结构平稳随机地震反应时域分析:方法

给出了三种常用的随机地震地面运动过程模型,即理想白噪声模型、金井清模型、改进金井清模型的相关函数表达式.引入状态向量,在状态空间中建立地震地面运动激励下的结构振动方程,并求解出结构的复模态特性和复模态反应.利用复模态叠加法推导出线性时不变多自由度体系在这三种随机地震动激励下的平稳协方差反应的解析式,可在时域内直接计算结构随机反应的统计特征.该方法物理概念清晰,结论简便明确,可作为实际工程结构平稳随机地震反应的实用分析方法.     

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.     

A stochastic model and synthesis for near‐fault impulsive ground motions

The orientations of ground motions are paramount when the pulse‐like motions and their unfavorable seismic responses are considered. This paper addresses the stochastic modeling and synthesizing of near‐fault impulsive ground motions with forward directivity effect taking the orientation of the strongest pulses into account. First, a statistical parametric analysis of velocity time histories in the orientation of the strongest pulse with a specified magnitude and various fault distances is performed. A new stochastic model is established consisting of a velocity pulse model with random parameters and a stochastic approach to synthesize high‐frequency velocity time history. The high‐frequency velocity history is achieved by integrating a stochastic high‐frequency accelerogram, which is generated via the modified K‐T spectrum of residual acceleration histories and then modulated by the specific envelope function. Next, the associated parameters of pulse model, envelope function, and power spectral density are estimated by the least‐square fitting. Some chosen parameters in the stochastic model of near‐fault motions based on correlation analysis are regarded as random variables, which are validated to follow the normal or lognormal distribution. Moreover, the number theoretical method is suggested to select efficiently representative points, for generating artificial near‐fault impulsive ground motions with the feature of the strongest pulse, which can be used to the seismic response and reliability analysis of critical structures conveniently. Finally, the simulated ground motions demonstrate that the synthetic ground motions generated by the proposed stochastic model can represent the impulsive characteristic of near‐fault ground motions. Copyright © 2014 John Wiley & Sons, Ltd.     

RESPONSE ANALYSIS FOR FUZZY STOCHASTIC DYNAMICAL SYSTEMS WITH MULTIPLE DEGREES OF FREEDOM

Most real-life structural/mechanical systems have complex geometrical and material properties and operate under complex fuzzy environmental conditions. These systems are certainly subjected to fuzzy random excitations induced by the environment. For an analytical treatment of such a system subjected to fuzzy random excitations, it becomes necessary to establish the general theory of dynamic response of a system to fuzzy random excitations. In this paper, we extend the work published in Reference [1], and discuss the case of Multi-Degree-of-Freedom (MDF) fuzzy stochastic dynamical systems. The theory of the response, fuzzy mean response and fuzzy covariance response of multi-degree-of-freedom system to fuzzy random excitations in the time domain and frequency domain is put forward. Two cases to determine the fuzzy response statistics of the fuzzy stochastic dynamical system with multiple degrees of freedom are discussed. Two examples are considered in order to demonstrate the rationality and validity of the theory. © 1997 by John Wiley & Sons, Ltd.     

均质土坝非平稳随机地震反应分析

考虑地震荷载的随机性及强度、频率的非平稳性,基于作者提出的适用于非平稳随机过程的一般随机地震动模型,采用虚拟激励法,建立了非平稳随机地震反应分析方法,并将其应用于某实际均质土坝动力分析中。土石坝及坝基体系采用整体有限元离散,坝体和坝基材料的动力非线性性能以等效线性化方法考虑。首先,基于目标加速度时程的强度和能量信息,确定了作为输入的加速度时—频演变功率谱密度;其次,比较了确定性时程动力分析和非平稳随机分析的结果,探讨了频率非平稳随机地震激励下的土石坝地震反应特性;最后,比较了2种不同坝基条件下的土石坝非平稳随机地震反应,探讨了频率非平稳随机激励下的土石—坝基动力相互作用。分析结果表明：地震动的频率非平稳性对土石坝动力反应有一定影响;坝体—坝基动力相互作用在地震过程中的不同阶段表现有所不同,主震阶段的相互作用显著。     

RANDOM SEISMIC RESPONSES OF MULTI-SUPPORT STRUCTURES IN EVOLUTIONARY INHOMOGENEOUS RANDOM FIELDS

An efficient approach is proposed for analysing the non-stationary random responses of complex structures located in an evolutionary inhomogeneous stochastic field. The approach is a kind of complete CQC method because the cross-correlation terms both between the participant modes and between the ground joint excitations are included in the response calculations. The effect of the loss of coherency between ground joints is also taken into account. For non-proportionally damped structures with many degrees of freedom, the order of the equations of motion can be reduced by using only real modes while structural non-stationary random responses can still be computed conveniently and accurately. © 1997 by John Wiley & Sons, Ltd.     

