accordingly.For the structure design of attenuating transient response of large deployed structure induced by orbital maneuver of spacecraft, the study of transient response analysis method is carried out. Firstly, by using the decoupling property of complex modes, the complex mode superposition method is studied. The modal convergence performances of complex modes and real modes are compared. The computational efficiency of complex mode superposition method and modal direct integration method are also compared. Whereafter, a semi-analytical pseudo-force mode superposition method is developed by using the analytical solution of mode superposition method for proportionally damped structure and the idea of transforming non-proportional damping to proportional damping of pseudo-force iterative method. Based on this method, for the design of structure that can be partitioned into substructures and connection element, the substructure synthesis method is developed. The method is emphasized on the design of connection element of the structure, and is computationally efficient.For the process from component design to system design of large and complex spacecraft, the component mode synthesis(CMS) method is studied. Especially for non-proportionally damped structure, an improved state space free interface component mode synthesis method is developed. The improved method bases on the state space residual flexibility and residual attachment modes, but the dynamic terms of truncated modes are added to them, so that the inertia and damping effects are kept in the modal transformation. The method achieves more accuracy and efficiency than the original method. To quantificationally rank the importance of modes, a criterion for the selection of retained complex modes is established on the frequency average of the FRF errors. A practical numerical procedure is given for the calculation of some important modal matrices of the method, so that the method is applicable to large engineering model.For the coupled dynamic characteristics design of spacecraft structure and attitude control, the methods of dynamic modeling and model reduction of damped whole-flexible spacecraft is studied. For general whole-flexible spacecraft, by modeling the elastic motion with multiple level fixed interface CMS method, a system equation of motion with simple form is established. The equation is convenient to analyse and design the parameters of the structure in modal space. Based on this equation, with special focus on the damped flexible connection structure of the spacecraft, a system equation of motion that contains the physical parameters of the connection structure is established. This equation is more appropriate for the analysis and design of the connection structure than the former equation. For collocated and noncollocated sensor and actuator, the transfer function of central body attitude and payload attitude are established, respectively. The effects of parameters of structure on the attitude dynamics are analyzed. For model reduction, a component mode reduction method based on transfer function is firstly developed with special consideration of the property of non-proportional damping. After that, the internal balanced model reduction method is improved so that certain physical coordinates of the system equation can be retained in the reduced model. This improvement makes the reduced model possess the same physical meaning of the original system equation, thus offers convenience for the coupled design and analysis of structure and control of spacecraft.For the design of damped spacecraft structure, the dissertation systematically carries out a series of studies of structural dynamic computational methods, proposes or improves some computational analysis methods. The dissertation is of certain value for the design of spacecraft structure.