Shaking table test and numerical analysis of offshore wind turbine tower systems controlled by TLCD

A wind turbine system equipped with a tuned liquid column damper(TLCD) is comprehensively studied via shaking table tests using a 1/13-scaled model. The effects of wind and wave actions are considered by inputting responseequivalent accelerations on the shaking table. The test results show that the control effect of the TLCD system is significant in reducing the responses under both wind-wave equivalent loads and ground motions, but obviously varies for different inputs. Further, a blade-hub-tower integrated numerical model for the wind turbine system is established. The model is capable of considering the rotational effect of blades by combining Kane’s equation with the finite element method. The responses of the wind tower equipped with TLCD devices are numerically obtained and compared to the test results, showing that under both controlled and uncontrolled conditions with and without blades’ rotation, the corresponding responses exhibit good agreement. This demonstrates that the proposed numerical model performs well in capturing the wind-wave coupled response of the offshore wind turbine systems under control. Both numerical and experimental results show that the TLCD system can significantly reduce the structural response and thus improve the safety and serviceability of the offshore wind turbine tower systems. Additional issues that require further study are discussed.     

THE THEORY OF RESPONSE ANALYSIS OF FUZZY STOCHASTIC DYNAMICAL SYSTEMS WITH A SINGLE DEGREE 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, the theory of response, fuzzy mean response and fuzzy covariance response of a single-degree-of-freedom (sdf) system to fuzzy random excitations in the time domain and frequency domain is put forward. The theory of response analysis of an sdf system to both stationary and non-stationary fuzzy random excitations in the time domain and frequency domain is established. Two examples are considered in order to demonstrate the rationality and validity of the theory, and the models of stationary filtered white noise and non-stationary filtered white noise fuzzy stochastic processes of the earthquake ground motion are set up. Methods of analysis for fuzzy random seismic response of sdf systems are put forward using the principles of response analysis of an sdf fuzzy random dynamic system.     

基于非平稳随机地震动模型的重力坝抗震可靠度分析

基于正交展开的非平稳随机地震动模型,并考虑混凝土材料的非线性和坝体与库水之间的流固耦合,对印度Koyna重力坝进行有限元分析,得到坝顶水平位移和坝颈拉应力,结合概率密度演化方法和等价极值事件的思想,获得丰富的概率信息。这为坝体结构的随机地震反应分析和可靠度研究提供新的途径。     

地震动功率谱与反应谱的转换关系

本文详细评述了现今常用的几种加速度反应谱与功率谱的转换关系。对于小阻尼单质点体系而言，考虑到输入地震动是一非平稳的随机过程，又由于其传递函数的窄频带滤波特性，它的加速度反应将是一窄频带的非平稳随机过程。对于峰值系数水平的超越不是独立的，而是成群超越。据此本文考虑非平稳效应和对峰值系数水平的成群效应，对前人的转换关系进行了修正，并基于随机振动理论，给出了对工程上常用的频率平稳、强度非平稳的地震;动模型的功率谱和反应谱的转换关系。此转换关系对于长、短持时的地震动记录和反应谱长、短周期部分以及不同阻尼比的反应谱都能给出精度较高的结果。     

Site dependent and spatially varying response spectra

The goal of this study is to provide a stochastic method to investigate the effects of the randomness of soil properties due to their natural spatial variability on the response spectra spatial variation at sites with varying conditions. For this purpose, Monte Carlo Simulations are used to include the variability of both incident ground motion and soil parameters in the response spectra by mean of an appropriate coherency loss function and a site-dependent transfer function, respectively. The approach is built on the assumption of vertical propagation of SH type waves in soil strata with uncertain parameters. The response spectra are obtained by numerical integration of the governing equation of a single-degree-of-freedom(SDOF) system under non-stationary site-dependent and spatially varying ground motion accelerations simulated with non-uniform spectral densities and coherency loss functions. Numerical examples showed that randomness of soil properties significantly affects the amplitudes of the response spectra, indicating that as the heterogeneity induced by the randomness of the parameters of the medium increases, the spectral ordinates attenuate.     

Variability of tall building response to earthquakes with changing epicentre direction

Using a 40-storey building as an example, the structural response under the excitation of horizontal earthquake ground motion is shown to vary greatly with the direction from the building site to the epicentre. Two mathematical models are used to represent the ground motion: the stationary random process model and the evolutionary-type non-stationary random process model. The former model is suitable if the duration of the most intense portion of an earthquake is much longer than the fundamental natural period of the structure. The maximum standard deviations of selected structural response quantities are computed and plotted for all possible epicentre directions, and the information is believed to be useful for design purposes.     

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.     

