地震动反应谱的数值计算精度和相关问题

定性讨论了采用精确法和其它数值方法计算地震动反应谱的精度和与之相关的问题。认为综合考虑精度、稳定性和效率3个因素,精确法仍然是计算地震动反应谱的首选方法。认为比值λh是影响反应谱计算精度的最重要因素,比值λ0则相对次要。讨论表明频域方法也是近似方法,不能作为度量其它方法精度的基准。指出计算地震动反应谱时,采用线性插值方法加密输入地震动,不能保证高频段反应谱的计算精度,建议深入研究这一问题以取得定量结果。     

线性土-结构动力相互作用时域-频域联合解法

提出一种线性土-结构动力相互作用时域-频域联合解法．首先，用近场波动数值模拟解耦技术求得在短时脉冲作用下采用Rayleigh阻尼系统的时域解；再对时域解进行富立叶变换得到相应频域解；然后根据阻尼与系统动力反应结果的关系，利用泰勒级数展开技术得到具有复阻尼系统的频域解．这一方法充分利用了时域解耦显式算法的优点，提高了线性土 结构动力相互作用分析的计算效率．      

单自由度系统地震动力反应的实时计算方法

本文对计算单自由度系统地震动力反应的频域方法和时域方法进行了分析比较。说明了目前时域方法所存在的问题,指出寻找一种在计算精度上与频域方法等价的时域算法是一个值得研究的重要课题。据此,本文提出了一套能较精确模拟单自由度系统传递函数的时域方法。其计算格式采用具有较高计算效率的递归格式。理论分析与数值试验表明,该方法具有精度优于其他时域算法、速度快的特点,可应用于强震观测台网中强地震动参数的实时计算。     

下辽河地区典型土层地震反应时域和频域方法对比

为了解决一维频域等效线性化方法在计算下辽河地区深覆盖场地地震反应时不够准确这一问题,本文采用一维时域非线性计算程序DEEPSOIL对该地区典型土层地震反应进行计算,并将结果进行对比分析。研究结果表明,在大震情况下,时域非线性方法有效地避免了等效线性化方法加速度峰值不合理和特征周期值偏高的现象。用时域非线性方法计算该类型场地大震情况,结果更加合理。     

窗函数对地基阻尼比测试的影响

根据某块体基础的实测数据,讨论了常见平滑方法对时域对数衰减法和频域点峰法竖向阻尼比测试的影响。结果表明,无论采用时域方法还是频域方法,分别对测试曲线进行相邻三点的滑动平均、汉宁窗、哈明窗平滑,阻尼比计算数值差别很小。平滑次数对时域阻尼比结果有影响,平滑次数越多,时域阻尼比有减少的趋势,而频域阻尼比有增大的趋势。滑动平均方法和平滑次数的合理选取,应通过理论和试验方法的研究进一步确定。     

中硬场地下两种土层地震反应方法与精确解的对比

基于谐波入射下的波动理论频域精确解,导出线性时域精确解,并在Matlab环境中编制相应的计算程序;选取8个简化的中硬场地剖面,用LSSRLI-1、精确解和SHAKE2000三种方法计算各场地在不同输入条件下的地震反应。结果表明:程序计算所得地表反应谱和土体剪应变分布与SHAKE2000结果一致;LSSRLI-1方法得到的地表反应谱与前二者结果一致;LSSRLI-1方法在某些情况下得到的土体剪应变分布与另外二者结果存在较大偏差,该偏差对地表反应谱有着不可忽略甚至非常显著的影响。     

基于滞变阻尼模型的反应谱CQC法

复阻尼模型具有每周期耗散能量与外激励频率无关的优点,但自由振动解中存在发散项。基于复阻尼模型的等效滞变阻尼模型不仅保留了相应的优点,且克服了时域发散的缺陷。本文在模态叠加法的基础上,提出了基于滞变阻尼模型的反应谱CQC法,并利用时域精确解验证了所提方法的正确性。在此基础上,以反应谱和相关系数为分析对象,对比了基于滞变阻尼模型的反应谱CQC法和基于黏性阻尼模型的反应谱CQC法。算例分析表明:小阻尼比情况下,两种方法的计算结果近似相等;大阻尼比情况下,两种方法计算所得的反应谱值和相关系数皆差异较大;大阻尼比结构需依据结构材料的阻尼特性,选择合适的反应谱CQC法。     

