波在二维周期结构中方向传播特性研究

发布时间：2018-08-12 17:20

【摘要】：周期结构具有独特的衰减域禁波特性,当弹性波的频率落在衰减域内时,弹性波不能在周期介质中传播。此外,频率在衰减域外的弹性波在经过特殊设计的周期结构中传播也可以具有方向特性,即波的能量只能沿着某些方向传递,而在其他方向产生振动盲区。利用波动传播的方向特性,就可以设计出具有减振、隔振功能的周期结构。这些周期结构可以应用到土木工程中的环境减振当中。近年来,有学者提出了利用空洞进行环境减振的措施,并进行了大量试验研究。然而,从周期性理论的角度看,该模型实际上就是一种由空洞与土组成的二维周期结构。本文将从固体物理学的周期性理论出发,结合群速度概念,研究由空洞与土组成的二维周期结构中波的方向传播特性。具体讲,本文将通过理论计算并结合数值模拟的研究方法,首先计算二维周期结构的频散曲线。然后,结合群速度概念用数值方法计算群速度。最后,利用有限元方法,建立合理的数值分析模型,模拟空洞与土组成的二维周期结构的环境减振特性。本文的研究内容主要有： (1)在固体物理学周期理论基础上,结合群速度分析了具有方向衰减特性的周期结构。 (2)研究了周期结构对平面内振动和平面外振动的方向衰减域,并对方向衰减域影响因素进行了系统研究；揭示了土的弹性模量、土的密度、空洞的半径和周期常数对方向衰减域的重要影响。 (3)结合频散曲线研究二维周期结构,并运用群速度方法,讨论方向衰减域外弹性波的方向传播特性。 (4)建立合理的有限元模型,对平面内振动进行数值模拟,体现方向衰减域和衰减域外弹性波传播的方向特性,为实际工程中环境减振设计提供参考。
[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.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TU435

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