The optimum design of a base isolation system with frictional elements

A linear multistorey structure with a seismic base isolation system consisting of rubber bearings and frictional elements is considered. The non-linear equations of motion are derived for the first mode vibration and the stochastic response to a white noise ground acceleration is determined. Based on this response, suitable objective functions are defined and the optimum design of the isolation system is performed. It is shown that a small amount offriction increases the effectiveness of the system compared with the same system but without frictional elements.     

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.     

Probabilistic seismic response and reliability assessment of isolated bridges

Bridge seismic isolation strategy is based on the reduction of shear forces transmitted from the superstructure to the piers by two means: shifting natural period and earthquake input energy reduction by dissipation concentrated in protection devices. In this paper, a stochastic analysis of a simple isolated bridge model for different bridge and device parameters is conducted to assess the efficiency of this seismic protection strategy. To achieve this aim, a simple nonlinear softening constitutive law is adopted to model a wide range of isolation devices, characterized by only three essential mechanical parameters. As a consequence of the random nature of seismic motion, a probabilistic analysis is carried out and the time modulated Kanai-Tajimi stochastic process is adopted to represent the seismic action. The response covariance in the state space is obtained by solving the Lyapunov equation for a stochastic linearized system. After a sensitivity analysis, the failure probability referred to extreme displacement and the mean value of dissipated energy are assessed by using the introduced stochastic indices of seismic bridge protection efficiency. A parametric analysis for protective devices with different mechanical parameters is developed for a proper selection of parameters of isolation devices under different situations.     

滞变—摩擦基底隔震系统的随机地震反应分析

本建立了滞变－摩擦基底隔震系统在地震作用下的运动微分方程，并将地震地面运动模拟成均值为零的两次过滤Ｇａｕｓｓ白噪声过程。使用等效线性化方法求解了这种隔震系统的地震反应统计特征，并分析了这种隔震系统参数的变化对其反应统计特征的影响。     

基于动力可靠性分析的滑移隔震体系的优化设计

本文探讨了滑移隔震体系在零均值高斯白噪声地震作用下的优化设计问题,首先利用编译等效线性化方法并按首次超超损坏泊松过程模型的双壁问题得到质点的滑移可靠性函数,然后采用拉格朗日乘子法进行了该滑移隔震体系基于动力可靠性分析的优化设计。     

平稳随机地震地面运动过程模型及其统计特征

地震地面运动过程具有强烈的随机性,应用随机理论对实际工程结构进行地震可靠性分析和抗震设计与加固时都需要建立合理的随机地震地面运动模型,本文选择3种典型的随机地震动模型,即理想白噪声模型、金井清模型和改进的金井消模型,分析了它们的物理概念、频域特征以及适用范围。引入状态向量,建立状态方程．通过复振型叠加法分析了地震地面运动过程的时域统计特性,推导出3种随机地震动模型的相关函数的解析表达式．这些结果可为结构随机地震反应时域分析和抗震可靠性评估提供基础。     

Degradation kinetics of dense nonaqueous phase liquids in the environment under impacts of mixed white and colored noises

This study presents three stochastic dense nonaqueous phase liquid degradation kinetic models, forced by Gaussian white noise, Ornstein–Uhlenbeck colored noise and their mixture, respectively. Compared to the previous efforts, the proposed mixed-noise forced model is a more generalized representation of conventional stochastic models. This feature exists because any of the stochastic terms (no matter they come from the inside or out of the system) can be accounted for by a deterministic term and a type of colored, white, or mixed noise. The implicit in the model solutions include: the colored noise may lead to a misunderstanding results and much attention should be received to recognize the impact of colored noises; the decrease of noise intensity and/or increase of correlation time change the probability distribution functions from bimodal to approximate unimodal shapes, implying increased ease of capturing the statistical properties of model solutions; the introduction of a new colored noise may counteract the function of a white noise, thus providing us an alternative for mitigating the impact of a known noise on model solutions. The ongoing work is undertaken to develop an integrated numerical-simulation and statistical-inference method for the characterization of white and colored noises based on observation data.     

Stochastic energy analysis of seismic isolated bridges

In this paper, a parametric stochastic analysis of isolated bridge is proposed with the aim to assess isolation performance and to investigate effects of energetic influence on protection efficiency. The analysis has been carried out in terms of two stochastic parameters of pear-deck maximum displacement and hysteretic energy response, of which a qualitative trend has been observed.Isolated bridge is described by a simple two degree of freedom (TDoF) Bouc–Wen hysteretic model, which has been introduced for its intrinsic ability in reproducing a wide range of real devices behavior. With the aim of taking into consideration intrinsic stochastic nature of seismic events, the ground motion and the structural response have been described by random vibration approach. Results obtained show that protection achieved by shifting structural natural period and reducing input energy by devices dissipation have counteracting effects if related to deck lateral displacement.     