基于复阻尼理论的混合结构Rayleigh阻尼模型

混合结构的阻尼矩阵不满足经典阻尼条件,导致传统的模态叠加法无法适用。复阻尼理论无法适用于时域计算,其自由振动响应中存在发散现象。针对混合结构的阻尼矩阵非比例性和复阻尼理论的时域发散性,基于频域等效原则构建了求解Rayleigh阻尼系数的数学优化模型,进而得到与复阻尼理论等效的Rayleigh阻尼运动方程。算例分析表明:依据位移时程响应和结构等效阻尼比可证明Rayleigh阻尼运动方程的正确性。基于本文研究成果,等效复阻尼理论的混合结构Rayleigh阻尼运动方程可直接采用模态叠加法,结合其确定的结构等效阻尼比,为混合结构的振型分解反应谱法提供理论依据。     

地电磁辐射宽频域采样观测方法

目前地电磁辐射的点域或有限多点频观测方法存在的事件漏测和测量结果缺乏精细度等问题，而宽频带快速时域采样又会带来数据存贮容量，数据处理和管理以及系统成本等一系列问题，针对这种情况，为克服点频测量的局限性，研究了一种与信号相位无关的正交锁定频域采样的地电磁辐射谱观测方法，并给出了相应的系统硬件实现结构，这种方法在一次地电磁辐射过程中谱特性不变或某一谱分量持续时间不小于扫描周期的情况下，能准确地测量信号     

成层地基自由场地面运动的随机模型

地表土层通常具有成层的特点,在地震工程中将覆盖土层简化为力学性质沿竖向成层变化,水平向为各向同性的层状半空间体才会得到更符合实际情况的解答.采用频域分析方法,对多层横观各向同性土层对垂直向上的入射剪切波的反应进行了分析.在此基础上,分析了自由场地面运动的频率响应函数,计算了响应位移的功率谱密度函数,并给出了算例.算例表明,多层土的功率谱密度函数具有多个峰值.采用频域分析方法计算层状土地基在地震作用下的位移和应力响应,避免了时域分析时对波在界面处多次反射和透射的反复追踪,思路清晰,步骤简明.     

Significance of ground motion time step in one dimensional site response analysis

The discrete nature of the numerical methods utilized in 1D site response analysis and calculation of the response spectra (e.g., frequency domain, Duhamel integral, and Newmark β methods) introduces time-step dependence in the resulting solution. Using an input ground motion with too large of a time-step leads to under-prediction of high-frequency characteristics of the system response due to limitations in the numerical solution of single and multiple degree of freedom systems. In order to reduce potential errors, using a sampling rate at least ten times greater than the maximum considered frequency is recommended. The preferred alternative is selection of input ground motions with a sufficiently small time step to avoid introducing numerical errors. However, where such motions are not available, then the time step of the ground motion can be reduced through interpolation. This paper demonstrates that the use of Fourier transform zero-padded interpolation is the preferred approach to obtain a ground motion with an adequate time step for the calculation of the elastic acceleration response spectra, and to analyze site response using either frequency or time domain methods.     

基于等效线性化方法的一维土层地震反应通用计算程序对比

基于等效线性化的一维土层地震反应计算是目前国内外普遍采用的方法,国外的SHAKE91、DEEPSOIL和我国的LSSRLI-1即是根据这一方法编制的通用计算程序。本文采用这3个程序进行了不同地震波、不同输入地震动幅值下不同场地类型的土层地震反应计算,并对三者的结果进行了全面的比较分析。结果表明:①SHAKE91和DEEPSOIL程序的计算结果完全相同;②当土层最大剪应变均采用时域计算时,LSSRLI-1程序的计算结果与SHAKE91和DEEPSOIL程序基本相同,但有微小差别,其原因是:在基于等效剪应变通过离散形式的剪切模量和阻尼比随等效剪应变变化的关系曲线确定等效剪切模量和阻尼比时,DEEPSOIL和SHAKE91采用的插值方法与LSSRLI-1不同;③当LSSRLI-1程序采用频域经验关系计算土层最大剪应变时,特别是在强地震动输入下得到的土层地表加速度峰值和加速度反应谱与另外两个程序的计算结果有差别,且土层最大剪应变随着输入加速度的增大出现较大的差别。因此,本文建议:当采用LSSRLI-1程序计算土层地震响应时,应使用程序中的时域解方法代替以往默认的频域经验关系方法。     

