Dynamic Equivalent Modeling And Vibration Control Of Large Space Structures

With the development of space technology, spacecraft structures are increasingly showing the characteristics of large-scale and lightweight. In order to ensure the good dynamic properities of these large space structures, and achieve the high precision, high reliability requirements of space mission, it is necessary to predict dynamic responses in their design stage. Furthermore, while working in space, large space structures will be inevitably affected by a variety of interferences such as thermal gradient, attitude adjustment of spacecraft, space debris impact, etc. Once excited, the induced dynamic response will be very difficult to decay by itself. In order to ensure the working performance of spacecraft structures, and keep the safty of satellites and space stations, the vibration control of spacecraft structures must be attentioned.This paper is aimed at dynamic equivalent modeling of two kinds of large deployable space structures-large deployable mesh antennas and inflatable parabolic membrane reflectors. Moreover, a study on vibration control of space flexible structures based on the distributed parameter system control theory is carried out. The contents are as follows:(1) The model reduction and continuum equivalent modeling of hoop truss structure are studied. For the planar truss element in the hoop truss structure, considering its in-plane and out-of-plane deformations at the same time, it would be equivalent to a spatial anisotropic beam based on the energy equivalence principle, and the stiffness parameters and mass parameters of the equivalent beam model is obtained in the form of analytic formulas. For anisotropic beam model, the element stiffness matrix and the element mass matrix are derived, and then the equivalent one-dimensional hoop beam structure is analysised by the finite element method. Under the condition of ignoring the anisotropy of the equivalent beam model, the hoop truss structure is simplified as a standard elastic ring. The validity of the equivalence method, as well as the feasibility of the simplified model of the ring is validated by using a numerical study.(2) By using energy equivalent method, the three-way parabolic cable-net structure is equivalent to a isotropic parabolic membrane under uniform tension, the calculation method for the equivalent membrane stiffness and mass parameters is presented. Finally, the natural frequencies and mode shapes of parabolic cable-net structure are compared with equivalent membrane model by using a calculation case, and the equivalent method is validated.(3) Based on Donnell nonlinear theory of thin shell, the nonlinear vibration equations of inflatable parabolic membrane are derived by using Hamilton principle, and the equations are simplified according to Donnell simplified theory for the vibration of thin shell and shallow shell approximation theory. The linear equations of motion of inflatable parabolic membranes are given according to the linearization of the nonlinear equations of motion, and the linear equations are solved analytically. Considering a fixed boundary, the frequency equations and mode shape functions of inflatable parabolic membranes are obtained, and are verified with the finite element model.(4) For a reflector structure consisting of inflatable parabolic membranes and inflatable torus, according to the force equilibrium and the displacement continuity between the membranes and the torus, the frequency equations and mode shape functions of the inflatable reflector structure in a free state are derived, and are also verified with the finite element model.(5) Based on distributed parameter model, the spectral factorization method is utilized to design linear quadratic optimal controllers for the vibration control of large flexible space structures. Taking the in-plane vibration of a lightly damped ring as an example, the linear quadratic optimal controller is designed by using the partial differential equations of motion of the ring. The effectiveness of the method is disclosed in terms of reducing the control spillover.