Stochastic earthquake response control of structures by liquid column vibration absorber with uncertain bounded system parameters

The present work deals with optimum design of liquid column vibration absorber (LCVA) for seismic vibration control of structures characterized by uncertain system parameters. This involves optimization of the frequency and damping properties of LCVA considering uncertain properties of the structure and ground motion parameters. The study on optimum design of tuned mass damper system considering random system parameters is noteworthy. But, the same is not the case for liquid dampers. Moreover, though the probabilistic methods are powerful, the approach cannot be applied in many real situations when the required detailed information about uncertain parameters is limited. In such cases, the interval method is a viable alternative. With the aid of matrix perturbation theory using first order Taylor series expansion of dynamic response function and its interval extension, the vibration control problem under bounded uncertainty is transformed to appropriate deterministic optimization problems. This requires optimizing two separate objective functions correspond to a lower bound and an upper bound optimum solutions. A numerical study is performed to study the effect of system parameter uncertainty on the optimization of LCVA parameters and its response reduction efficiency. Though the efficiency is not completely eliminated, the advantage of the LCVA tends to reduce as the level of uncertainty increases. It is also seen that neglecting the effect of system parameter uncertainty may overestimate the damper performance.     

On the reliability-based design of structures including passive energy dissipation systems

This contribution presents a methodology for stochastic design of structures including vibration protection systems. The approach is then used to investigate the effect of uncertain model parameters on the reliability-based optimal design of structures with a class of passive energy dissipation systems. The uncertainty of structural parameters as well as the variability of future excitations are characterized in a probabilistic manner. The optimal design problem is formulated as a non-linear constrained minimization problem involving multiple design requirements, including reliability constraints related to the structural performance. Failure events defined by a large number of random variables are used to characterize the reliability measures. A sequential optimization approach based on global conservative, convex and separable approximations is implemented for solving the optimization problem. The effects of uncertain model parameters on the performance, robustness and reliability of protected systems is illustrated by two example problems that consider multi-story buildings under stochastic ground excitation.     

Optimal design of hysteretic dampers connecting adjacent structures using multi-objective genetic algorithm and stochastic linearization method

An optimal design method is proposed for nonlinear hysteretic dampers that enhance the seismic performance of two adjacent structures. The proposed method employs nonlinear random vibration analyses by use of a stochastic linearization method in order to efficiently estimate the stochastic responses of coupled buildings without performing numerous nonlinear time-history analyses. The main objectives of the optimal design are not only to reduce the seismic responses but also to minimize the total cost of the damper system. To deal with such conflicting objectives, a multi-objective genetic algorithm is adopted. This approach systematically obtains a set of Pareto optimal solutions that are non-inferior or non-superior to each other. The process for choosing a reasonable design from the optimal surface of Pareto solutions is also discussed. As an example of a nonlinear hysteretic damping device, this study considers passive-type magneto-rheological dampers with fixed input voltages. The optimal voltages and numbers of installed dampers are simultaneously determined. The robustness of the optimal design against uncertain characteristics of ground motions is examined through extensive nonlinear random vibration analyses.     

Structural reliability under monotony: Properties of FORM, simulation or response surface methods and a new class of Monotonous Reliability Methods (MRM)

In many mechanical or physical systems, the failure function, albeit complex and computationally intensive, happens to be monotonous with respect to its uncertain model inputs. In that case, some properties can be derived on the partial robustness of classical methods such as FORM, Monte–Carlo or response surfaces to estimate rare failure probabilities under the constraint of the number of expensive model runs, such as robust probability bounds, saved number of model runs or guaranteed variance reduction. A new formulation taking full advantage of monotony is introduced along with a family of associated Monotonous Reliability Methods (MRM). They consist in narrowing progressively some robust upper and lower bounds on the failure probability through an adaptive design of experiment. A number of variants can be considered: they comprise adaptive Monte–Carlo, dedicated response surfaces and deterministic design of experiments or hybrid variants with classical FORM or simulation methods. Their common advantages are that the prediction accuracy of the failure probability is guaranteed with certainty; additional model runs always ameliorate the accuracy; a change of the uncertainty model is possible without additional runs. Performance is compared on benchmarks including a nuclear finite-element mechanical study and a simple flooding model. Simple MRM variants appear quite promising in low input dimensions with highly efficient computation of a bounding established with certainty. Research perspectives are given to extend the efficiency of the methods in higher dimensions and address the relaxing of full monotony hypotheses.     

