周期性结构及周期性隔震基础
发布时间：2018-08-22 19:00
【摘要】：隔震技术是一种减小结构地震动力响应的有效方法。鉴于传统隔震技术的一些不足,开发新型隔震技术己成为目前研究的一个热点课题。1993年,凝固态物理学中提出了声子晶体型周期性结构的概念。这种周期性结构具有独特的滤波特性,即处于某些频段(衰减域)范围内的波不能透过该结构。受此启发,本文将研究周期性结构的滤波特性以及该结构一种的潜在应用——周期性隔震基础。 本论文研究内容包括：周期性结构频散关系的数值计算方法研究、周期性结构基本理论研究、周期性结构工程应用数值模拟和模型试验。在频散关系数值计算方法研究中,分析了傅里叶级数法的两个数学基础,并讨论了材料参数及几何参数对该方法收敛性的影响。在周期性结构理论研究中,首先讨论了周期性结构的滤波特性,分析了有限周期性结构对振动能量的衰减作用；其次对二维周期性结构研究了方向性衰减域的特性,提出了基于模态的局域共振频散关系绘制方法,并分析了与内部振子振动模态相对应的局域共振方向性衰减域。在工程应用数值模拟研究中,分析了一维层状、二维及三维有限周期性结构的衰减域特性,模拟了周期性基础对地震动的抑制作用；分析了改进的一维层状周期性基础模型及具有方向性衰减域的二维复合周期性基础对多种场地条件下地震动的阻隔作用。在模型试验研究中,首先完成了一维层状周期性基础的振动台测试,随后又完成了二维周期性基础的自由场振动测试。 研究发现：傅里叶级数法收敛性受Gibbs振荡及乘积函数的一致收敛性算式影响。散射型周期性结构的滤波特性由组成周期性结构的不同材料相互作用产生；局域共振型周期性结构的滤波特性是由周期单元的子结构局域共振产生。当周期单元的对称程度较低时,周期性结构容易形成方向性衰减域；相对于对称程度较高的周期单元,对称程度较低的周期单元在实现低频宽带衰减域同时可有效减小周期性基础的尺寸。数值分析结果表明,只需3个周期单元,衰减域即可有效抑制外部激励的传播。地震动模拟结果表明,利用周期性基础抑制地震动的传播是可行的。由于周期性基础减小了地震动向上部结构输入的能量,从而降低了上部结构的地震动响应。改进的层状周期性基础和具有方向性衰减域的二维复合周期性基础,可适用于多种场地条件下的地震隔离。振动台试验验证了层状周期性基础对地震动的阻隔作用,自由场测试验证了二维周期性基础隔震应用的可行性。
[Abstract]:Isolation technique is an effective method to reduce the seismic dynamic response of structures. In view of the shortcomings of traditional isolation technology, the development of new isolation technology has become a hot topic. In 1993, the concept of phonon crystal periodic structure was put forward in the physics of solidified solid state. This kind of periodic structure has unique filtering characteristics, that is, the wave in some frequency band (attenuation domain) can not pass through the structure. Inspired by this, this paper will study the filtering characteristics of periodic structures and the basis of periodic isolation, a potential application of this structure. The main contents of this thesis are as follows: numerical calculation method of periodic structure dispersion relation, basic theory of periodic structure, numerical simulation and model test of periodic structure engineering. In the study of numerical calculation method of dispersion relation, two mathematical foundations of Fourier series method are analyzed, and the influence of material parameters and geometric parameters on the convergence of the method is discussed. In the theoretical study of periodic structures, firstly, the filtering characteristics of periodic structures are discussed, and the attenuation of vibration energy by finite periodic structures is analyzed, and the characteristics of directional attenuation domain for two-dimensional periodic structures are studied. In this paper, a modal based method for drawing the local resonance dispersion relationship is proposed, and the local resonance directivity attenuation domain corresponding to the internal vibration mode is analyzed. In the numerical simulation of engineering application, the attenuation domain characteristics of one-dimensional layered, two-dimensional and three-dimensional finite periodic structures are analyzed, and the effect of periodic foundation on ground motion suppression is simulated. The effects of the improved one-dimensional layered periodic foundation model and the two-dimensional composite periodic foundation with directional attenuation domain on the isolation of ground motion under various site conditions are analyzed. In the research of model test, the shaking table test of one-dimensional periodic foundation is completed first, and then the free-field vibration test of two-dimensional periodic foundation is completed. It is found that the convergence of Fourier series method is affected by Gibbs oscillation and uniform convergence of product function. The filtering characteristics of scattering periodic structures are generated by the interaction of different materials which make up periodic structures, and the filtering characteristics of local resonance periodic structures are generated by local resonance of substructures of periodic elements. When the symmetry degree of periodic unit is low, the periodic structure is easy to form a directional attenuation region, compared with the periodic unit with a higher degree of symmetry, The periodic cell with low symmetry can reduce the size of periodic foundation effectively while realizing the low frequency broadband attenuation domain. The numerical results show that the attenuation domain can effectively suppress the propagation of external excitation in only 3 periodic units. The simulation results show that it is feasible to suppress the propagation of ground motion by using periodic foundation. Because of the periodic foundation, the input energy of the superstructure is reduced, thus the seismic response of the superstructure is reduced. The improved layered periodic foundation and the two-dimensional composite periodic foundation with directional attenuation domain are suitable for seismic isolation under various site conditions. The vibration table test verifies the barrier effect of layered periodic foundation to ground motion, and the free field test verifies the feasibility of the application of two-dimensional periodic foundation isolation.
