周期梁结构的能带特性分析

发布时间：2018-09-19 19:21

【摘要】：为了便于加工制造与在轨组装,大型空间结构均为周期性模块化结构,例如空间桁架结构、伸展臂、蜂窝夹层板、太阳帆板等。周期结构对于特定频率波具有完全反射特性,可以阻断波振动能量的传播,从而形成波禁带特性。因此,本文以周期梁结构为研究对象,结合行波分析方法和Bloch定理对周期梁结构的能带特性进行了分析。论文的主要研究工作如下:首先,研究了变截面梁结构的行波动力学响应。基于微元体的力平衡方程,建立了拉压、扭转和弯曲变形下变截面梁结构的连续体波导方程,提取了变截面梁的波模式状态转换方程。利用联接结点的力平衡条件与位移协调条件,建立了变截面结构的波散射与波传递方程。联立波散射与波传递方程,求解获得了表征位移响应的波模式向量。利用行波方法分析了变截面的单根悬臂梁与梁框架结构的频率响应,揭示了材料与几何尺寸参数变化对位移响应的影响。研究结果说明了行波法能更精确描述结构动力学特性,可为大型空间框架梁结构的动力学分析提供高准确性、高计算效率的分析方法。其次,研究了一维周期梁结构的能带特性。以位移和力为状态矢量,利用建立的行波模型,推导了包含激励频率的周期结构输入与输出状态矢量的关系。引入Bloch定理,推导了包含波数的周期结构输入与输出状态矢量的关系。基于这两种关系,建立了含有激励频率与波数关系的能带特性通用方程。分析对比了周期等截面梁和周期变截面梁结构的能带特性,研究了材料与几何尺寸参数对周期梁结构能带特性的影响,为二维周期梁结构能带特性分析以及后续设计提供了基础。最后,研究了二维周期梁结构的能带特性。以一个正交铰接的二维周期梁结构为对象,推导了周期单元的力学方程,包括位移协调方程和力平衡方程。按照波矢量输入的四个方向,定义了四种波传播方式,推导了输入波在周期单元中的反射系数和散射系数。引入声子晶体中的Bloch定理推导了波传播的Bloch边界条件,结合波传输方程,推导出结构中波数与频率的关系。通过一个二维周期结构的能带特性的分析,验证了实际工程中设计二维周期梁结构来实现振动隔离和滤波的可行性。
[Abstract]:In order to facilitate fabrication and on-orbit assembly, large-scale spatial structures are periodic modular structures, such as space truss structures, stretching arms, honeycomb sandwich panels, solar panels and so on. Periodic structures have complete reflection characteristics for specific frequency waves, which can block the propagation of wave vibration energy, thus forming a wave-gap characteristics. The main research work of this paper is as follows: Firstly, the dynamic response of the beam with variable cross-section is studied. Based on the force balance equation of the element body, the beam knots with variable cross-section under tension, compression, torsion and bending deformation are established. The wave-mode transition equation of a beam with variable cross-section is obtained by constructing the continuum waveguide equation. The wave-scattering and wave-transfer equations of the structure with variable cross-section are established by using the force balance condition and the displacement compatibility condition of the joints. The wave-mode vectors representing the displacement response are obtained by solving the simultaneous wave-scattering and wave-transfer equations. Frequency response of a single cantilever beam with variable cross-section and a beam-frame structure is analyzed, and the effect of material and geometric parameters on displacement response is revealed. Secondly, the energy band characteristics of one-dimensional periodic beam structures are studied. The relationship between input and output state vectors of periodic structures with excitation frequencies is deduced by using the traveling wave model with displacement and force as state vectors. The energy band characteristics of periodic beams with constant cross-section and periodic beams with variable cross-section are analyzed and compared. The effects of material and geometric size parameters on the energy band characteristics of periodic beams are studied. The energy band characteristics of two-dimensional periodic beams are analyzed and designed. Finally, the energy band characteristics of a two-dimensional periodic beam structure are studied. Taking a two-dimensional periodic beam structure with orthogonal hinges as the object of study, the mechanical equations of the periodic element, including the displacement compatibility equation and the force balance equation, are derived. The Bloch boundary condition of wave propagation is deduced by introducing the Bloch theorem in phononic crystals, and the relation between wave number and frequency in the structure is deduced by combining the wave propagation equation. The feasibility of dynamic isolation and filtering.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：V414

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