设置负刚度装置的大跨长联连续梁桥地震反应分析

为完善大跨长联连续梁桥的减震和隔震技术,提出将负刚度装置引入某带有摩擦摆支座隔震的大跨长联连续梁桥中组成新型减震和隔震系统.基于CSIBridge软件建立全桥有限元模型,负刚度装置采用弹性多段线模拟,摩擦摆支座采用双线性恢复力模型,输入7条地震波进行了非线性时程分析,考查了新型减震和隔震系统下桥梁结构的地震反应,探究了...     

高速列车-桥梁竖向随机振动的时域分析方法

提出时间相关多维有色噪声形式的轨道不平顺激励下列车-桥梁耦合系统协方差响应的时域递推方法。用白噪声滤波法生成轨道不平顺有色噪声过程,在宽频带内识别滤波器参数以同时实现滤波成型和波长截断功能。提出基于高阶Pade近似的累次时滞系统,以实现列车多轮对下轨道不平顺激励的大时滞再现;再结合成型滤波器构造列车下轨道不平顺激励的一致白噪声模型。建立列车-桥梁垂向振动的状态方程,将其与激励模型联立得到一致白噪声激励下的列车-桥梁扩阶状态方程。将方差递推法推广到时变系统,求解列车-桥梁系统的随机振动。分析结果与Monte Carlo模拟法符合良好,表明了方法的正确性。     

Analysis of block random rocking

The stochastic rocking of a rigid block due to shaking of its foundation is examined. The foundation is flexible (Winkler) and its independent springs and dashpots separate from the block base when tension is incipient. Modulated white noise is used as a model of horizontal acceleration of the foundation. The statistics of the rocking response are found by an analytical procedure which involves a combination of static condensation and stochastic linearization. The analytical solution is computationally efficient and compares well with pertinent data obtained by numerical simulations.     

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.     

Optimal design of superelastic‐friction base isolators for seismic protection of highway bridges against near‐field earthquakes

The seismic response of a multi‐span continuous bridge isolated with novel superelastic‐friction base isolator (S‐FBI) is investigated under near‐field earthquakes. The isolation system consists of a flat steel‐Teflon sliding bearing and a superelastic NiTi shape memory alloy (SMA) device. The key design parameters of an S‐FBI system are the natural period of the isolated bridge, the yielding displacement of the SMA device, and the friction coefficient of the sliding bearings. The goal of this study is to obtain optimal values for each design parameter by performing sensitivity analysis of a bridge isolated by an S‐FBI system. First, a three‐span continuous bridge is modeled as two‐degrees‐of‐freedom with the S‐FBI system. A neuro‐fuzzy model is used to capture rate‐ and temperature‐dependent nonlinear behavior of the SMA device. Then, a set of nonlinear time history analyses of the isolated bridge is performed. The variation of the peak response quantities of interest is shown as a function of design parameters of the S‐FBI system and the optimal values for each parameter are evaluated. Next, in order to assess the effectiveness of the S‐FBI system, the response of the bridge isolated by the S‐FBI system is compared with the response of the non‐isolated bridge and the same bridge isolated by pure‐friction (P‐F) sliding isolation system. Finally, the influence of temperature variations on the performance of the S‐FBI system is evaluated. The results show that the optimum design of a bridge with the S‐FBI system can be achieved by a judicious specification of design parameters. Copyright © 2010 John Wiley & Sons, Ltd.     

基于经验模式分解的随机子空间识别方法

提出了基于经验模式分解（EMD）的环境激励结构模态参数随机子空间识别（SSI）方法。该方法用设置间断频率的EMD将结构环境振动响应原始信号分解成若干个基本模式分量（IMF）,使每一个基本模式分量仅为结构的某一阶固有模态,进而用随机子空间方法进行模态参数识别。实桥环境振动实验分析结果表明,该方法能有效地避免结构各阶模态之间的相互影响,能够更清晰方便地得到结构的模态参数。     

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.     

Generation of critical stochastic earthquakes

A stochastic critical excitation is defined as that excitation with a given variance that maximizes the variance in the dynamic response of a system. A non-stationary filtered shot noise is used to develop a stochastic critical excitation model of an earthquake ground motion process, and the response statistics for a linear system are determined in both time and frequency domains. The sensitivity of response to several assumed earthquake pulse arrival rate functions is examined. Responses to recorded strong ground motion and to stochastic critical excitations with the same total energy are compared to assess the degree of conservatism in the procedure. An application of the procedure to seismic qualification of equipment is presented.     

