周期性結構及周期性隔震基礎
發(fā)布時間：2018-08-22 19:00
【摘要】：隔震技術是一種減小結構地震動力響應的有效方法。鑒于傳統(tǒng)隔震技術的一些不足,開發(fā)新型隔震技術己成為目前研究的一個熱點課題。1993年,凝固態(tài)物理學中提出了聲子晶體型周期性結構的概念。這種周期性結構具有獨特的濾波特性,即處于某些頻段(衰減域)范圍內的波不能透過該結構。受此啟發(fā),本文將研究周期性結構的濾波特性以及該結構一種的潛在應用——周期性隔震基礎。 本論文研究內容包括：周期性結構頻散關系的數(shù)值計算方法研究、周期性結構基本理論研究、周期性結構工程應用數(shù)值模擬和模型試驗。在頻散關系數(shù)值計算方法研究中,分析了傅里葉級數(shù)法的兩個數(shù)學基礎,并討論了材料參數(shù)及幾何參數(shù)對該方法收斂性的影響。在周期性結構理論研究中,首先討論了周期性結構的濾波特性,分析了有限周期性結構對振動能量的衰減作用；其次對二維周期性結構研究了方向性衰減域的特性,提出了基于模態(tài)的局域共振頻散關系繪制方法,并分析了與內部振子振動模態(tài)相對應的局域共振方向性衰減域。在工程應用數(shù)值模擬研究中,分析了一維層狀、二維及三維有限周期性結構的衰減域特性,模擬了周期性基礎對地震動的抑制作用；分析了改進的一維層狀周期性基礎模型及具有方向性衰減域的二維復合周期性基礎對多種場地條件下地震動的阻隔作用。在模型試驗研究中,首先完成了一維層狀周期性基礎的振動臺測試,隨后又完成了二維周期性基礎的自由場振動測試。 研究發(fā)現(xiàn)：傅里葉級數(shù)法收斂性受Gibbs振蕩及乘積函數(shù)的一致收斂性算式影響。散射型周期性結構的濾波特性由組成周期性結構的不同材料相互作用產生；局域共振型周期性結構的濾波特性是由周期單元的子結構局域共振產生。當周期單元的對稱程度較低時,周期性結構容易形成方向性衰減域；相對于對稱程度較高的周期單元,對稱程度較低的周期單元在實現(xiàn)低頻寬帶衰減域同時可有效減小周期性基礎的尺寸。數(shù)值分析結果表明,只需3個周期單元,衰減域即可有效抑制外部激勵的傳播。地震動模擬結果表明,利用周期性基礎抑制地震動的傳播是可行的。由于周期性基礎減小了地震動向上部結構輸入的能量,從而降低了上部結構的地震動響應。改進的層狀周期性基礎和具有方向性衰減域的二維復合周期性基礎,可適用于多種場地條件下的地震隔離。振動臺試驗驗證了層狀周期性基礎對地震動的阻隔作用,自由場測試驗證了二維周期性基礎隔震應用的可行性。
[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.
【學位授予單位】：北京交通大學
【學位級別】：博士
【學位授予年份】：2014
【分類號】：TU352.12
本文編號：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.
【學位授予單位】：北京交通大學
【學位級別】：博士
【學位授予年份】：2014
【分類號】：TU352.12
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，本文編號：2198020
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