基于H ∞ 理论的结构鲁棒性分析

基于H ∞理论,提出一种定量评价结构鲁棒性的新方法。采用状态空间模型描述结构系统,基于H ∞最优,采用系统传递函数的H ∞范数作为结构鲁棒性的定量评价指标。对线性系统,分离刚度矩阵的不确定性,给出了H ∞结构鲁棒性指标的计算方法;对非线性系统,引入L 2性能准则表达鲁棒性。通过单自由度体系和桁架结构,明确了鲁棒性指标的物理意义,分析影响结构鲁棒性的因素。结果表明：基于H ∞理论的结构鲁棒性指标代表了结构稳态振动反应的最大振幅与干扰幅值之比,可以反映外部干扰和结构内部的不确定性与结构的响应是否成比例;提高结构整体承载力储备、耗能能力以及关键构件的冗余度可以增强结构的鲁棒性;且H ∞鲁棒性指标对结构参数变化较为敏感。     

土-结构相互作用对结构风振响应的影响

通过框架结构的风振响应计算，说明土-结构相互作用（简称SSI）对结构风振响应的影响，计算结果表明，在结构的风振响应分析中，考虑SSI并不总是安全的，在土中阻尼较小时，考虑SSI后，体系的第一频率较不考虑SSI时（即所谓的“刚性地基”）明显降低，而弹性位移反而较刚性地基时的值大，后一现象在相对刚度较小时更加明显。此外，考虑SSI后，无论结构高度如何，结构各楼层的总位移总是远无远大于刚性地基时的位移，这可能使人体产生明显的不舒适感，因此，在风振响应分析中应当考虑SSI效应。     

Control of wind-induced vibration of long-span bridges and tall buildings

With the rapid increase in scales of structures, research on controlling wind-induced vibration of large-scale structures, such as long-span bridges and super-tall buildings, has been an issue of great concern. For wind-induced vibration of large-scale structures, vibration frequencies and damping modes vary with wind speed. Passive, semiactive, and active control strategies are developed to improve the wind-resistance performance of the structures in this paper. The multiple tuned mass damper (MTMD) system is applied to control vertical bending buffeting response. A new semiactive lever-type tuned mass damper (TMD) with an adjustable frequency is proposed to control vertical bending buffeting and torsional buffeting and flutter in the whole velocity range of bridge decks. A control strategy named sinusoidal reference strategy is developed for adaptive control of wind-induced vibration of super-tall buildings. Multiple degrees of freedom general building aeroelastic model with a square cross-section is tested in a wind tunnel. The results demonstrate that the proposed strategies can reduce vibration effectively, and can adapt to wind-induced vibration control of large-scale structures in the uncertain dynamic circumstance.     

An efficient methodology for robustness evaluation by advanced interval analysis using updated second-order Taylor series expansion

An enhanced and efficient methodology for interval analysis is proposed to evaluate the robustness of an uncertain structure. While a basic assumption of “inclusion monotonic” is introduced in some of the interval analyses, the possibility is taken into account of occurrence of the extreme value of the objective function in an inner domain of interval parameters. It is shown that the critical combination of interval parameters can be derived explicitly so as to maximize the objective function by second-order Taylor series expansion. Two different approaches, called the FRP (Fixed Reference-Point) method and the URP (Updated Reference-Point) method, are proposed to obtain such a critical combination of interval parameters. The method is applied to building structures with passive dampers sustained by flexible supports. The objective function is given by the sum of the mean squares of interstorey drifts under random input. The damper capacity, its supporting member stiffness and building storey stiffness are taken as interval parameters. In order to investigate the validity of the proposed methods, numerical analyses are conducted for 2- and 20-storey building models including passive dampers. By comparing the results with the reference solution and those by other conventional methods, it is demonstrated that the URP method can provide the most accurate response bounds without hard computational effort.     

Multi-objective fuzzy control of smart base isolated spatial structure

Base isolation systems are used widely to reduce the dynamic responses of structures subjected to a seismic load. Recently, research has been conducted actively on smart base isolation systems that can effectively reduce the dynamic responses of isolated structures without accompanying increases in the base drifts. On the other hand, control performance of smart base isolation systems for spatial structures has not attracted significant attention. This study examined the dynamic response reduction capacity of a smart base isolation system for a spatial structure subjected to seismic excitation. MR dampers and low damping elastomeric bearings were used to compose a smart base isolation system, and its vibration control performance was compared with that of the optimally-designed, lead-rubber bearing (LRB) isolation system. A fuzzy controller was used to effectively control the spatial structure with a smart base isolation system. The dynamic responses of the spatial structure with an isolation system conflicted with the base drift. Therefore, these two responses were selected as the objective functions to apply a multi-objective genetic algorithm to optimize a fuzzy controller. The numerical simulation results showed that the smart base isolation system proposed in this study can reduce drastically the base drifts and seismic responses of the example spatial structure compared to the optimally designed LRB isolation system.     

