【摘要】：周期結(jié)構(gòu)具有獨特的衰減域禁波特性,當彈性波的頻率落在衰減域內(nèi)時,彈性波不能在周期介質(zhì)中傳播。此外,頻率在衰減域外的彈性波在經(jīng)過特殊設計的周期結(jié)構(gòu)中傳播也可以具有方向特性,即波的能量只能沿著某些方向傳遞,而在其他方向產(chǎn)生振動盲區(qū)。利用波動傳播的方向特性,就可以設計出具有減振、隔振功能的周期結(jié)構(gòu)。這些周期結(jié)構(gòu)可以應用到土木工程中的環(huán)境減振當中。 近年來,有學者提出了利用空洞進行環(huán)境減振的措施,并進行了大量試驗研究。然而,從周期性理論的角度看,該模型實際上就是一種由空洞與土組成的二維周期結(jié)構(gòu)。本文將從固體物理學的周期性理論出發(fā),結(jié)合群速度概念,研究由空洞與土組成的二維周期結(jié)構(gòu)中波的方向傳播特性。具體講,本文將通過理論計算并結(jié)合數(shù)值模擬的研究方法,首先計算二維周期結(jié)構(gòu)的頻散曲線。然后,結(jié)合群速度概念用數(shù)值方法計算群速度。最后,利用有限元方法,建立合理的數(shù)值分析模型,模擬空洞與土組成的二維周期結(jié)構(gòu)的環(huán)境減振特性。本文的研究內(nèi)容主要有： (1)在固體物理學周期理論基礎上,結(jié)合群速度分析了具有方向衰減特性的周期結(jié)構(gòu)。 (2)研究了周期結(jié)構(gòu)對平面內(nèi)振動和平面外振動的方向衰減域,并對方向衰減域影響因素進行了系統(tǒng)研究；揭示了土的彈性模量、土的密度、空洞的半徑和周期常數(shù)對方向衰減域的重要影響。 (3)結(jié)合頻散曲線研究二維周期結(jié)構(gòu),并運用群速度方法,討論方向衰減域外彈性波的方向傳播特性。 (4)建立合理的有限元模型,對平面內(nèi)振動進行數(shù)值模擬,體現(xiàn)方向衰減域和衰減域外彈性波傳播的方向特性,為實際工程中環(huán)境減振設計提供參考。
[Abstract]:The periodic structure has the unique attenuation domain forbidden wave characteristic, when the elastic wave frequency falls in the attenuation domain, the elastic wave cannot propagate in the periodic medium. In addition, the propagation of the elastic wave in the attenuation region can also have a directional characteristic in a specially designed periodic structure, that is, the energy of the wave can only be transmitted along some directions, while the vibration blind area can be produced in other directions. By using the directional characteristics of wave propagation, a periodic structure with the function of vibration absorption and isolation can be designed. These periodic structures can be applied to environmental vibration reduction in civil engineering. In recent years, some scholars have put forward the measures of using cavity to reduce environmental vibration, and a lot of experimental research has been carried out. However, from the perspective of periodicity theory, the model is actually a two-dimensional periodic structure composed of voids and soils. Based on the periodic theory of solid state physics and the concept of group velocity, the directional propagation characteristics of waves in a two-dimensional periodic structure composed of voids and soils are studied in this paper. In detail, the dispersion curve of two-dimensional periodic structure is calculated by theoretical calculation and numerical simulation. Then, the group velocity is calculated by numerical method combined with the concept of group velocity. Finally, the finite element method is used to establish a reasonable numerical analysis model to simulate the vibration absorption characteristics of a two-dimensional periodic structure composed of voids and soils. The main contents of this paper are as follows: (1) based on the periodic theory of solid state physics, The periodic structures with directional attenuation characteristics are analyzed in combination with group velocity. (2) the effects of periodic structures on the directional attenuation domain of in-plane and out-of-plane vibration are studied systematically. The important effects of elastic modulus, density, radius of cavity and periodic constant on the attenuation region of soil are revealed. (3) the two-dimensional periodic structure is studied by means of dispersion curve, and the group velocity method is used. The directional propagation characteristics of directionally attenuated extra-territorial elastic waves are discussed. (4) A reasonable finite element model is established to simulate the in-plane vibration, which reflects the directional characteristics of the directional attenuation domain and the attenuation extra-territorial elastic wave propagation. It provides a reference for the design of environmental vibration absorption in practical engineering.
【學位授予單位】：北京交通大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：TU435

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