Stochastic earthquake response of secondary systems in base-isolated structures

This paper studies the stochastic responses of secondary systems in base-isolated shear beam structures. A number of base isolation systems such as the laminated rubber bearing (LRB), the resilient-friction base isolator (R-FBI) with or without sliding upper plate, and the EDF system are considered. The stochastic models for the El Centro 1940 and the Mexico City 1985 earthquakes which preserve the non-stationary evolutions of amplitude and frequency content of ground accelerations are used as earthquake excitations. The technique of equivalent linearization is utilized and the mean-square response statistics of secondary systems and primary structure are evaluated. The accuracy of the linearization scheme is verified by comparison with the Monte Carlo simulation results. Statistically estimated peak responses of the secondary system are evaluated and the results are compared with the response spectra for actual earthquake accelerograms. It is shown that the use of base isolation systems, generally, provides considerable protection for structural contents. In particular, the LRB system is remarkably effective in reducing responses of secondary systems. Results for the Mexico City earthquake show that the base-isolated structures are sensitive to long period ground excitations.     

多点激励下结构随机地震反应分析的反应谱方法

基于随机振动理论,提出了多点激励作用下线性系统随机地震反应分析的均值反应谱方法,给出了结构峰值反应的均值、标准差以及反应平均频率的反应谱组合公式。这可以将反应谱方法推广应用到多点激励结构的抗震可靠度分析中。鉴于组合公式中谱参数和相关系数需要由烦琐的数值积分得到,本文进一步针对它们给出合理的简化计算式,从而使得建议的反应谱方法的计算效率大大增加。最后,以一个双塔斜拉桥为例,对本文方法进行了验证。基于建议方法的计算结果与Monte Carlo模拟结果吻合较好。与经典的多点激励反应谱方法(MSRS法)比较,本文方法具有其无法比拟的计算效率。     

随机地震动场多点激励下宽幅大跨桥梁结构地震响应研究

为了研究随机地震动场多点激励作用下宽幅大跨桥梁结构的地震响应,基于二维相干模型,考虑地震波非平稳性合成桥址各支承点的人工地震加速度时程波,采用多项式拟合法在时域内对各支承点处的人工合成加速度波进行校正,并对校正前后加速度波的响应谱进行比较校验;随后以某大跨自锚式悬索桥为例,利有限元软件中线性时程分析模块,将所合成的加速度地震波施加于结构,对比研究一致激励与随机地震动多点激励下宽幅大跨桥梁结构的地震响应。分析表明,考虑二维相干和地震波非平稳性合成的各支承点地震加速度时程波可采用多项式拟合法进行基线漂移现象的校正,同时应对修正前后加速度波的反应谱进行比较校验;对于大跨且横桥向支承点相距较远的桥梁结构应考虑横桥向地震波的非一致性。     

Effective linear damping and stiffness coefficients of nonlinear systems for design spectrum based analysis

A stochastic approach for obtaining reliable estimates of the peak response of nonlinear systems to excitations specified via a design seismic spectrum is proposed. This is achieved in an efficient manner without resorting to numerical integration of the governing nonlinear equations of motion. First, a numerical scheme is utilized to derive a power spectrum which is compatible in a stochastic sense with a given design spectrum. This power spectrum is then treated as the excitation spectrum to determine effective damping and stiffness coefficients corresponding to an equivalent linear system (ELS) via a statistical linearization scheme. Further, the obtained coefficients are used in conjunction with the (linear) design spectrum to estimate the peak response of the original nonlinear systems. The cases of systems with piecewise linear stiffness nonlinearity, along with bilinear hysteretic systems are considered. The seismic severity is specified by the elastic design spectrum prescribed by the European aseismic code provisions (EC8). Monte Carlo simulations pertaining to an ensemble of nonstationary EC8 design spectrum compatible accelerograms are conducted to confirm that the average peak response of the nonlinear systems compare reasonably well with that of the ELS, within the known level of accuracy furnished by the statistical linearization method. In this manner, the proposed approach yields ELS which can replace the original nonlinear systems in carrying out computationally efficient analyses in the initial stages of the aseismic design of structures under severe seismic excitations specified in terms of a design spectrum.     

