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 (…     

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．      

Synthetic Seismograms for a Layered Earth Geological Model Using the Absorption and Dispersion Phenomena

—An algorithm has been developed to compute the dispersive and dissipative seismic response using FUTTERMAN’S (1962) third attenuation-dispersion relationship. In the computation, frequency-dependent velocity and quality factor Q have been used but in the case of the nondispersive synthetic seismogram, frequency-independent velocity has been used. The model’s parameters are density, phase velocity, quality factors and thicknesses of the layers. Dispersive and nondispersive synthetic seismograms have been computed with and without absorption for a layered earth geological model. Fast Fourier transform (FFT) technique has been adopted for converting the frequency domain response into the time domain. The frequency spacing, Δf = 0.976?Hz, has been considered to avoid the aliasing effect. The results have revealed changes in the reflected waveforms in the frequency domain as well as in the time domain for absorption and dispersion cases. It is also concluded that dispersion reduces the arrival time and this effect is increasing with the travel time. The effect of constant Q on the seismic response has also been studied.     

Analysis and usage of linear relationships between the magnetic field components recorded by INTERMAGNET

An analysis of linear relationships between the ground-level components of the Earth’s magnetic field measured at different sites is a relatively new topic compared to the analysis of data at a single location. The data collected by the INTERMAGNET observation network provide perfect set of data to which this analysis can be used. An important tool in this analysis may be developing a method of determination of the impulse response for linear systems in the time domain. An advantage of calculations in the time domain over the generally known and applied methods in the frequency domain is the possibility of determining prediction of output signals. By that, simultaneously with the analysis of linear relationships, a tool for recovering missing records in incomplete observation data is obtained. Filling-in the missing data may increase interest and possibility of using the observational data by researchers experimenting with the analysis in the frequency domain where gaps in data records are a significant limitation.     

含流体层的河谷场地对地震波散射的间接边界元法模拟

结合单相介质动力格林函数和流体域格林函数,将间接边界元方法拓展到含流体层河谷对地震波散射的求解,并结合具体算例进行大量参数分析。研究结果表明,含流体层河谷地形对平面P波、SV波入射时的地震响应受控于入射波频率、入射波角度及流体深度等多种因素。总体来看:① 在低频域内,含流体河谷底部及附近地表的频谱特性与不含流体的河谷反应基本一致;② P波入射时在水层体系共振频率处,河谷底部位移缩小效应显著,而此频率处流体表面位移达到最大;③ 流体层具有吸收地震波能量的作用,流体深度越大,河谷表面及附近地表的地震动位移越小。研究成果可在一定程度上为河谷地形附近地震动效应的评估及防震减灾工作提供理论依据。      

Test of frequency characteristic for well and its response to seismic waves

The permeation parameters have been calculated by forefathers on the basis of permeation theory by means of the Slug test (Yin, Zheng, 1992) and the restoration curves of well level. We are interested in oscillation of the well level when we make Slug test. Both the permeation parameters and frequency parameters, i.e., natural period and damping coefficients of well aquifer, have been calculated on the basis of vibration theory by means of the oscillation curves. Not only this has given a new method, but also the different response of well level to seismic waves has been explained by it in theory.     

微分求积法在结构动力分析中的应用

微分求积法（DQM）是1种求解微分方程初（边）值问题的数值方法,通常以较小的计算工作量即可获得较高的数值精度。这种方法应用于工程领域时多用来解决梁、板等结构的静力分析或结构特征值分析等问题,即对边值问题的微分方程的求解。结构动力分析属于初值问题,荷载和结构反应都具有特殊性,直接套用DQM求解边值问题并不能获得问题的解。本文尝试利用微分求积原理建立求解结构动力反应的具体方法。借鉴单元法的思想,将荷载持时划分为若干个时步,在每个时步内对动态荷载和结构反应进行离散,然后用DQM对时步逐个进行求解,得到体系在整个时域内的反应过程。通过对3种不同自振周期的线弹性单自由度体系在不同频率简谐激励下反应的计算,阐释了本文方法的可行性以及高精度、高效率的特点,通过数值试验确定了时步内相对较优的节点数,并为时步长度的选取提供了建议。     

Dynamic response analysis in the frequency domain

Analysis in the frequency domain using discrete Fourier transforms is an efficient means of calculating the dynamic response of linear systems. In fact, for systems with frequency dependent parameters and also in those cases where the complex frequency response functions are more easily determined, frequency domain analysis may be the only effective means of determining the dynamic response. The use of discrete transforms along with finite summation requires that the forcing function and the impulse function be converted into periodic forms. This modification may introduce unacceptable errors in the results of analysis, unless appropriate steps are taken to avoid or minimize the effect of aliasing or overlapping. For single-degree-of-freedom systems, procedures that will eliminate the effect of aliasing have already been developed. However, problems related to frequency domain analysis still exist for multi-degree-of-freedom systems with non-proportional damping, in analysis through substructuring and in those cases where a continuum solution is involved. A new procedure which addresses these problems and is applicable to both single- and multi-degree-of-freedom system as well as to analysis through substructuring is presented here.     