阶跃响应测定地震计周期与阻尼的精度研究

对阶跃响应波形的时域测定与频域测定两种方法进行对比计算,结果表明,频域测定法的计算精度提高约1个数量级。研究地震计周期与阻尼参数的影响因素,应优先选用频域测定法。     

Dynamic-stiffness matrix in time domain of unbounded medium by infinitesimal finite element cell method

To calculate the dynamic-stiffness matrix in the time domain (unit-impulse response functions) of the unbounded medium, the infinitesimal finite element cell method based solely on the finite element formulation and working exclusively in the time domain is developed. As in the cloning algorithm, the approach is based on similarity of the unbounded media corresponding to the interior and exterior boundaries of the infinitesimal finite element cell. The derivation can be performed exclusively in the time domain, or alternatively in the frequency domain. At each time station a linear system of equations is solved. The consistent-boundary method to analyse a layered medium in the frequency domain and the viscous-dashpot boundary method are special cases of the infinitesimal finite element cell method. The error is governed by the finite element discretization in the circumferential direction, as the width of the finite-element cell in the radial direction is infinitesimal. The infinitesimal finite element cell method is thus ‘exact in the finite-element sense’. This method leads to highly accurate results for a vast class of problems, ranging from a one-dimensional spherical cavity to a rectangular foundation embedded in a half-plane.     

A hybrid analysis method for linear dynamic soil-structure interaction in time and frequency domain

IntroductionThe analysis of dynamic soil-structure interaction for important engineering project is still based on linear model (including equivalent linear model) with complex damping, and traditional frequency domain method (Lysmer, et al, 1975, 1981; DING, et al, 1999). Namely, first calculating frequency domain solution by Fourier transform, and then calculating time domain solution by Fourier inverse transform. The motion equation of a system in frequency domain is usually written as (…     

强震区非对称连续梁桥地震响应及性能评价

为研究高烈度地区不等跨连续梁桥的抗震性能，依托某高速公路上一座主跨为（40+60+35）m的典型不等跨连续梁桥，建立其动力分析有限元模型，获得该桥的模态特性。在E1概率和E2概率两种地震水平作用下，同时采用反应谱分析和时程分析法，对不等跨桥梁结构的地震响应进行分析。最后根据桥墩验算截面的弯矩-曲率关系曲线，探讨该桥梁的抗震性能。研究结果表明：动态时程反应分析与反应谱分析所得的结果基本吻合，由于反应谱分析假定结构线弹性状态而时程反应分析考虑了材料的弹塑性，在E2概率水平下，两者个别响应值有较大差别；由于反应谱法是对各阶模态下最大响应的组合，动态时程反应分析是同一时刻各地震波引起的结构响应的组合，因而时域和频域计算结果会存在一些误差，频域结果偏于保守；E1、E2概率地震作用下，主桥桥墩检算截面仍然在弹性范围内工作，满足弹性设计要求。     

Non-stationary frequency response function

Using the Duhamel’s integral concept, a non-stationary frequency response function (complete-FRF) for the dynamic response of a single degree of freedom system initially at rest has been developed. Although the procedure is devised to be applied in the frequency domain, this new function is time dependent and can be employed to calculate the transient response of a system in a forced vibration case. The method has been successfully checked with two different cases of loading in the time domain which have either analytical solution or accurate numerical solution using Newmark’s algorithm. The method has been compared with the solution obtained from the commonly used steady frequency response function, and a detailed analysis of the four parameters that appear in the complete-FRF function: time, damping ratio, natural period and input frequency is presented. Finally, the proposed non-steady FRF has been applied to the calculation of an elastic displacement response spectrum to confirm the great influence of the natural period of the system and the frequency content of the solicitation in frequency-domain spectral analysis.     

FDE index for goodness‐of‐fit between measured and calculated response signals

A method is presented for determining the goodness‐of‐fit between measured and calculated structural response signals. The method is termed as the frequency domain error (FDE) index, which is a value between 0 and 1 where zero indicates a perfect correlation. The FDE is calculated from the Fourier spectra of the measured and calculated waveforms, using a relatively simple calculation procedure, readily implemented using standard fast Fourier transform (FFT) libraries. The FDE is demonstrated herein using three different types of problems: simple harmonic waves, a large number of earthquake response simulations, and a set of limited simulations. Along with the FDE concept, effective methods for displaying the results are presented. Copyright © 2009 John Wiley & Sons, Ltd.