摘 要

随着航天事业的发展，航天器需要在太空完成越来越复杂的作业，空间桁架由于具有大折叠比的特性，成为航天器广泛运用的结构之一。空间桁架的铰链是其关键部件，关乎桁架的服役强度和使用寿命。铰链结构受力复杂且存在间隙，不可避免地会产生非线性动力学响应，使结构的工作精度降低，对空间铰链结构进行非线性动态特性分析是解决问题的关键。本文主要的研究工作如下：

首先，介绍了空间铰链结构动态特性的研究背景和研究意义。综述了空间铰链结构非线性建模方法的研究现状，非线性模态的研究现状，介绍了非线性模态的几种定义，讨论了非线性模态中常存在的基本特性，通过对两自由度非线性弹簧质量系统的模态分析，验证了频能曲线能够较为直观地体现结构的非线性特征：频能相关性、内共振和模态分岔。探究了非线性模态常用的分析方法，给出了本文主要使用的谐波平衡法的计算方法及其优点，并用Duffing振子进行了说明。

其次，对空间柔性铰链结构进行了等效建模，建立了柔性铰链结构的等效非线性动力学模型，将一种常见的单片柔性铰链结构等效为柔性边界梁，再进一步等效成具有立方非线性的多自由度系统，利用谐波平衡法计算其线性及非线性频率-能量曲线，研究铰链结构的非线性特性。通过计算对不同阶次的非线性模态，发现铰链结构非线性模态的两处分岔出现了交换先后位置并不断靠近的现象，说明高阶的非线性模态更加不稳定。

最后，探究柔性铰链结构线性刚度及非线性刚度变化时，对结构产生的影响。铰链结构的非线性模态影响因素分析表明，线性刚度变化主要影响结构初始模态频率，非线性刚度变化则会导致铰链结构非线性特征的敏感性增强。当铰链结构非线性刚度增大时，更低的能量的水平即可产生非线性现象，当铰链结构的线性刚度减弱时，非线性特性减弱。此外，铰链结构非线性刚度对低能量水平的模态振型影响较小，结构的非线性现象主要出现在高能量水平下。

关键词：非线性模态；空间柔性铰链；非线性刚度；频能图

Analysis and Verification of Nonlinear Dynamic Characteristics of Spatial Hinge Structures

ABSTRACT

With the development of space industry, spacecraft need to complete more and more complex operations in space. Space truss has become one of the widely used structures of spacecraft due to its large folding ratio. The hinge of space truss is the key part, which is related to the service strength and service life of the truss. The hinge structure is subjected to complex forces and has gaps, which inevitably leads to nonlinear dynamic response and reduces the working accuracy of the structure. The key to solve the problem is to analyze the nonlinear dynamic characteristics of spatial hinge structure. The main research work of this paper is as follows:

Firstly, the research background and significance of dynamic characteristics of spatial hinge structures are introduced. The paper summarizes the research situation of space hinge structure nonlinear modeling method, the research status of nonlinear modal. Several nonlinear modal definitions are introduced, the basic characteristics of nonlinear modal are discussed, based on the modal analysis of two degrees of freedom nonlinear spring mass system, which can verify that the frequency curve can intuitively reflect the nonlinear characteristics of structures: frequency-energy dependence, internal resonance and modal bifurcation. The methods of nonlinear modal analysis are studied. The calculation method of harmonic balance method is given with the example of Duffing oscillator.

Second, the equivalent modeling of space flexure hinge structure is carried out, which established the equivalent nonlinear dynamic model of flexible hinge structure. A common form of monolithic flexure hinge structure is equivalent to the flexible boundary beams, equivalent further into the multi degree of freedom system with cubic nonlinear, using the harmonic balance method to calculate the linear and nonlinear frequency-energy curve, in order to study the nonlinear characteristics of the hinge structure. By calculating the nonlinear modes of different orders, it is found that the two branches of the nonlinear modes of the hinge structure change successively and get closer together, which indicates that the higher order nonlinear modes are more unstable.

Finally, the influence of linear stiffness and nonlinear stiffness on flexure hinge structure is studied. The analysis of the influencing factors of the nonlinear mode of hinge structure shows that the change of the linear stiffness mainly affects the initial modal frequency of the structure, and the change of the nonlinear stiffness will lead to the increase of the sensitivity of the nonlinear characteristics of hinge structure. When the nonlinear stiffness of hinge structure increases, the lower energy level can produce nonlinear phenomenon. When the linear stiffness of hinge structure weakens, the nonlinear characteristic weakens. In addition, the nonlinear stiffness of the hinge structure has little influence on the mode at the low energy level, and the nonlinear phenomenon of the structure mainly occurs at the high energy level.

Key words：Nonlinear mode；Space flexible hinge；Nonlinear stiffness；Frequency-energy curve

目 录

1 绪论…………………………………………………………………………………………1

1.1 研究背景和意义…………………………………………………………………1

1.2 空间铰链结构非线性建模方法研究现状…………………………………………2

1.3 非线性模态研究现状………………………………………………………………2

1.4 本文主要研究内容…………………………………………………………………3

2 空间铰链结构非线性模态仿真分析………………………………………………………5

2.1 引言…………………………………………………………………………………5

2.2 非线性模态理论……………………………………………………………………5

2.3 非线性模态基本特性………………………………………………………………6