摘要
摘要：本文从固体物理学的周期性理论出发,研究了土木工程中的周期性排桩(如周期性实心／空心排桩、周期性填充排桩和周期性分形排桩)和周期性波屏障结构。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。另外,即使弹性波的频率在衰减域外,经过特殊设计的周期结构对弹性波的传播具有方向特性,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。利用衰减域的禁波特性和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以及地震动的隔离当中。本文的研究目的是通过对这类周期结构的系统研究,为土木工程减振(震)方法提出新思路。本文通过理论研究、数值模拟以及对比其他研究者的试验结果的研究方法,首先利用级数展开技术和有限元法,求解了不同形式周期结构的频散曲线。然后,利用有限元技术,建立合理的分析模型和边界条件,进而分析了各种二维、三维周期结构的散射波场。通过和其他作者的实验结果对比,说明了理论结果的正确性和衰减域的存在性。本文的创新性成果主要有：
(1)提出利用固体物理学中的周期性理论分析排桩的桩-土相互作用,用衰减域的概念解释周期性排桩对弹性波的频散特性；提出利用周期性排桩的衰减域特性实现对环境振动的衰减。
(2)获得了周期实心排桩和周期空心排桩的衰减域,并对衰减域的影响因素进行了系统研究；揭示了土的弹性模量、桩的半径和周期常数对周期性排桩衰减域的重要影响,得出常见尺寸的排桩易于隔离中频振动的结论。
(3)研究了周期填充排桩的面内和面外衰减域,并对衰减域的影响因素进行了分析；利用局域共振机理和布拉格散射机理对周期填充排桩衰减域的合理性进行了解释,将局域共振型周期填充排桩拓展用于低频减振。
(4)对周期分形排桩的衰减域和方向传播特性,进行了理论研究和数值模拟,揭示了代数和填充率对周期分形排桩衰减域的影响规律。
(5)设计了具备三维隔振(震)能力的周期性波屏障,为环境减振以及地震动隔离提出新思路。
通过本文研究,不仅可以深入了解周期结构对弹性波的散射机制和减振效果,而且对揭示周期性排桩的桩-土相互作用机理、弹性波在桩-土之间的能量转换和耗散机理、建立周期性排桩在人工振动下的理论分析模型与设计方法、以及新型波屏障的设计,均具有非常重要的指导意义。
ABSTRACT:This paper utilizes periodic theory of solid-state physics to study periodic pile barriers (such as periodic pile barriers with solid piles or hollow piles, periodic in-filled pile barriers and periodic fractal pile barriers) and periodic wave barriers in Civil Engineering. Periodic structures own the distinctive feature of wave forbidden characteristic of attenuation zones. When the frequencies of elastic waves are located on the attenuation zones, these waves cannot propagate through the periodic mediums. Moreover, even though the frequencies of elastic waves are out of the attenuation zones, periodic structures with a particular design can have the directional characteristics of elastic wave propagation. That means energy of waves just can flow in certain directions and other directions are called as "dead zones". We can design periodic structures with the capacity of vibration reduction or isolation by attenuation zones and the directional characteristics of wave propagation. Thus these periodic structures can be used to environmental vibration reduction and seismic isolation in Civil Engineering. The purpose of this paper is to find the new approaches on vibration reduction and seismic isolation in Civil Engineering by systematically studying the periodic structures. In this paper, the theoretical analysis and numerical simulation are conducted and the results are compared with others' experimental results. First, this paper uses series expansion technique and finite element method to study the dispersion curves of different periodic structures. Then, the scattering field of two-dimensional and three-dimensional periodic structures are studied by finite element method with reasonable models and boundary conditions. The correctness of the theoretical results and the existence of attenuation zones are validated by comparing with others' experimental results. The innovations can be drawn as follows.
(1) Periodic theory of solid-state physics is firstly used to study the pile-soil interaction in pile barriers. The dispersion characteristics of periodic pile barriers for elastic waves are explained by the concept of attenuation zones. This paper proposes utilizing attenuation-zone characteristics of periodic pile barriers to environmental vibration reduction.
(2) The attenuation zones of periodic pile barriers with solid piles and hollow piles are obtained. The influential factors on attenuation zones are studied comprehensively. The research reveals elastic modulus of soil, the pile radii and the periodic constant have an important influence on the attenuation zones of periodic pile barriers. It concludes that piles with the common size can easily help to middle-frequency vibration isolation.
(3) The in-plane and out-of-plane attenuation zones of periodic in-filled pile barriers are investigated and the affecting factors on attenuation zones are analyzed. The locally resonant mechanism and Bragg scattering mechanism are used to explain the rationality of attenuation zones in periodic in-filled pile barriers. The periodic in-filled pile barriers based on locally resonant mechanism are expanded to low-frequency vibration reduction.
(4) The attenuation zones and directional characteristics of periodic fractal pile barriers are discussed by theoretical analyses and numerical simulation. The influencing rule of generations and filling fraction on the attenuation zones of periodic fractal pile barriers are discovered.
(5) Periodic wave barrier is designed to block the vibrations and seismic waves from three dimensional space. This new mentality is presented for the environmental vibration reduction and seismic isolation.
Based on the study in this paper, the findings can help to deeply understand the scattering mechanism of periodic structures for elastic waves and the effectiveness of vibration reduction. Moreover, the findings have a guiding significance on understanding the mechanism of the pile-soil interaction in periodic pile barriers, the energy transfer and consumption of elastic waves between pile and soil. Theoretical model and design method of periodic pile barriers subjected to artificial vibrations can be found in this paper. This paper also provides the inspiration for designing new wave barriers.
引文
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