空间变化地震动下变形敏感大跨度结构响应分析
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摘要
大跨度结构是人类现代文明的重要组成部分，负有重要的社会职能，它们的安全性受到了格外的重视。地震时地面运动是一个复杂的时间—空间过程，以前的抗震设计研究往往把注意力放在地震动的时变特性上，而对地震动的空间变化特性考虑较少。行波效应、不相干效应和局部场地效应是地震动空间变化主要原因。对于平面尺寸较大的结构物，考虑地面运动的空间变化是一种更加合理的输入方式。
本文主要围绕空间变化地震动下变形敏感大跨度结构的响应分析展开。
在对本领域研究理论进行系统综述(第一章)的基础上，本文第二章主要讨论地震地面运动随机过程模型及参数的确定。在本章中，首先回顾了常见的地震动随机模型，归纳总结了基于过滤白噪声模型的改进模型，并对它们的滤波特性，低频特性及高频特性进行了对比分析。结合随机振动的最大反应估计理论求解单自由度体系在平稳地震动输入下的反应谱，运用等效平稳的方法求解非平稳地震动输入下的反应谱。运用随机振动的理论，采用迭代法实现了功率谱与反应谱转换。以我国现行《建筑抗震设计规范》(GB50011—2001)给出的建筑结构地震影响系数曲线为目标反应谱，采用迭代法编制了规范反应谱转换为功率谱程序RSTOPS，进而形成了与规范反应谱相对应的功率谱库。运用非线性拟合的最小二乘法对功率谱库曲线进行洪峰—江近仁谱的参数拟合，给出了高通滤波器参数ω_h和谱强因子G_0的数值。
第三章主要讨论了一致及多点激励地震动合成方法。在本章中，首先回顾了地震动三要素及其衡量的物理量。介绍了拟合反应谱的一致激励人工波合成原理，提出了功率谱与幅值谱联合调整的方法，编制了与规范反应谱相一致人工地震波合成程序。运用随机过程的理论推导了多点地震动的幅值谱及相位谱与互功率谱矩阵元素之间的关系，通过对互功率谱密度函数矩阵的简化，提出了一种多点地震动合成的简化方法。该方法只需要对迟滞相干函数这一实对称矩阵进行Cholesky分解，不需要对互功率谱矩阵这一复数矩阵进行分解，避免了复杂的复数矩阵运算，从而提高了合成的效率。运用这一简化方法编制了多点地震动合成程序。
第四章主要讨论了多点激励时程分析法及其应用。在本章中，首先介绍了多点地震动激励下结构的运动方程及一种无条件收敛的数值求解方法：Wilson-θ法。本章的重点是以某体育场大跨度拱式钢结构为工程背景，运用时程分析法对其进行计算分析。主要内容包括：有限元模型的建立，时程分析所需一致及多点激励地震波的合成，大质量法在多点激励时程分析法的实现，分析了计算结果并得出了一些结论。
第五章主要探讨了多点激励反应谱分析方法及其应用。在本章中，首先介绍了一致及多点激励反应谱的基本原理。对比分析了常用的多点激励反应谱分析方法：B-K法，H-V法，MSRS法及Y-T法。MSRS(Multiple-Support Response Spectrum Method)法是基于严格的随机振动理论推导出来的，因此理论依据充分，可以看作CQC方法在多点激励情况下的推广。本章采用MSRS方法计算了两种形式的两跨连续梁：柔性梁和刚性梁，分析了空间变化地震动对这两种形式梁反应的影响特点并得出了一些有益的结论。
Large span structure being a part of modern civilization undertakes importantsocial functions. Safety of large span structure is given special consideration. Seismicground motion is a complicated time-space process. Previous seismic design and-research are always concerned with seismic time variation characteristics instead ofits spatial variation. Wave-passage effect, incoherence effect and local site effect aremain factors of spatial variation of seismic ground motion. Considering spatialvariation is a more feasible input method to structures with large planar dimension.
The dissertation is mainly concerned in response analysis for deformationsensitive large span structure under spatial variation seismic ground motion.
