發(fā)布時間：2018-09-19 19:21

【摘要】：為了便于加工制造與在軌組裝,大型空間結構均為周期性模塊化結構,例如空間桁架結構、伸展臂、蜂窩夾層板、太陽帆板等。周期結構對于特定頻率波具有完全反射特性,可以阻斷波振動能量的傳播,從而形成波禁帶特性。因此,本文以周期梁結構為研究對象,結合行波分析方法和Bloch定理對周期梁結構的能帶特性進行了分析。論文的主要研究工作如下:首先,研究了變截面梁結構的行波動力學響應�；谖⒃w的力平衡方程,建立了拉壓、扭轉和彎曲變形下變截面梁結構的連續(xù)體波導方程,提取了變截面梁的波模式狀態(tài)轉換方程。利用聯接結點的力平衡條件與位移協調條件,建立了變截面結構的波散射與波傳遞方程。聯立波散射與波傳遞方程,求解獲得了表征位移響應的波模式向量。利用行波方法分析了變截面的單根懸臂梁與梁框架結構的頻率響應,揭示了材料與幾何尺寸參數變化對位移響應的影響。研究結果說明了行波法能更精確描述結構動力學特性,可為大型空間框架梁結構的動力學分析提供高準確性、高計算效率的分析方法。其次,研究了一維周期梁結構的能帶特性。以位移和力為狀態(tài)矢量,利用建立的行波模型,推導了包含激勵頻率的周期結構輸入與輸出狀態(tài)矢量的關系。引入Bloch定理,推導了包含波數的周期結構輸入與輸出狀態(tài)矢量的關系。基于這兩種關系,建立了含有激勵頻率與波數關系的能帶特性通用方程。分析對比了周期等截面梁和周期變截面梁結構的能帶特性,研究了材料與幾何尺寸參數對周期梁結構能帶特性的影響,為二維周期梁結構能帶特性分析以及后續(xù)設計提供了基礎。最后,研究了二維周期梁結構的能帶特性。以一個正交鉸接的二維周期梁結構為對象,推導了周期單元的力學方程,包括位移協調方程和力平衡方程。按照波矢量輸入的四個方向,定義了四種波傳播方式,推導了輸入波在周期單元中的反射系數和散射系數。引入聲子晶體中的Bloch定理推導了波傳播的Bloch邊界條件,結合波傳輸方程,推導出結構中波數與頻率的關系。通過一個二維周期結構的能帶特性的分析,驗證了實際工程中設計二維周期梁結構來實現振動隔離和濾波的可行性。
[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.
【學位授予單位】：西安電子科技大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：V414

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