结构随机地震响应分析的复模态法

本文对多自由度基础平动结构随机地震响应问题进行了系统研究。针对用第1振型近似代表上部结构所得方程为非经典阻尼和非对称结构情况。用复模态法解耦。获得了以第1振型表示的结构地震响应的解析解。对单自由度体系。此解即为结构响应的精确解。本文方法也可用于带TMD减震结构等的随机地震响应分析与优化设计。     

Stochastic seismic response analysis of hysteretic multi-degree-of-freedom structures

Analytical study of random vibration of non-linear mutli-degree-of-freedom (MDF) systems is generally difficult. This is particularly true for MDF inelastic systems due to the highly non-linear and hereditary behaviour of the restoring force. On the other hand, to obtain the response statistics using a step-by-step Monte Carlo simulation requires a large sample, and it could be very costly. The purpose of this paper is to present a practical analytical-empirical method for an MDF yielding system. The method is based on a substitute structure (SS) concept in which the SS parameters are determined from empirical results of single-degree-of-freedom systems, i.e. each element in the system is replaced by a linear counterpart with ductility-dependent stiffness and damping. Based on a linear random vibration response analysis, the statistics of the maximum response (ductility) of each element are obtained by iteration. Numerical examples are given for multi-storey buildings with deteriorating (reinforced concrete frame) or non-deteriorating (steel frame) restoring forces. Comparisons with empirical results are satisfactory qualitatively. The main advantage of this method is that it requires relatively insignificant computation time, e.g. 1 s of execution time on the IBM 360–75 system for an eight-storey steel frame.     

A faster simulation method for the stochastic response of hysteretic structures subject to earthquakes

A semi-analytical forward-difference Monte Carlo simulation procedure is proposed for the determination of the lower order statistical moments and the joint probability density function of the stochastic response of hysteretic non-linear multi-degree-of-freedom structural systems subject to nonstationary gaussian white noise excitation, as an alternative to conventional direct simulation methods. The method generalizes the so-called Ermak-Allen algorithm developed for simulation applications in molecular dynamics to structural hysteretic systems. The proposed simulation procedure rely on an assumption of local gaussianity during each time step. This assumption is tantamount to various linearizations of the equations of motion. The procedure then applies an analytical convolution of the excitation process, hereby reducing the generation of stochastic processes and numerical integration to the generation of random vectors only. Such a treatment offers higher rates of convergence, faster speed and higher accuracy. The procedure has been compared to the direct Monte Carlo simulation procedure, which uses a fourth-order Runge-Kutta scheme with the white noise process approximated by a broad band Ruiz-Penzien broken line process. The considered system was a multi-dimenensional hysteretic shear frame, where the constitutive equation of the hysteretic shear forces are described by a bilinear hysteretic model. The comparisons show that significant savings in computer time and accuracy can be achieved.     

Shear hysteretic elasto-plastic earthquake response of soil systems

An analytical/numerical procedure is developed to calculate the shear hysteretic elasto-plastic earthquake response of soil systems. Dynamic level ground response as well as earth-dam response is evaluated on the basis of the analytical one-dimensional (ID) shear-beam and shear-wedge models respectively. Soil is modelled as an elasto-plastic hysteretic material following the principles of flow or incremental plasticity. Stiffness and strength degradation of this material may be specified as a function of accumulated plastic strain and associated pore-pressure build-up. The entire numerical procedure may be executed on a personal computer and consequently qualifies as a versatile tool in conducting preliminary design calculations or parametric-type investigations. Using this procedure, the responses of the Mexico City SCT site during the September 19, 1985 earthquake, and the California Wildlife site during the November 24, 1987 earthquake are computed and compared to those actually observed.     

A substructure method for earthquake analysis of structures including structure-soil interaction

A general substructure method for analysis of response of structures to earthquake ground motion, including the effects of structure-soil interaction, is presented. The method is applicable to complex structures idealized as finite element systems and the soil region treated as either a continuum, for example as a viscoelastic halfspace, or idealized as a finite element system. The halfspace idealization permits reliable analysis for sites where essentially similar soils extend to large depths and there is no rigid boundary such as soil-rock interface. For sites where layers of soft soil are underlain by rock at shallow depth, finite element idealization of the soil region is appropriate; in this case, the direct and substructure methods would lead to equivalent results but the latter provides the better alternative. Treating the free field motion directly as the earthquake input in the substructure method eliminates the deconvolution calculations and the related assumption—regarding type and direction of earthquake waves—required in the direct method. Spatial variations in the input motion along the structure-soil interface of embedded structures or along the base of long surface supported structures are included in the formulation. The substructure method is computationally efficient because the two substructures—the structure and the soil region—are analysed separately; and, more important, it permits taking advantage of the important feature that response to earthquake ground motion is essentially contained in the lower few natural modes of vibration of the structure on fixed base.     