Wind field simulation and wind‐induced responses of large wind turbine tower‐blade coupled structure

Herein, by a case study on a 5‐MW wind turbine system developed by Nanjing University of Aeronautics and Astronautics, the wind field simulation and wind‐induced vibration characteristics of wind turbine tower‐blade coupled systems is analyzed. First, the blade‐nacelle‐tower‐basis integrated finite element model with centrifugal forces induced by rotational blades is established. Then, based on a harmony superposition method and the modified blade element‐momentum theory, the fluctuating wind field of tower‐blade coupled systems is simulated, which considers wind shear effect, tower shadow effect, rotational effect, blade‐tower dynamic and model interaction effects. Finally, the wind‐induced dynamic responses and wind vibration coefficients of the wind turbine tower‐blade coupled structure are discussed through the ‘consistent coupled method’ previously proposed by us. The results indicate that the wind‐induced responses of a large wind turbine tower‐blade coupled structure present complicated modal responses and multimode coupling effect. Additionally, the rotational effect would amplify aerodynamic loads on blades with high frequency, wind‐induced dynamic responses and wind vibration coefficients of wind turbine tower. The centrifugal force effect could also amplify natural vibration frequency of the tower‐blade coupled system and reduce the wind‐induced dynamic responses and wind vibration coefficients of wind turbine tower. The research could contribute to wind‐resistant design of structure for a large‐scale wind turbine tower‐blade system. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust optimum design of tuned liquid column damper in seismic vibration control of structures under uncertain bounded system parameters

The optimum design of a tuned liquid column damper (TLCD) considering system parameter uncertainty is usually performed by minimising the performance measure obtained by the total probability theory without any consideration to the variation of its performance due to parameter uncertainty. However, such a design method does not necessarily correspond to an optimum design in terms of maximum response reduction as well as its minimum dispersion. Furthermore, such approach cannot be applied in many real situations when the required detailed information about the uncertain parameters is limited. The robust design optimisation (RDO) of a TLCD system to mitigate seismic vibration effect in which the bounds on the magnitude of the uncertain properties of the structural and ground motion model parameters are only required is attempted in this study. The RDO is formulated as a two-criterion optimisation problem where the weighted sum of the maximum root mean square displacement of the structure and its dispersion is minimised. The conventional interval analysis-based bounded optimum solution is also obtained to demonstrate the effectiveness of the proposed RDO approach. A numerical study elucidates the effect of parameter uncertainty on the RDO of TLCD parameters by comparing the RDO results with the bounded optimum results.     

筏板厚度对双塔楼大底盘高层建筑地震反应的影响

考虑土-结构动力相互作用,建立了双塔楼大底盘高层建筑动力响应分析的三维有限元模型,研究了筏板厚度变化对结构振动特性和地震响应的影响。不同筏板厚度结构动力响应的对比分析结果表明,随着筏板厚度增加,结构主振周期呈减小趋势,地震侧移呈增加趋势,地震剪力在塔楼部分呈增加趋势但在地下室部分呈减小趋势。筏板的动挠度除在两塔楼外侧的边跨范围内,一般随板厚增加而减小,动弯矩除靠近地下室外墙局部范围内,一般则随板厚增加而增加。可见,筏板厚度并非越大越安全,应在满足承载力和冲切等基本要求的前提下经过优选后确定。     

Random vibration of a train traversing a bridge subjected to traveling seismic waves

Non-stationary random vibration of 3D time-dependent train-bridge systems subjected to multi-point earthquake excitations, including wave passage effect, is investigated using the pseudo-excitation method (PEM). The motion equation of such a system is established by coupling the train and bridge through wheel-rail contact relationships and accounting for the phase-lags between pier excitations. The horizontal and vertical earthquake excitations are both assumed to be uniformly modulated, fully coherent random excitations with different phases, while the excitation due to track irregularities is assumed to be a 3D, fully coherent random excitation with velocity-dependent time lags. PEM is first proven to be applicable to such time-dependent systems, and is then used to transform the random excitations into a series of deterministic pseudo excitations. By solving for the corresponding deterministic pseudo responses, various non-stationary random responses, including the time-dependent power spectral density functions (PSD) and standard deviations (SD), can be obtained easily. A case study is then presented in which the China-Star high-speed train traverses a seven-span continuous bridge that is being excited by an earthquake. The results show the effectiveness and accuracy of the proposed method by comparison with a Monte Carlo simulation. Additionally, the influences of seismic apparent wave velocity and train speed on the system random responses are discussed.     

