周期性结构及周期性隔震基础
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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。
Base isolation is an effective way to decrease structural responses under earthquake actions. However, because of the disadvantages of traditional base isolation systems, it is a hot topic to develop new seismic isolation systems. In1993, some investigations in the field of solid-state-physics show that phononic crystal, a novel periodic structure, can be designed as a filter for elastic wave. In some frequency regions, named band gap or attenuation zone, elastic waves cannot propagate in this type of periodic structure. Based on this idea, this work aims to investigate the filtering effect of this type of periodic structure and to study possible applications of periodic structure, named periodic seismic isolation foundation, in civil engineering.
In this dissertation, attentions are focused on four topics:1, numerical method for the dispersion relationship of periodic structure;2, basic theory of periodic structure;3, numerical simulations of periodic foundations; A, experimental studies of periodic foundations. On the first topic, the convergence of the Fourier expansion method in calculating the band structures of elastic waves propagating in periodic composites is discussed based on its two mathematical backgrounds. And influences of the material parameters and the geometrical parameters on the convergence are analyzed. On the second topic, by using mass-spring models, the filtering effect of periodic structure for elastic wave is studied and the attenuation mechanism of energy flow in finite periodic structure is illustrated. To study the directional attenuation zone of local-resonant periodic structure, dispersion curves of local-resonant periodic structure are presented according to the vibration mode of the inner oscillator. On the third topic, numerical simulations are conducted to verify the efficiency of the attenuation zone of finite periodic structure and to show the filtering effect of periodic foundation for seismic waves. As using the improved layered periodic foundation or the two-dimensional periodic foundation with directional attenuation zones, seismic responses of upper-structures under different types of seismic waves are also simulated. On the fourth topic, shake table tests and free field tests are conducted for the layered periodic foundation and two-dimensional periodic foundation, respectively.
Some conclusions are obtained:the convergence of the Fourier expansion method is influenced by the Gibbs oscillation and the uniform convergence formula for the product function. For the scattering periodic structure, the filtering effect is related to the interaction between different materials; for the local resonant periodic structure, the filtering effect is related to the resonance of the inner oscillator. Directional attenuation zones can be opened easily for non-symmetric periodic structures. Compared to symmetric periodic structures, the small-size non-symmetric periodic structures can open low-frequency broadband attenuation zones, which are much beneficial for engineering applications. Numerical simulation results show that vibrations in attenuation zones can be obviously lowered after three unit cells. Seismic simulation results show it is feasible to isolate seismic waves by using periodic foundations. Seismic responses of upper structure are decreased because the input energy is lowered by the periodic foundation. The improved layered periodic foundation and the two-dimensional periodic foundation with directional attenuation zones can be used to protect upper-structures in different sites. The efficiency of the layered periodic foundation is proved by the shaking table tests results, and the feasibility of two-dimensional periodic foundation is verified by the free field tests results.
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。
Base isolation is an effective way to decrease structural responses under earthquake actions. However, because of the disadvantages of traditional base isolation systems, it is a hot topic to develop new seismic isolation systems. In1993, some investigations in the field of solid-state-physics show that phononic crystal, a novel periodic structure, can be designed as a filter for elastic wave. In some frequency regions, named band gap or attenuation zone, elastic waves cannot propagate in this type of periodic structure. Based on this idea, this work aims to investigate the filtering effect of this type of periodic structure and to study possible applications of periodic structure, named periodic seismic isolation foundation, in civil engineering.
In this dissertation, attentions are focused on four topics:1, numerical method for the dispersion relationship of periodic structure;2, basic theory of periodic structure;3, numerical simulations of periodic foundations; A, experimental studies of periodic foundations. On the first topic, the convergence of the Fourier expansion method in calculating the band structures of elastic waves propagating in periodic composites is discussed based on its two mathematical backgrounds. And influences of the material parameters and the geometrical parameters on the convergence are analyzed. On the second topic, by using mass-spring models, the filtering effect of periodic structure for elastic wave is studied and the attenuation mechanism of energy flow in finite periodic structure is illustrated. To study the directional attenuation zone of local-resonant periodic structure, dispersion curves of local-resonant periodic structure are presented according to the vibration mode of the inner oscillator. On the third topic, numerical simulations are conducted to verify the efficiency of the attenuation zone of finite periodic structure and to show the filtering effect of periodic foundation for seismic waves. As using the improved layered periodic foundation or the two-dimensional periodic foundation with directional attenuation zones, seismic responses of upper-structures under different types of seismic waves are also simulated. On the fourth topic, shake table tests and free field tests are conducted for the layered periodic foundation and two-dimensional periodic foundation, respectively.
Some conclusions are obtained:the convergence of the Fourier expansion method is influenced by the Gibbs oscillation and the uniform convergence formula for the product function. For the scattering periodic structure, the filtering effect is related to the interaction between different materials; for the local resonant periodic structure, the filtering effect is related to the resonance of the inner oscillator. Directional attenuation zones can be opened easily for non-symmetric periodic structures. Compared to symmetric periodic structures, the small-size non-symmetric periodic structures can open low-frequency broadband attenuation zones, which are much beneficial for engineering applications. Numerical simulation results show that vibrations in attenuation zones can be obviously lowered after three unit cells. Seismic simulation results show it is feasible to isolate seismic waves by using periodic foundations. Seismic responses of upper structure are decreased because the input energy is lowered by the periodic foundation. The improved layered periodic foundation and the two-dimensional periodic foundation with directional attenuation zones can be used to protect upper-structures in different sites. The efficiency of the layered periodic foundation is proved by the shaking table tests results, and the feasibility of two-dimensional periodic foundation is verified by the free field tests results.
引文
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