基于非线性色散方程组的全柔性航天器的动力学分析

Dynamical Analysis of a Highly Flexible Spacecraft Based on Nonlinear Dispersive Equations

空间太阳能电站等大型结构由于采用轻质材料且结构尺寸大,呈全柔性状态,即不存在刚性构架,使得传统的中心刚体附加截断模态的方法在处理动力学问题时会出现显著的误差.从连续空间的角度对空间太阳能电站的动力学性质进行分析,以确定不同条件下起主导作用的动力学行为,为控制系统设计提供足够准确的模型简化原则.将空间太阳能电站看作平面内运动的自由边界非线性梁,根据Hamilton原理得到描述局部弹性运动与全局刚性运动的动力学模型.分析小变形情形下动力学方程在给定初始条件下的稳态解及其渐进性,讨论模态解或考虑了波动效应的色散解与结构尺寸、刚度等参数的关系,初步分析有限变形情形下可能出现的动力学行为,如动力刚化、非线性正规模态和孤立子解.总结空间太阳能电站在不同结构参数或运动条件下的动力学模型简化原则.对关键要素分析结果进行数值仿真,以此验证了理论分析结果.

The space solar power station is an ultra-large and lightweight space structure,due to the high flexibil-ity,which may result in a notable spillover when treated as the classical modal-based dynamics equations with arti-ficial modal truncation.In response to this phenomenon,when modeling the flexible spacecraft dynamics,a contin-uous spatial domain method is used,to study the asymptotic behavior of the coupled rigid-body and flexible system,to determine the dominated dynamical behavior and to provide a guiding principle of a reasonable reduced model for the controller design.The space solar power satellite is approximated by a planar nonlinear free-free beam with global large overall rigid-body motions and local elastic vibration with finite extension and bending,to depict the strain hardening exactly.By Hamilton’s principle,a system of nonlinear dispersive equations in the quotient func-tion spaces corresponding to an affine action of the rigid-body motion which is described by a floating reference frame is obtained.Then,with the nonlinear dispersive equations,relative equilibrium and their linear stability,as well as the relation between the mode solutions or the dispersive solutions and structual parameters are analyzed in the case of small deformation.Nonlinear dynamical behavior including strain hardening,nonlinear normal modes and solitons are analyzed primarily in the finite deformation case.The principle of adopting a promising reduced model is summarized according to the structural parameters and initial conditions.Numerical simulations illustrate the validity of the key analytical results.