PREM-ZSCHAU滞弹地球模型对表面负荷的脉冲响应

利用PREM模型及ZSCHAU的地球内部粘滞性模型,解算了地球对表面负荷的脉冲响应问题,包括频率域和时间域的解.得到的复勒夫数及复格林函数表明,在ω>10~(-8)/s的频段内,地球的响应可视为基本上是弹性的,只有像冰后调整、地幔对流这样长期的运动,粘滞性才起重要作用;在ω<10~(-13)/s的频段,地球响应呈流体状态.     

Stability of the time‐domain analysis method including a frequency‐dependent soil–foundation system

A number of methods have been proposed that utilize the time‐domain transformations of frequency‐dependent dynamic impedance functions to perform a time‐history analysis. Though these methods have been available in literature for a number of years, the methods exhibit stability issues depending on how the model parameters are calibrated. In this study, a novel method is proposed with which the stability of a numerical integration scheme combined with time‐domain representation of a frequency‐dependent dynamic impedance function can be evaluated. The method is verified with three independent recursive parameter models. The proposed method is expected to be a useful tool in evaluating the potential stability issue of a time‐domain analysis before running a full‐fledged nonlinear time‐domain analysis of a soil–structure system in which the dynamic impedance of a soil–foundation system is represented with a recursive parameter model. Copyright © 2015 John Wiley & Sons, Ltd.     

A numerical comparison of time and frequency‐domain marine electromagnetic methods for hydrocarbon exploration in shallow water

In shallow water the frequency domain controlled source electromagnetic method is subject to airwave saturation that strongly limits the sensitivity to resistive hydrocarbon targets at depth. It has been suggested that time‐domain CSEM may offer an improved sensitivity and resolution of these deep targets in the presence of the airwave. In order to examine and test these claims, this work presents a side‐by‐side investigation of both methods with a main focus on practical considerations, and how these effect the resolution of a hydrocarbon reservoir. Synthetic noisy data for both time‐domain and frequency domain methods are simulated using a realistic frequency dependent noise model and frequency dependent scaling for representative source waveforms. The synthetic data studied here include the frequency domain response from a compact broadband waveform, the time‐domain step‐response from a low‐frequency square wave and the time‐domain impulse response obtained from pseudo‐random binary sequences. These data are used in a systematic resolution study of each method as a function of water‐depth, relative noise and stacking length. The results indicate that the broadband frequency domain data have the best resolution for a given stacking time, whereas the time‐domain data require prohibitively longer stacking times to achieve similar resolution.     

基于阶跃响应在时域解析测定地震计参数

提出基于阶跃响应在时域解析测定地震计参数的方法，并对合理确定响应的时间零点提供了一种方法。对JC-V100 3D型便携式短周期地震计及与其配套的EDAS-3M型16位地震数据采集记录仪组成的系统进行了测试。结果表明：对JC-V1003D短周期地震计的传递函数进行测试是可行的，对地震计的阻尼系数Dc和自振周期Tc的测试结果是令人满意的。     

Response of a non-linear system with restoring forces governed by fractional derivatives—Time domain simulation and statistical linearization solution

In this paper, the random response of a non-linear system comprising frequency dependent restoring force terms is examined. These terms are accurately modeled in seismic isolation and in many other applications using fractional derivatives. In this context, an efficient numerical approach for determining the time domain response of the system to an arbitrary excitation is first proposed. This approach is based on the Grunwald–Letnikov representation of a fractional derivative and on the well-known Newmark numerical integration scheme for structural dynamic problems. Next, it is shown that for the case of a stochastic excitation, in addition to the time domain solutions, a frequency domain solution can be readily determined by the method of statistical linearization. The reliability of this solution is established in a Monte Carlo simulation context using the herein adopted time domain solution scheme. Furthermore, several related parameter studies are reported.     

对人造地震动反应谱求解及拟合的几个相关问题探讨

为更高效合理地生成与设计反应谱相符的人造地震动信号,本文基于自主开发的地震动信号处理软件EQSignal对人造地震动生成过程中涉及的几个问题进行了探讨,并通过对单自由度简谐共振体系的响应分析,提出了具体的解决建议:① 反应谱求解时应该对高频段和低频段分别采用频域传递函数法和逐步积分法求解;② 反应谱周期控制点的分布模式也应分段处理,短周期段宜采用对数平均分布,长周期段宜采用线性平均分布,反应谱总周期控制点不宜少于120个;③ 人造地震动反应谱与设计反应谱拟合的过程中,使用频域方法与时域方法相结合可兼顾效率与收敛性。      

New Methodology for Computation of the Earth’s Polarizability from Telluric Borehole Logging Measurements Taken at Different Frequencies

An important approach for computation of the earths polarizability is achieved by developing a novel method with new parameters called Natural Percent Frequency Effect (NPFE) and Natural Metal Factor (NMF) resulting from telluric logging data taken at different frequencies. The essential advantage of the developed approach relies on using natural electrical currents instead of an artificial electrical source usually needed in the standard frequency domain applied in the induced polarization method. Furthermore, a good qualitative correlation has been found between the new parameters and those of the traditional induced polarization method obtained in time and frequency domains. The new method has been tested in well 32 in the Rouez mine in France, where sulphide mineralization is well known to occur.     