大高宽比隔震结构地震反应的实用分析方法

本文提出了高层隔震结构等大高宽比隔震结构体系地震反应分析的单质点、2质点和3质点剪切型简化计算模型,同时还提出了高宽比影响系数的概念和计算式。这种纯剪切的简化计算模型成功地模拟了剪切加转动多质点计算模型的动力特性,通过高宽比影响系数对剪切型计算模型得到的剪力系数进行非线性放大,使数十质点的隔震结构体系都能够简化成单质点、2质点和3质点体系进行地震反应分析。文末对22层高宽比为5．01的某22层隔震结构进行了算例分析,简化计算理论的计算结果和时程分析法计算结果一致性良好。     

Non-linear seismic behavior of structures with limited hysteretic energy dissipation capacity

This paper investigates the non-linear seismic behavior of structures such as slender unreinforced masonry shear walls or precast post-tensioned reinforced concrete elements, which have little hysteretic energy dissipation capacity. Even if this type of seismic response may be associated with significant deformation capacity, it is usually not considered as an efficient mechanism to withstand strong earthquakes. The objective of the investigations is to propose values of strength reduction factors for seismic analysis of such structures. The first part of the study is focused on non-linear single-degree-of-freedom (SDOF) systems. A parametric study is performed by computing the displacement ductility demand of non-linear SDOF systems for a set of 164 recorded ground motions selected from the European Strong Motion Database. The parameters investigated are the natural frequency, the strength reduction factor, the post-yield stiffness ratio, the hysteretic energy dissipation capacity and the hysteretic behavior model (four different hysteretic models: bilinear self-centring, with limited or without energy dissipation capacity, modified Takeda and Elastoplastic). Results confirm that the natural frequency has little influence on the displacement ductility demand if it is below a frequency limit and vice versa. The frequency limit is found to be around 2 Hz for all hysteretic models. Moreover, they show that the other parameters, especially the hysteretic behavior model, have little influence on the displacement ductility demand. New relationships between the displacement ductility demand and the strength reduction factor for structures having little hysteretic energy dissipation capacity are proposed. These relationships are an improvement of the equal displacement rule for the considered hysteretic models. In the second part of the investigation, the parametric study is extended to multi-degree-of-freedom (MDOF) systems. The investigation shows that the results obtained for SDOF systems are also valid for MDOF systems. However, the SDOF system overestimates the displacement ductility demand in comparison to the corresponding MDOF system by approximately 15%.     

Response analysis of hysteretic multi-storey frames under earthquake excitation

Local incremental stiffness relations are formulated for a class of elasto-plastic beam elements. The earthquake acceleration is modelled as a filtered white noise process. The Itǒ differential equations of the integrated system made up of the structural system and the excitation process are then formulated. Instead of the original system an equivalent nonlinear system is considered, in which the drift vector is given by a series expansion of order n ≧ 1, where n = 1 represents the well-known case of equivalent linearization. Only components of the drift vector representing the non-analytieal constitutive equations are replaced by a polynomial expansion. The coefficients of this expansion are determined from a least mean square criterion, and are sequentially updated. Especially an equivalent system with a cubic expansion to the drift vector is investigated. The hierarchy of statistical moment equations is closed by a cumulant neglect closure scheme. The method has been applied to a two-storey frame. The results are compared to those of numerical simulation, and provide substantial improvements compared to equivalent linearization.     

Response uncertainty and time-variant reliability analysis for hysteretic MDF structures

Response uncertainty evaluation and dynamic reliability analysis corresponding to classical stochastic dynamic analysis are usually restricted to the uncertainties of the excitation. The inclusion of the parameter uncertainties contained in structural properties and excitation characteristics has become an increasingly important problem in many areas of dynamics. In the present paper, a point estimate procedure is proposed for the evaluation of stochastic response uncertainty, and a response surface approach procedure in standard normal space is proposed for analysis of time-variant reliability analysis for hysteretic MDF structures having parameter uncertainties. Using the proposed procedures, the response uncertainties and time-variant reliability can be easily obtained by several repetitions of stochastic response analysis under given parameters without conducting sensitivity analysis, which is considered to be one of the primary difficulties associated with conventional methods. In the time-variant reliability analysis, the failure probability can be readily obtained by improving the accuracy of the first-order reliability method using the empirical second-order reliability index. The random variables are divided into two groups, those with CDF and those without CDF. The latter are included via the high-order moment standardization technique. A numerical example of a 15F hysteretic MDF structure that takes into account uncertainties of four structural parameters and three excitation characteristics is performed, based on which the proposed procedures are investigated and the effects of parameter uncertainties are discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