Multi-objective stochastic-structural-optimization of shape-memory-alloy assisted pure-friction bearing for isolating building against random earthquakes

The optimal stochastic performance of pure friction system supplemented with SMA-restrainer (SMA-PF) is presented based on a framework of multi-objective optimization. The evaluation of system response for this is based on nonlinear random vibration analysis. The optimizing design variables are based on two mutually conflicting objectives, involving maximizing the isolation efficiency as well as isolator displacement. The proposed optimal design, thus, not only maximizes the isolation efficiency but also impose due consideration to the bearing displacement. The optimal bearing is shown to substantially reduce the bearing displacement with nominal sacrifice in isolation efficiency. Comparison of the multi-objective Pareto fronts reveals much facilitated trade-off among the mutually conflicting objectives in SMA-PF than in PF system. The viability of the optimal performance is further verified under recorded ground motions, which is observed to be in parity to the stochastic response behavior. The reduction in the residual bearing displacement is also observed.     

Effects of seismic isolation on the seismic response of a California high‐speed rail prototype bridge with soil‐structure and track‐structure interactions

With the launch of the high‐speed train project in California, the seismic risk is a crucial concern to the stakeholders. To investigate the seismic behavior of future California High‐Speed Rail (CHSR) bridge structures, a 3D nonlinear finite‐element model of a CHSR prototype bridge is developed. Soil‐structure and track‐structure interactions are accounted for in this comprehensive numerical model used to simulate the seismic response of the bridge and track system. This paper focuses on examining potential benefits and possible drawbacks of the a priori promising application of seismic isolation in CHSR bridges. Nonlinear time history analyses are performed for this prototype bridge subjected to two bidirectional horizontal historical earthquake ground motions each scaled to two different seismic hazard levels. The effect of seismic isolation on the seismic performance of the bridge is investigated through a detailed comparison of the seismic response of the bridge with and without seismic isolation. It is found that seismic isolation significantly reduces the deck acceleration and the force demand in the bridge substructure (i.e., piers and foundations), especially for high‐intensity earthquakes. However, seismic isolation increases the deck displacement (relative to the pile cap) and the stresses in the rails. These findings imply that seismic isolation can be promisingly applied to CHSR bridges with due consideration of balancing its beneficial and detrimental effects through using appropriate isolators design. The optimum seismic isolator properties can be sought by solving a performance‐based optimum seismic design problem using the nonlinear finite‐element model presented herein. Copyright © 2016 John Wiley & Sons, Ltd.     

Behavior of a seismically isolated bridge crossing a fault rupture zone

The effect of the fault rupture zone traversing a seismically isolated bridge is investigated utilizing a finite element model of a section of the Bolu Viaduct and a set of synthetic broadband strong ground motions simulated for the Bolu Viaduct site due to the 1999 Duzce earthquake. Both the original and a potential retrofit seismic isolation system designs are considered in the analyses. The results show double isolation system demands when fault crossing is considered, as compared to the case where fault crossing is ignored. The pier drift demands, however, remain comparable in both cases. Furthermore, the location of fault crossing along the bridge length, as well as the fault orientation with respect to the bridge longitudinal direction are shown to influence substantially the response of the seismically isolated bridge. Isolation system permanent displacements are greatly influenced by the restoring force capability of the isolation system when fault crossing effects in the excitations are ignored. In the case of fault crossing, the permanent displacements of the isolation system are dominated by the substantial permanent tectonic displacement along the fault trace which is imposed upon the structure. The results of this study contribute to developing a better understanding of how seismically isolated bridges respond when traversed by fault rupture zones. The lack of analyses and design guidelines for bridges crossing faults in international standards renders this study a useful reference for the profession.     

Probabilistic analysis for the response of nonlinear base isolation system under the ground excitation induced by high dam flood discharge

According to theoretical analysis,a general characteristic of the ground vibration induced by high dam flood discharge is that the dominant frequency ranges over several narrow frequency bands,which is verified by observations from the Xiangjiaba Hydropower Station.Nonlinear base isolation is used to reduce the structure vibration under ground excitation and the advantage of the isolation application is that the low-frequency resonance problem does not need to be considered due to its excitation characteristics,which significantly facilitate the isolation design.In order to obtain the response probabilistic distribution of a nonlinear system,the state space split technique is modified.As only a few degrees of freedom are subjected to the random noise,the probabilistic distribution of the response without involving stochastic excitation is represented by theδfunction.Then,the sampling property of theδfunction is employed to reduce the dimension of the Fokker-PlanckKolmogorov(FPK)equation and the low-dimensional FPK equation is solvable with existing methods.Numerical results indicate that the proposed approach is effective and accurate.Moreover,the response probabilistic distributions are more reasonable and scientific than the peak responses calculated by conventional time and frequency domain methods.