大型刚-柔耦合动力学系统建模中柔性梁的非线性变形研究

Better Dynamic Modeling of a Flexible Beam in Rigid-Flexible Coupling Spacecraft

在一次耦合模型变形模式的基础上,根据大型刚-柔耦合动力学系统中柔性梁的结构特点,从连续介质力学原理出发,在柔性梁的纵向变形中计及了变形的二次耦合项;在空间柔性梁的3个方向变形中均考虑了变形的相互耦合作用及轴向扭转效应,得出了描述柔性体变形的较为精确的几何非线性变形模式。从变形位移-应变关系出发,对一次耦合模型和文中模型的剪应变进行了分析,在相同的简化下,对平面柔性梁,采用文中模型得出的剪应变为零;对空间柔性梁,采用文中模型得出的剪应变值小于一次耦合模型,从而说明采用文中模型更有理由忽略剪切效应,符合细长梁的建模理论。

Aim. Flexible beams are widely found in astronautical applications, particularly in spacecraft. The dynamic modeling of a flexible beam is essential, yet existing such models are, in our opinion, deficient in several respects. In this paper, we do our best to propose a better model. In the full paper, we explain in detail the deficiencies of existing models and then our better model. In this abstract, we just add some pertinent remarks to listing the three topics of explanation. The first topic is ： the description of the deformation of a flexible beam with the existing first-order coupling model. In the last paragraph of the first topic, we point out the deficiencies of the existing first-order coupling model ;they are mainly that the longitudinal extension, the lateral and transverse deflection, and, most importantly, their interactions are not taken into account. The second topic is： the accurate description of the nonlinear deformation of a flexible beam. In the second topic, we point out how to include the two following essential items in our description of the nonlinear deformation of a flexible beam： （1） the second-order coupling terms of longitudinal deformation; （2） the coupling terms among four types of deformation the deformation in the vertical plane, that in the horizontal plane, the axial deformation, and the torsional deformation. The third topic is： the analysis of the nonlinear displacement-strain relationships. In the third topic, our analysis produces the tentative conclution that shearing strains, originally considered not negligible in the existing first-order coupling model, should actually be neglected.