求解反应谱的小波方法及汶川地震反应谱分析

采用四阶基数B-样条小波模拟地震动加速度时程,进而建立一种求地震反应的通用方法,解的误差仅来自于对地震动加速度时程的模拟。并用小波分解,将地震波分解为不同周期成分之和,以各分量最大加速度值的大小来衡量其在原波中的比重,可以清楚看到距震中不同远近地震波的性态,并做定量分析和观察各分量卓越周期的变化。求地震波及各分量的反应谱,从各分量的标准加速度反应谱中,可以看到地震波不同周期分量对体系固有周期的影响,这是以往做不到的。将上述方法应用于汶川8.0级地震加速度记录,研究不同地震记录的性态。     

Predictive optimal control for seismic analysis of non-linear and hysteretic structures

In this paper, an effective active predictive control algorithm is developed for the vibration control of non-linear hysteretic structural systems subjected to earthquake excitation. The non-linear characteristics of the structural behaviour and the effects of time delay in both the measurements and control action are included throughout the entire analysis (design and validation). This is very important since, in current design practice, structures are assumed to behave non-linearly, and time delays induced by sensors and actuator devices are not avoidable. The proposed algorithm focuses on the instantaneous optimal control approach for the development of a control methodology where the non-linearities are brought into the analysis through a non-linear state vector and a non-linear open-loop term. An autoregressive (AR) model is used to predict the earthquake excitation to be considered in the prediction of the structural response. A performance index that is quadratic in the control force and in the predicted non-linear states, with two additional energy related terms, and that is subjected to a non-linear constraint equation, is minimized at every time step. The effectiveness of the proposed closed-open loop non-linear instantaneous optimal prediction control (CONIOPC) strategy is presented by the results of numerical simulations. Since non-linearity and time-delay effects are incorporated in the mathematical model throughout the derivation of the control methodology, good performance and stability of the controlled structural system are guaranteed. Copyright © 1999 John Wiley & Sons, Ltd.     

Nonlinear earthquake response analysis and energy calculation for seismic slit shear wall structures

Based on the concept of structural passive control, a new type of slit shear wall, with improved seismic performance when compared to an ordinary solid shear wall, was proposed by the authors in 1996. The idea has been verified by a series of pseudo-static and dynamic tests. In this paper a macro numerical model is developed for the wall element and the energy dissipation device. Then, nonlinear time history analysis is carried out for a 10-story slit shear wall model tested on a shaking table. Furthermore, the seismic input energy and the individual energy dissipated by the components are calculated by a method based on Newmark-β assumptions for this shear wall model, and the advantages of this shear wall are further demonstrated by the calculation results from the viewpoint of energy. Finally, according to the seismic damage criterion on the basis of plastic accumulative energy and maximum response, the optimal analysis is carried out to select design parameters for the energy dissipation device.     

Tuned liquid dampers for controlling earthquake response of structures

Numerical simulations of a single‐degree‐of‐freedom (SDOF) structure, rigidly supporting a tuned liquid damper (TLD) and subjected to both real and artificially generated earthquake ground motions, show that a properly designed TLD can significantly reduce the structure's response to these motions. The TLD is a rigid, rectangular tank with shallow water in it. Its fundamental linear sloshing frequency is tuned to the structure's natural frequency. The TLD is more effective in reducing structural response as the ground excitation level increases. This is because it then dissipates more energy due to sloshing and wave breaking. A larger water‐depth to tank‐length ratio than previous studies suggested, which still falls within the constraint of shallow water theory, is shown to be more suitable for excitation levels expected in strong earthquake motions. A larger water‐mass to structure‐mass ratio is shown to be required for a TLD to remain equally effective as structural damping increases. Furthermore, the reduction in response is seen to be fairly insensitive to the bandwidth of the ground motion but is dependent on the structure's natural frequency relative to the significant ground frequencies. Finally, a practical approach is suggested for the design of a TLD to control earthquake response. Copyright © 2000 John Wiley & Sons, Ltd.     

基础隔震结构随机地震响应分析的复模态法

本文对多自由度基础隔震结构的随机地震响应问题进行了系统研究，首先建立了运动方程，然后用第一振型将上部结构展开，针对所得方程为非经典阻尼、非对称质量和非对称刚度情况，用复模态法解耦，获得了以第一振型表示的结构地震响应的解析解，对单自由度体系，此解即为结构响应的精确解，从而建立了两自由度体系在任意非经典阻尼与非对称质量和刚度情况下随机地震响应解析解分析的一般方法。本文方法也可用于带TMD减震结构、无损伤“加层减震”加固结构的随机地震响应分析与优化设计。     