Based on the systematical summarization on the past research work in the field(Chapter 1), random process model of seismic ground motion is discussed and itsparameters are specified in Chapter 2. Firstly, common random models of seismicground motion are reviewed in this chapter. Then modified models based on filteredwhite noise model are summed up. Analysis and contrast of wave filtering lowfrequency and high frequency characteristics are carded out. With maximum responseestimate theory of random vibration, response spectrum of single degree of freedom(SDF) system under stationary seismic ground motion is calculated. Throughequivalent stationary method, response spectrum under non-stationary seismic groundmotion is calculated. By adopting random vibration theory, conversion between powerspectrum and response spectrum is realized by iteration method By adopting seismiceffect factor curve of Chinese current structure seismic design code (GB50011-2001)as object response spectrum, conversion program between power spectrum andresponse spectrum (RSTOPS) is compiled by iteration method, thus power spectrumarchive compatible with response spectrum of seismic code is built. By adoptingnonlinear fitting method, parameters of Hong feng-Jiang jin ten model are fitted withcalculated power spectrum and its two parameters:ω_h,G_0 are given in this Chapter.
Chapter 3 mainly discusses generation method of seismic ground motion. Firstly,three main factors of seismic ground motion and physical descriptive variables arereviewed in this chapter. Generation principle of uniform excitation artificial seismicground motion compatible with response spectrum of Chinese seismic code isintroduced. The method of power spectrum with amplitude spectrum modification isproposed in this chapter. Program of generation of artificial seismic ground motion compatible with response spectrum of Chinese code is complied. Based on randomprocess theory, a method of simulation of spatial correlated multi-point ground motionhas been proposed by simplification of cross power spectral density matrix. Onlydecomposition of lagged coherent density matrix is required instead of Choleskydecomposition of cross power spectral density matrix. Thus complex matrixcomputation is avoided and simulation efficiency is improved. A correspondingprogram has been compiled using the method.
Chapter 4 mainly discusses time history analysis method and its application.Firstly, structural motion equilibrium under multi-point seismic ground motionexcitation is built. An unconditioned convergence solving method (wilson-θmethod) is introduced in this chapter. The emphasis of this chapter is applying timehistory analysis method to calculate seismic response of a steel large span arch of astadium. The main contents conclude: build of finite element model, seismic wavegeneration under uniform and multi-point excitation, apply big mass method to timehistory method. Calculation results are analyzed and some conclusions are given.
Chapter 5 mainly discusses response spectrum method of multi-point excitationand its application. Firstly, basic principles of response spectrum method underuniform and multi-point excitation are introduced. Contrast and analysis of responsespectrum methods under uniform and multi-point excitation which include: B-Kmethod, H-V method, MSRS method and Y-T method. MSRS (Multiple-SupportResponse Spectrum Method)method is deduced by strict random vibration theory andregarded as an application of CQC method. Responses of two types of continuousbeams with two span: flexible beam and stiff beam are calculated by MSRS method.Responses characteristics of two types of beam under spatial variation seismic groundmotion are analyzed and some conclusions are given.
本文主要围绕空间变化地震动下变形敏感大跨度结构的响应分析展开。
在对本领域研究理论进行系统综述(第一章)的基础上，本文第二章主要讨论地震地面运动随机过程模型及参数的确定。在本章中，首先回顾了常见的地震动随机模型，归纳总结了基于过滤白噪声模型的改进模型，并对它们的滤波特性，低频特性及高频特性进行了对比分析。结合随机振动的最大反应估计理论求解单自由度体系在平稳地震动输入下的反应谱，运用等效平稳的方法求解非平稳地震动输入下的反应谱。运用随机振动的理论，采用迭代法实现了功率谱与反应谱转换。以我国现行《建筑抗震设计规范》(GB50011—2001)给出的建筑结构地震影响系数曲线为目标反应谱，采用迭代法编制了规范反应谱转换为功率谱程序RSTOPS，进而形成了与规范反应谱相对应的功率谱库。运用非线性拟合的最小二乘法对功率谱库曲线进行洪峰—江近仁谱的参数拟合，给出了高通滤波器参数ω_h和谱强因子G_0的数值。
第三章主要讨论了一致及多点激励地震动合成方法。在本章中，首先回顾了地震动三要素及其衡量的物理量。介绍了拟合反应谱的一致激励人工波合成原理，提出了功率谱与幅值谱联合调整的方法，编制了与规范反应谱相一致人工地震波合成程序。运用随机过程的理论推导了多点地震动的幅值谱及相位谱与互功率谱矩阵元素之间的关系，通过对互功率谱密度函数矩阵的简化，提出了一种多点地震动合成的简化方法。该方法只需要对迟滞相干函数这一实对称矩阵进行Cholesky分解，不需要对互功率谱矩阵这一复数矩阵进行分解，避免了复杂的复数矩阵运算，从而提高了合成的效率。运用这一简化方法编制了多点地震动合成程序。
第四章主要讨论了多点激励时程分析法及其应用。在本章中，首先介绍了多点地震动激励下结构的运动方程及一种无条件收敛的数值求解方法：Wilson-θ法。本章的重点是以某体育场大跨度拱式钢结构为工程背景，运用时程分析法对其进行计算分析。主要内容包括：有限元模型的建立，时程分析所需一致及多点激励地震波的合成，大质量法在多点激励时程分析法的实现，分析了计算结果并得出了一些结论。
