挠性航天器动力学模型的非约束模态分析

挠性航天器动力学建模中的挠性耦合影响系数是动力学建模中的重要力学概念,它反映了航天器姿态和轨道运动与挠性附件的弹性振动效应. 挠性耦合影响系数间的恒等式关系,即惯性完备性准则,是挠性航天器动力学模型降阶和模态截断的重要依据. 以中心刚体带挠性附件航天器为研究对象,采用约束模态和非约束模态法描述挠性附件结构变形,利用欧拉-拉格朗日方程建立挠性航天器的动力学模型. 基于 Hughes 的研究成果,对挠性航天器的非约束模态恒等式及其用于动力学模型降阶的惯性完备性准则进行了证明和应用研究. 探讨了两种动力学模型惯量间的关系,并利用约束模态惯性完备性准则,推导了非约束模态惯性完备性准则. 最后,对中心刚体带双侧太阳帆板和带单侧太阳帆板构成的挠性航天器模型进行数值仿真计算,求出挠性附件非约束模态平动耦合系数,分析了非约束模态特征值和平动耦合系数随着刚柔质量比的变化情况,并尝试用非约束模态惯性完备性准则的质量特征恒等式对挠性航天器模型进行了检验. 

UNCONSTRAINED MODAL ANALYSIS OF DYNAMIC MODEL OF FLEXIBLE SPACECRAFT

The influence coefficient of flexible coupling in dynamic modeling of flexible spacecraft is an important mechanical concept in dynamic modeling, which reflects the elastic vibration effect of spacecraft attitude and orbit motion and flexible accessories. The equivalent relationship between the influence coefficients of the flexible coupling, i.e. the inertial completeness criterion, is an important basis for the reduction of the order and the mode truncation of the dynamic model of the flexible spacecraft. Taking the center rigid body spacecraft with flexible appendages as the research object, the constrained mode and unconstrained mode are used to describe the structural deformation of flexible appendages, and the dynamic model of flexible spacecraft is established by using Euler Lagrange equation. Based on the research results of Hughes, the unconstrained modal identity of flexible spacecraft and the inertial completeness criterion for dynamic model reduction are proved and applied. The relationship between the inertia of two dynamic models is discussed, and the inertial completeness criterion of unconstrained mode is derived by using the inertial completeness criterion of constrained mode. Finally, the numerical simulation of the flexible spacecraft model composed of the central rigid body with two side solar panels and one side solar panels is carried out to find out the unconstrained mode translational coupling coefficient of the flexible appendages. The change of the unconstrained mode eigenvalue and translational coupling coefficient with the rigid flexible mass ratio is analyzed, and the mass characteristic identity of the unconstrained mode inertial completeness criterion is used to test the model The flexible spacecraft model is tested.