瞬变电磁场时域格林函数解

近源时间域电磁场具有信号强、探测深度大、精度高等优点,但传统勘探电磁场理论中偶极子近似在近源会引起较大误差,导致这一优势的发挥受到了制约.开展直接时间域电磁场解析式研究,是解决这一问题的途径之一.本文提出在点电荷微元假设下,引入时域格林函数,求取瞬变电磁场时间域解析解.采用积分运算法,把电磁场阻尼波动方程的求解问题转化为求其格林函数积分形式解的问题;建立辅助路径解决奇点问题,利用复分析中的约当引理、留数定理和广义函数等理论和方法,推导计算出时间域格林函数的时空四重广义积分.得到达朗贝尔方程的直接时域格林函数精确解析式,与传统方法“比拟”出的公式具有相同的形式,验证了本文推导的时域格林函数解析公式的正确性;推导出扩散方程的直接时间域解析解.通过与时变点电荷源时间域的电磁响应近似表达式进行对比,得出本文所推导的公式计算精度较高的结论;建立了全空间回线源瞬变电磁场问题的直接时间域求解公式.为解决全场区瞬变电磁场精细探测直接时域解析问题提供了基础理论.     

Transverse response of offshore pipelines to random ground motion

A method is presented for the determination of the transverse response of the idealized suspended span of an offshore pipeline to random seismic input. The method is based on spatial discretization of the pipe with nodal lumped masses. The earthquake is assumed to be a stationary random process characterized by a power spectral density function. The cross spectral density function between two random seismic excitations along the pipe length is defined with the help of a local earthquake power special density function, which is assumed to be the same for the two end supports of the pipeline, and a frequency dependent weighted function which decays exponentially with distance from the pipe supports. The solution is obtained in the frequency domain using the spectral approach and is presented in terms of r.m.s. displacements and stresses. The formulation adequately includes the pressure drag effect which tends to dampen the pipe motions. Utilizing this method of analysis, several idealized pipe sea bed configurations, in which the pipe is anchored between two end blocks and subjected to horizontal ground excitations normal to the pipe axis, have been analysed to predict the influence of certain important parameters on the response.     

Stability and identification for rational approximation of frequency response function of unbounded soil

Exact representation of unbounded soil contains the single output–single input relationship between force and displacement in the physical or transformed space. This relationship is a global convolution integral in the time domain. Rational approximation to its frequency response function (frequency‐domain convolution kernel) in the frequency domain, which is then realized into the time domain as a lumped‐parameter model or recursive formula, is an effective method to obtain the temporally local representation of unbounded soil. Stability and identification for the rational approximation are studied in this paper. A necessary and sufficient stability condition is presented based on the stability theory of linear system. A parameter identification method is further developed by directly solving a nonlinear least‐squares fitting problem using the hybrid genetic‐simplex optimization algorithm, in which the proposed stability condition as constraint is enforced by the penalty function method. The stability is thus guaranteed a priori. The infrequent and undesirable resonance phenomenon in stable system is also discussed. The proposed stability condition and identification method are verified by several dynamic soil–structure‐interaction examples. Copyright © 2009 John Wiley & Sons, Ltd.     

考虑坝体材料非线性的混凝土拱坝地震反应分析

本文基于可信概率水准的破坏性强震作用,针对小湾高拱坝进行了考虑坝体材料非线性的拱坝地震反应分析。在分析模型中,同时考虑了无约束域地震能量辐射效应和近域地基材料非均匀性的影响。为了实现非线性条件下的静、动力组合分析,利用显式有限元结合修正的黏弹性人工边界的开放系统时域静、动力统一分析方法进行了求解,对在自重作用下的初始静力解计算采用了动力松弛技术。     

Stochastic analysis of structures and piping systems subjected to stationary multiple support excitations

A stochastic method has been developed for seismic analysis of structures and piping systems subjected to multiple support excitations. In either the time or the frequency domain, mean and extreme values of structural and piping system response can be found, including the effects of cross-correlations of modal response and cross-correlations of multiple support excitations. Stationary white noise and stationary filtered white noise ground excitations are used. A computer program has been developed to carry out the stochastic seismic analysis. Results for a realistic nuclear power plant structure and piping system with and without modal cross-correlations and support excitation cross-correlations are compared. From these results, it is concluded that neglecting cross-correlations can lead to large errors. The stochastic method reported is shown to be more accurate than the response spectrum method and more economical than the time-history method; therefore, it is recommended for seismic analysis of nuclear power plants.