【摘要】：為了便于加工制造與在軌組裝,大型空間結(jié)構(gòu)均為周期性模塊化結(jié)構(gòu),例如空間桁架結(jié)構(gòu)、伸展臂、蜂窩夾層板、太陽(yáng)帆板等。周期結(jié)構(gòu)對(duì)于特定頻率波具有完全反射特性,可以阻斷波振動(dòng)能量的傳播,從而形成波禁帶特性。因此,本文以周期梁結(jié)構(gòu)為研究對(duì)象,結(jié)合行波分析方法和Bloch定理對(duì)周期梁結(jié)構(gòu)的能帶特性進(jìn)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(jié)構(gòu)的行波動(dòng)力學(xué)響應(yīng)。基于微元體的力平衡方程,建立了拉壓、扭轉(zhuǎn)和彎曲變形下變截面梁結(jié)構(gòu)的連續(xù)體波導(dǎo)方程,提取了變截面梁的波模式狀態(tài)轉(zhuǎn)換方程。利用聯(lián)接結(jié)點(diǎn)的力平衡條件與位移協(xié)調(diào)條件,建立了變截面結(jié)構(gòu)的波散射與波傳遞方程。聯(lián)立波散射與波傳遞方程,求解獲得了表征位移響應(yīng)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(jié)構(gòu)的頻率響應(yīng),揭示了材料與幾何尺寸參數(shù)變化對(duì)位移響應(yīng)的影響。研究結(jié)果說(shuō)明了行波法能更精確描述結(jié)構(gòu)動(dòng)力學(xué)特性,可為大型空間框架梁結(jié)構(gòu)的動(dòng)力學(xué)分析提供高準(zhǔn)確性、高計(jì)算效率的分析方法。其次,研究了一維周期梁結(jié)構(gòu)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(dǎo)了包含激勵(lì)頻率的周期結(jié)構(gòu)輸入與輸出狀態(tài)矢量的關(guān)系。引入Bloch定理,推導(dǎo)了包含波數(shù)的周期結(jié)構(gòu)輸入與輸出狀態(tài)矢量的關(guān)系�；谶@兩種關(guān)系,建立了含有激勵(lì)頻率與波數(shù)關(guān)系的能帶特性通用方程。分析對(duì)比了周期等截面梁和周期變截面梁結(jié)構(gòu)的能帶特性,研究了材料與幾何尺寸參數(shù)對(duì)周期梁結(jié)構(gòu)能帶特性的影響,為二維周期梁結(jié)構(gòu)能帶特性分析以及后續(xù)設(shè)計(jì)提供了基礎(chǔ)。最后,研究了二維周期梁結(jié)構(gòu)的能帶特性。以一個(gè)正交鉸接的二維周期梁結(jié)構(gòu)為對(duì)象,推導(dǎo)了周期單元的力學(xué)方程,包括位移協(xié)調(diào)方程和力平衡方程。按照波矢量輸入的四個(gè)方向,定義了四種波傳播方式,推導(dǎo)了輸入波在周期單元中的反射系數(shù)和散射系數(shù)。引入聲子晶體中的Bloch定理推導(dǎo)了波傳播的Bloch邊界條件,結(jié)合波傳輸方程,推導(dǎo)出結(jié)構(gòu)中波數(shù)與頻率的關(guān)系。通過(guò)一個(gè)二維周期結(jié)構(gòu)的能帶特性的分析,驗(yàn)證了實(shí)際工程中設(shè)計(jì)二維周期梁結(jié)構(gòu)來(lái)實(shí)現(xiàn)振動(dòng)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(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：V414

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