Bayesian estimates of marine radiocarbon reservoir effect in northern Iberia during the Early and Middle Holocene

Reconstructing the past variability of marine radiocarbon reservoir effects (MRE) is crucial for generating reliable chronologies for marine species and their consumers. We investigated the temporal MRE variability at the Early-to Mid-Holocene site of El Mazo (Asturias, northern Spain) by using a combination of new and previously published radiocarbon measurements on marine and terrestrial samples. The El Mazo site is characterized by overall well-defined archaeological layers of unknown occupation length with the predominant presence of two mollusc species (Patella vulgata Linnaeus, 1758 and topshell Phorcus lineatus [da Costa, 1778]) which were analysed for radiocarbon measurements. We employed the recently released IntCal20 calibration curve for the northern hemisphere and Bayesian modelling to reconstruct the site's chronology and temporal variability in MREs according to mollusc species. Obtained radiocarbon modelling results, although the estimate precision is not high, reveal a temporal variability in MREs that can be interpreted in view of known past climatic and environmental events such as the 8.2 ka event. The results also revealed differences in MREs according to mollusc species, which need to be taken into account in future chronological modelling. Overall, our results provide reference MRE values for the study of chronologies in northern Iberia during the Early-to Mid-Holocene. In this respect, a non-conservative ΔR reference for local marine samples dating earlier than c. 8.1 ka cal BP is −238 ± 28 ¹⁴C years.     

Non-stationary random vibrations of a shear beam under high frequency seismic effects

Band-limited, non-stationary random vibrations of a shear beam are studied in order to investigate high frequency seismic effects on building structures. A solution for the evolutionary spectral density of the shear beam response to a time segment of band-limited white noise is given in a closed form. The root mean square (rms) and peak response of the shear beam are studied for two characteristic frequency bands: the conventional 1–4 Hz and higher frequency 4–16 Hz, characteristic for rockburst ground motion. Applying the criterion of equal excitation intensity with constant rms velocity, both responses are analyzed in detail and compared. The “switching off” fundamental mode for high frequency excitations results in characteristic overshoot of the stationary response level by the non-stationary rms response and an amplification of the response in the upper part of the shear beam.     

Response spectrum analysis for non-classically damped linear system with multiple-support excitations

A new response spectrum method, which is named complex multiple-support response spectrum (CMSRS) method in this article, is developed for seismic analysis of non-classically damped linear system subjected to spatially varying multiple-supported ground motion. The CMSRS method is based on fundamental principles of random vibration theory and properly accounts for the effect of correlation between the support motions as well as between the modal displacement and velocity responses of structure, and provides an reasonable and acceptable estimate of the peak response in term of peak seismic ground motions and response spectra at the support points and the coherency function. Meanwhile, three new cross-correlation coefficients or cross covariance especially for the non-classically damped linear structures with multiple-supports excitations are derived under the same assumptions of the MSRS method of classically damped system. The CMSRS method is examined and compared to the results of time history analyses in two numerical examples of non-classically damped structures in consideration of the coherences of spatially variable ground motion. The results show that for non-classically damped structure, the cross terms representing the cross covariance between the pseudo-static and dynamic component are also quite small just as same as classically damped system. In addition, it is found that the usual way of neglecting all the off-diagonal elements in transformed damping matrix in modal coordinates in order to make the concerned non-classically damped structure to become remaining proportional damping property will bring some errors in the case of subjected to spatially excited inhomogeneous ground motion.     

Dynamic soil–structure interaction effects on the seismic response of suspension bridges

A stochastic approach has been formulated for the linear analysis of suspension bridges subjected to earthquake excitations. The transfer functions of various responses have been formulated while including the effects of dynamic Soil–Structure Interaction (SSI) via the use of the fixed-base modes of the structure. The excitation has been characterized by the ‘equivalent stationary’ processes corresponding to the free-field motions at each support and by an assumed coherency function between these motions. The proposed formulation considers the non-stationarity in the structural response due to sudden application of excitation by considering (i) the time-dependent frequency response functions, and (ii) the order statistics formulation for the peak factors in evolutionary response processes. The formulation has been illustrated by analysing the seismic response of the Golden Gate Bridge at San Francisco for two example excitations conforming to USNRC-specified design spectra. The significance of various governing parameters on the dynamic soil–structure interaction effects on the seismic response of suspension bridges has also been studied. It has been found that the contribution of the vertical component of ground motion to the bridge response increases with increasing soil compliance. Also, the extent to which the spatial variation of ground motion affects the bridge response depends on how significant the SSI effects are. Copyright © 1999 John Wiley & Sons Ltd.     