FPS隔震结构的水平和竖向振动响应分析

建立了FPS(FrictionPendulumSystem)隔震多层剪切型结构水平和竖向耦合振动微分方程 ,通过时程响应计算阐述了水平地震作用下FPS的隔震效果和结构的水平和竖向振动响应规律。     

巨-子结构减震体系基于能量的参数优化分析

建立了巨-子减震结构体系简化模型的运动方程,推导了结构弹性变形能等效速率功率谱。结构在随机地震激励下,分别以巨-子结构底层主结构弹性变形能和等效两自由度体系下部结构弹性变形能最小为优化目标,对比分析其最优参数以及减震系数。结果表明,质量比较小时减震机理表现为TMD质量调谐,质量比较大时为基础隔震,而中间区域为层间隔震。最后,通过减震系数的对比,体现了巨-子减震结构具有更好的鲁棒性。     

传递矩阵法在十字轴万向联轴器振动研究中的应用

以十字轴万向联轴器为例，阐述了机构振动研究中如何应用传递矩阵法解决机构中存在运动和动力参数不连续点的振动问题．在分析中，同时考虑了两个方向的横向振动、轴向振动和扭转振动，讨论并建立了包括不连续点在内的系统的传递矩阵和传递关系，并用实例求出了系统的各阶固有频率和主振型，为十字轴万向联轴器系统的动儿性能分析提供了理论依据．     

基于模态区间分析的结构不确定性损伤评估

针对实际工程结构中难以避免的不确定性因素,如材料非均质、边界条件不清晰、测试误差、模型误差等,提出利用模态区间分析求解包含不确定性参数的梁损伤评估方法。首先建立钢箱梁和钢筋混凝土梁的计算模型,以区间形式定义梁几何、材料参数的不确定性,体现各参数的可能波动范围;然后将结构静力学方程扩展成区间方程,通过模态逻辑对区间方程进行重新释义;最后在梁上施加集中荷载,计算得到梁关键应变点的区间工作状态。分析中通过降低梁单元的弹性模量来模拟损伤,再比较确定性方法、经典区间算法和模态区间分析的计算结果。结果表明:与确定性损伤评估方法不同,区间算法允许结构包含不确定性参数,认为落在区间包络线内的应变值是合理的,而当某荷载下应变值超出包络范围时说明梁发生了损伤;模态区间分析计算得到的区间包络范围要明显小于经典区间算法,能够有效避免计算过程的参数区间扩张,而且可以及时发现梁的损伤和损伤时所对应的外荷载,避免结构损伤进一步的恶化。     

地下结构纵向抗震动力可靠度分析

将沉埋隧道地震反应分析的数学模型应用于地下结构随机地震响应分析,阐述了采用动力分析方法求结构体系的脉冲响应函数的原理和方法,采用傅立叶变换原理和随机振动理论,建立了地下结构纵向随机地震响应统计特征的数学表达式。将结构随机地震响应看成是1个泊松过程,建立了采用首次超越破坏理论计算地下结构抗震可靠度的数学公式。以南京长江越江隧道初步设计方案(沉管段)为例,计算了其在高斯平稳随机过程地震动作用下的动力反应均方根值和纵向抗震动力可靠度。为地下结构整体随机地震反应分析及动力可靠度的研究提供了一种分析途径,为以可靠性理论为基础的地下结构抗震概率设计规范的制订奠定了理论基础。     

U型水箱对高层建筑和高耸结构风振控制的试验和研究

本文在试验分析的基础上提出了U型水箱对高层建筑和高耸结构脉动风振反应控制的工作原理、计算方法和水箱参数对结构风振控制效果的影响。计算分析结果表明,U型水箱是种简单,经济和实用的,可用于结构大振幅风振反应的控制装置。     

Uncertain linear systems in dynamics: Retrospective and recent developments by stochastic approaches

This paper provides an overview along with a critical appraisal of available methods for uncertainty propagation of linear systems subjected to dynamic loading. All uncertain structural properties are treated as random quantities by employing a stochastic approach. The loading can be either of deterministic or stochastic nature, described by white noise, filtered white noise, and more generally, by a Gaussian stochastic process.The assessment of the variability of the uncertain response in terms of the mean and variance is described by reviewing the random eigenvalue problem and procedures to evaluate the first two moments of the stochastic (uncertain) response. Computational procedures which are efficiently applicable for general FE-models are the focus of this work.Most recent developments for the reliability assessment–besides a retrospective review–are summarized, with particular emphasis on numerical Monte Carlo Simulation approaches. This review comprises methods to assess the first excursion probability directly by efficient numerical methods. General “black box” procedures and approaches applicable only for linear systems are critically discussed. Specific procedures applicable to linear systems subjected to general Gaussian excitation are subsequently addressed. Methods applicable for deterministic structural systems are introduced first. Finally, a procedure to exploit the solutions for deterministic linear systems for stochastic uncertain systems in an efficient manner is described.