TMD多点控制体系随机地震响应分析的虚拟激励法

对于频率分布密集或受频带较宽的地震激励的结构，其响应不再以某一单一振型为主，须考虑采用多点控制。本文对受TMD多点控制的结构进行了研究。文中建立了带有多个子结构系统的以模态坐标和子结构自由度为未知量的统一运动方程。针对所得方程为非对称质量、非对称刚度、非经典阻尼的情况，本文给出了使用直接法求解的格式。地震随机响应分析采用了虚拟激励法，可以考虑各振型之间的耦合项，计算量小且精度高。本文的方法适用于带有多个子结构的系统的一般性问题，具有广泛的应用价值。     

安装粘弹性阻尼器的滞变结构抗震可靠度分析

以Boue-Wen滞变恢复力模型模拟剪切型滞变结构的非线性特性，采用等价线性化建立了安装粘弹性阻尼器的滞变结构体系在地震作用下的随机响应计算方法，首当其冲在此基础上分别以结构的层间最大变形和阻尼器阻尼材料的最大剪切变形为结构和阻尼器打有限状态随机变量，探讨了剪切型滞变结构在安装粘弹性阻尼器后的抗震可靠度和阻尼器可靠度的计算方法。     

An equivalent SDOF system model for estimating the response of R/C building structures with proportional hysteretic dampers subjected to earthquake motions

For the purpose of estimating the earthquake response, particularly the story drift demand, of reinforced concrete (R/C) buildings with proportional hysteretic dampers, an equivalent single‐degree‐of‐freedom (SDOF) system model is proposed. Especially in the inelastic range, the hysteretic behavior of an R/C main frame strongly differs from that of hysteretic dampers due to strength and stiffness degradation in R/C members. Thus, the proposed model, unlike commonly used single‐spring SDOF system models, differentiates the restoring force characteristics of R/C main frame and hysteretic dampers to explicitly take into account the hysteretic behavior of dampers. To confirm the validity of the proposed model, earthquake responses of a series of frame models and their corresponding equivalent SDOF system models were compared. 5‐ and 10‐story frame models were studied as representative of low‐ and mid‐rise building structures, and different mechanical properties of dampers—yield strength and yield deformation—were included to observe their influence on the effectiveness of the proposed model. The results of the analyses demonstrated a good correspondence between estimated story drift demands using the proposed SDOF system model and those of frame models. Moreover, the proposed model: (i) led to better estimates than those given by a single‐spring SDOF system model, (ii) was capable of estimating the input energy demand and (iii) was capable of estimating the total hysteretic energy and the participation of dampers into the total hysteretic energy dissipation, in most cases. Results, therefore, suggest that the proposed model can be useful in structural design practice. Copyright © 2010 John Wiley & Sons, Ltd.     

隔震结构地震反应分析的实用计算方法

根据上部结构和隔震单元特性对隔震结构反应的影响,提出了可用于隔震结构反应分析的简易方法,避免从数学上求解耦联的非线性方程.将隔震层的恢复力模型等效线性化,以结构动力响应的Duhamel积分为基础,提出了一种新的结构动力响应的数值计算方法.     

Nonlinear numerical method for earthquake site response analysis II — case studies

This paper presents two numerical case studies of medium and strong motion events, namely Loma-Prieta 1989 and Hyogoken-Nambu (Kobe) 1995. These simulations were performed using CyberQuake model. The cyclic elastoplastic constitutive model is fully detailed in the companion paper. Through these case studies, we demonstrate the importance of using appropriate constitutive modelling when the part played by nonlinear phenomena is preponderant. The need to account for 3D kinematics (i.e. the three components of the input motion), is also demonstrated, even though a 1D geometry is considered, as the plastic coupling existing between components of motion during the earthquake, strongly affects the seismic soil response.     

A method for stochastic seismic response analysis of non-classically damped structures

A method to calculate the stationary random response of a non-classically damped structure is proposed that features clearly-defined physical meaning and simple expression. The method is developed in the frequency domain, The expression of the proposed method consists of three terms, i.e., modal velocity response, modal displacement response, and coupled (between modal velocity and modal displacement response), Numerical results from the parametric study and three example structures reveal that the modal velocity response term and the coupled term are important to structural response estimates only for a dynamic system with a tuned mass damper. In typical cases, the modal displacement term can provide response estimates with satisfactory accuracy by itself, so that the modal velocity term and coupled term may be ignored without loss of accuracy, This is used to simplify the response computation of non-classically damped structures. For the white noise excitation, three modal correlation coefficients in closed form are derived. To consider the modal velocity response term and the coupled term, a simplified approximation based on white noise excitation is developed for the case when the modal velocity response is important to the structural responses. Numerical results show that the approximate expression based on white noise excitation can provide structural responses with satisfactory accuracy~