Stochastic considerations in seismic analysis of structures

A method is presented for stochastic modelling of a design earthquake by a power spectral density function for seismic analysis of structures. The method can be adopted with information currently available in the form of design response spectra for earthquake motion. Accurate seismic responses of structures can be easily obtained using such stochastic models. The methods for accurate response analysis of structures with closely spaced modes and for generation of floor response spectra of a building using a prescribed ground response spectrum directly are also presented. The hypothesis that a design earthquake can be modelled by a power spectral density function is used only implicitly in developing these methods.     

考虑水流-结构强耦合作用的水流动力效应分析

在深水桥墩及桩基础等结构地震反应中,地震激励下的水流动水压力对水中结构的作用以及结构位形变化对水体的反作用,属于典型的流固强界面耦合问题。以一顶端伸出水面的圆柱式结构为研究对象,基于任意拉格朗日-欧拉描述的Navier-stokes方程,建立了考虑水流-结构强耦合效应的水流-结构三维有限元模型。以正弦位移波输入,考察结构材料模量、水流流速和水位、激振频率和位移幅值等多种因素,分析了结构表面作用的动水压力反应特征以及水流动力效应,探讨了水流动力效应的主要影响因素。结果表明：考虑流固强耦合作用时,结构表面作用的动水压力及其分布具有强烈的频率依赖性,高频激励可显著增强动水压力作用;由于结构周围流体具有一定的粘滞性及动载作用下具有较强的辐射阻尼效应,水流动力效应对结构的位移、内力反应均有一定的抑制作用;激振频率、水流流速和水位以及结构材料模量等因素,对水流动力效应均有一定的影响。     

Arch responses to correlated multiple excitations

This paper analyses the in-plane stochastic responses of incompressible circular arches to spatially correlated multiple excitations. The dynamic, quasi-static and total structural displacements, moments, shear and axial forces are calculated. The results are compared with those obtained by various simplified excitations. The effects of the ground motion spatial variations on arch responses are examined. The results indicate that the responses may be underestimated or overestimated by neglecting the ground motion spatial variations, depending upon the structure and ground motion properties, the locations where the responses are evaluated, and the response quantity under consideration.     

Cross-correlation coefficients and modal combination rules for non-classically damped systems

In stochastic analysis the knowledge of cross-correlation coefficients is required in order to combine the response of the modal Single-Degree-Of-Freedom (SDOF) oscillators for obtaining the nodal response. Moreover these coefficients play a fundamental role in the seismic analysis of structures when the response spectrum method is used. In fact they are used in some modal combination rules in order to obtain the maximum response quantities starting from the modal maxima. Herein a method for the evaluation of the cross-correlation coefficients for non-classically damped systems is presented. It is defined in the time domain instead of the frequency domain as usually encountered in the literature. Although non-classically damped structures possess complex eigenproperties, the great advantage in using this approach lies in the fact that the evaluation of these coefficients does not require complex quantities. Moreover a further particularization of the presented method allows a simple application of the spectrum analysis requiring only one response spectrum for an assigned damping ratio. Copyright © 1999 John Wiley & Sons, Ltd.     

Peak earthquake response of structures under multi-component excitations

Accurate estimation of the peak seismic responses of structures is important in earthquake resistant design. The internal force distributions and the seismic responses of structures are quite complex, since ground motions are multi- directional. One key issue is the uncertainty of the incident angle between the directions of ground motion and the reference axes of the structure. Different assumed seismic incidences can result in different peak values within the scope of design spectrum analysis for a given structure and earthquake ground motion record combination. Using time history analysis to determine the maximum structural responses excited by a given earthquake record requires repetitive calculations to determine the critical incident angle. This paper presents a transformation approach for relatively accurate and rapid determination of the maximum peak responses of a linear structure subjected to three-dimensional excitations within all possible seismic incident angles. The responses can be deformations, internal forces, strains and so on. An irregular building structure model is established using SAP2000 program. Several typical earthquake records and an artifi cial white noise are applied to the structure model to illustrate the variation of the maximum structural responses for different incident angles. Numerical results show that for many structural parameters, the variation can be greater than 100%. This method can be directly applied to time history analysis of structures using existing computer software to determine the peak responses without carrying out the analyses for all possible incident angles. It can also be used to verify and/or modify aseismic designs by using response spectrum analysis.