【学位授予单位】：北京交通大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TU352.12
本文编号：2198020
[Abstract]:Isolation technique is an effective method to reduce the seismic dynamic response of structures. In view of the shortcomings of traditional isolation technology, the development of new isolation technology has become a hot topic. In 1993, the concept of phonon crystal periodic structure was put forward in the physics of solidified solid state. This kind of periodic structure has unique filtering characteristics, that is, the wave in some frequency band (attenuation domain) can not pass through the structure. Inspired by this, this paper will study the filtering characteristics of periodic structures and the basis of periodic isolation, a potential application of this structure. The main contents of this thesis are as follows: numerical calculation method of periodic structure dispersion relation, basic theory of periodic structure, numerical simulation and model test of periodic structure engineering. In the study of numerical calculation method of dispersion relation, two mathematical foundations of Fourier series method are analyzed, and the influence of material parameters and geometric parameters on the convergence of the method is discussed. In the theoretical study of periodic structures, firstly, the filtering characteristics of periodic structures are discussed, and the attenuation of vibration energy by finite periodic structures is analyzed, and the characteristics of directional attenuation domain for two-dimensional periodic structures are studied. In this paper, a modal based method for drawing the local resonance dispersion relationship is proposed, and the local resonance directivity attenuation domain corresponding to the internal vibration mode is analyzed. In the numerical simulation of engineering application, the attenuation domain characteristics of one-dimensional layered, two-dimensional and three-dimensional finite periodic structures are analyzed, and the effect of periodic foundation on ground motion suppression is simulated. The effects of the improved one-dimensional layered periodic foundation model and the two-dimensional composite periodic foundation with directional attenuation domain on the isolation of ground motion under various site conditions are analyzed. In the research of model test, the shaking table test of one-dimensional periodic foundation is completed first, and then the free-field vibration test of two-dimensional periodic foundation is completed. It is found that the convergence of Fourier series method is affected by Gibbs oscillation and uniform convergence of product function. The filtering characteristics of scattering periodic structures are generated by the interaction of different materials which make up periodic structures, and the filtering characteristics of local resonance periodic structures are generated by local resonance of substructures of periodic elements. When the symmetry degree of periodic unit is low, the periodic structure is easy to form a directional attenuation region, compared with the periodic unit with a higher degree of symmetry, The periodic cell with low symmetry can reduce the size of periodic foundation effectively while realizing the low frequency broadband attenuation domain. The numerical results show that the attenuation domain can effectively suppress the propagation of external excitation in only 3 periodic units. The simulation results show that it is feasible to suppress the propagation of ground motion by using periodic foundation. Because of the periodic foundation, the input energy of the superstructure is reduced, thus the seismic response of the superstructure is reduced. The improved layered periodic foundation and the two-dimensional composite periodic foundation with directional attenuation domain are suitable for seismic isolation under various site conditions. The vibration table test verifies the barrier effect of layered periodic foundation to ground motion, and the free field test verifies the feasibility of the application of two-dimensional periodic foundation isolation.
【学位授予单位】：北京交通大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TU352.12
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