第五章主要探讨了多点激励反应谱分析方法及其应用。在本章中，首先介绍了一致及多点激励反应谱的基本原理。对比分析了常用的多点激励反应谱分析方法：B-K法，H-V法，MSRS法及Y-T法。MSRS(Multiple-Support Response Spectrum Method)法是基于严格的随机振动理论推导出来的，因此理论依据充分，可以看作CQC方法在多点激励情况下的推广。本章采用MSRS方法计算了两种形式的两跨连续梁：柔性梁和刚性梁，分析了空间变化地震动对这两种形式梁反应的影响特点并得出了一些有益的结论。
Large span structure being a part of modern civilization undertakes importantsocial functions. Safety of large span structure is given special consideration. Seismicground motion is a complicated time-space process. Previous seismic design and-research are always concerned with seismic time variation characteristics instead ofits spatial variation. Wave-passage effect, incoherence effect and local site effect aremain factors of spatial variation of seismic ground motion. Considering spatialvariation is a more feasible input method to structures with large planar dimension.
The dissertation is mainly concerned in response analysis for deformationsensitive large span structure under spatial variation seismic ground motion.
Based on the systematical summarization on the past research work in the field(Chapter 1), random process model of seismic ground motion is discussed and itsparameters are specified in Chapter 2. Firstly, common random models of seismicground motion are reviewed in this chapter. Then modified models based on filteredwhite noise model are summed up. Analysis and contrast of wave filtering lowfrequency and high frequency characteristics are carded out. With maximum responseestimate theory of random vibration, response spectrum of single degree of freedom(SDF) system under stationary seismic ground motion is calculated. Throughequivalent stationary method, response spectrum under non-stationary seismic groundmotion is calculated. By adopting random vibration theory, conversion between powerspectrum and response spectrum is realized by iteration method By adopting seismiceffect factor curve of Chinese current structure seismic design code (GB50011-2001)as object response spectrum, conversion program between power spectrum andresponse spectrum (RSTOPS) is compiled by iteration method, thus power spectrumarchive compatible with response spectrum of seismic code is built. By adoptingnonlinear fitting method, parameters of Hong feng-Jiang jin ten model are fitted withcalculated power spectrum and its two parameters:ω_h,G_0 are given in this Chapter.
Chapter 3 mainly discusses generation method of seismic ground motion. Firstly,three main factors of seismic ground motion and physical descriptive variables arereviewed in this chapter. Generation principle of uniform excitation artificial seismicground motion compatible with response spectrum of Chinese seismic code isintroduced. The method of power spectrum with amplitude spectrum modification isproposed in this chapter. Program of generation of artificial seismic ground motion compatible with response spectrum of Chinese code is complied. Based on randomprocess theory, a method of simulation of spatial correlated multi-point ground motionhas been proposed by simplification of cross power spectral density matrix. Onlydecomposition of lagged coherent density matrix is required instead of Choleskydecomposition of cross power spectral density matrix. Thus complex matrixcomputation is avoided and simulation efficiency is improved. A correspondingprogram has been compiled using the method.
Chapter 4 mainly discusses time history analysis method and its application.Firstly, structural motion equilibrium under multi-point seismic ground motionexcitation is built. An unconditioned convergence solving method (wilson-θmethod) is introduced in this chapter. The emphasis of this chapter is applying timehistory analysis method to calculate seismic response of a steel large span arch of astadium. The main contents conclude: build of finite element model, seismic wavegeneration under uniform and multi-point excitation, apply big mass method to timehistory method. Calculation results are analyzed and some conclusions are given.
Chapter 5 mainly discusses response spectrum method of multi-point excitationand its application. Firstly, basic principles of response spectrum method underuniform and multi-point excitation are introduced. Contrast and analysis of responsespectrum methods under uniform and multi-point excitation which include: B-Kmethod, H-V method, MSRS method and Y-T method. MSRS (Multiple-SupportResponse Spectrum Method)method is deduced by strict random vibration theory andregarded as an application of CQC method. Responses of two types of continuousbeams with two span: flexible beam and stiff beam are calculated by MSRS method.Responses characteristics of two types of beam under spatial variation seismic groundmotion are analyzed and some conclusions are given.
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