强震地面运动超随机特性的几点注记

本文详细论述了功率谱与功率谱密度、平方和SS与平方平均值MS的适用范围及物理意义,比较深入地分析了平稳和非平稳加速度时间历程的统计特征,通过引入时域包线获取特定相位的方法,考虑了非平稳特性。本文基于非平稳时间历程,在不考虑频率非平稳性的基础上,提出了设计地震动三要素:(1)平方和SS;(2)归一化自相关函数或其对应的功率谱;(3)地震动时域包线.本文提出了在设计地震动合成中考虑超随机特性的实用方法,并指出地震动的超随机特性(即归一化功率谱的锯齿状波动部分,或归一化自相关函数的随机噪声部分)与相位的随机性是地震动随机特性的两个重要方面。本文将地震动的统计分析直接建立在非平稳时间历程的基础之上,从而避开了要对地震动进行平稳化处理的困难。这样提取出的地震动统计特征完全是以真实地震动记录为基础的。应用这些统计特征,可模拟出符合统计要求的基于非平稳时间历程的设计地震动。最后本文还讨论了工程上常用的将反应谱近似转换为功率谱的转换式的一些缺陷。     

Statistical insight into constant-ductility design using a non-stationary earthquake ground motion model

A recently developed earthquake ground motion model non-stationary in both intensity and frequency content is validated at the inelastic Single-Degree-Of-Freedom (SDOF) structural response level. For the purpose of this study, the earthquake model is calibrated for two actual earthquake records. The objective of a constant (or target) displacement ductility used in conventional earthquake-resistant design is examined from the statistical viewpoint using this non-stationary earthquake model. The non-linear hysteretic structural behaviour is modelled using several idealized hysteretic SDOF structural models. Ensemble-average inelastic response spectra corresponding to various inelastic SDOF response (or damage) parameters and conditioned on a constant displacement ductility response are derived from the two identified stochastic ground motion models. The effects of the type of hysteretic behaviour, the structural parameters, the target displacement ductility factor, and the ground motion model on the statistics of the inelastic response parameters are thoroughly investigated. The results of this parametric study shed further light on the proper interpretation and use of inelastic response or damage parameters in earthquake-resistant design in order to achieve the desirable objective of ‘constant-damage design’. © 1997 by John Wiley & Sons, Ltd.     

Seismic response of light internal equipment in base-isolated structures

The seismic response of light secondary systems in a building is dependent on the response of the primary structural system to the seismic ground motion with the result that very high accelerations can be induced in such secondary systems. This response can be reduced through the use of aseismic base isolation which is a design strategy whereby the entire building can be decoupled from the damaging horizontal components of seismic ground motion by the use of some form of isolation system. The paper presents a theoretical analysis of the response of light equipment in isolated structures and a parallel experimental programme both of which show that the use of base isolation can not only attenuate the response of the primary structural system but also reduce the response of secondary systems. Thus, the design of equipment and piping in a base-isolated building is very much simpler than that for a conventionally founded structure: inelastic response and equipment-structure interaction need not be considered and multiple support response analysis is rendered unnecessary. Although an isolation system with linear elastic bearings can reduce the acceleration of the structure, it may be accompanied by large relative displacements between the structure and the ground. A system using lead-rubber hysteretic bearings, having a force-displacement relation which is approximately a bilinear loop, can reduce these displacements. A parallel experimental programme was carried out to investigate the response of light equipment in structures isolated using lead-rubber bearings. The experimental results show that these bearings can dissipate energy and limit the displacement and acceleration of the structure but are less effective in reducing the accelerations in the internal equipment. The results of both the analysis and the tests show that base isolation is a very effective method for the seismic protection of light equipment items in buildings.     

Stability of elastic frames subjected to earthquake excitations

Dynamic stability of elastic multistorey frame structures subjected to vertical earthquake ground accelerations is studied. Different stationary, non-stationary, white and non-white random models for earthquake strong motion are considered. The concepts of mean-square and almost-sure stability are reviewed and the corresponding stability theorems are presented. Several general criteria regarding the dynamic stability of the equilibrium state of multistorey frames subjected to random excitations are developed. A few examples concerning the stability of single and multi-degree-of-freedom structures under earthquake excitations are presented. The stability of motion of frames under combined horizontal–vertical acceleration is also briefly discussed.     

Dynamic analysis of stacked rigid blocks

The dynamic behavior of a structural model of two stacked rigid blocks subjected to ground excitation is examined. Assuming no sliding, the rocking response of the system standing free on a rigid foundation is investigated. The derivation of the equations of motion accounts for the consecutive transition from one pattern of motion to another, each being governed by a set of highly nonlinear differential equations. The system behavior is described in terms of four possible patterns of response and impact between either the two blocks or the base block and the ground. The equations governing the rocking response of the system to horizontal and vertical ground accelerations are derived for each pattern, and an impact model is developed by conservation of angular momentum considerations. Numerical results are obtained by developing an ad hoc computational scheme that is capable of determining the response of the system under an arbitrary base excitation. This feature is demonstrated by using accelerograms from the Northridge, CA, 1994, earthquake. It is hoped that the two-blocks model used herein can facilitate the development of more sophisticated multi-block structural models.     

地震动强度非平稳特性参数与结构响应之间的近似定量关系分析

本文在对实际地震加速度记录统计分析的基础上,给出了能够合理描述地震动强度非平稳特性的参数及其取值范围;然后引入实验设计方法,建立了适合于地震动强度非平稳特性参数分析的实验设计算法,用来分析地震动强度非平稳特性参数的变化对结构响应的影响;最后通过与近似技术相结合,建立了地震动强度非平稳特性参数与结构响应之间的近似定量关系模型.结果表明,本文提出的实验设计方法适合于对地震动强度非平稳特性参数进行分析,该方法在有效地减小计算量的同时,获得了结构响应与参数变化之间的对应关系.基于实验设计方法进行的特性参数方差分析结果表明:地震动的稳态持时对结构地震响应的影响比较显著;对于周期较小的结构,特性参数之间的交互作用对结构地震响应的影响显著,但当周期大于1 s时,则不显著.本文建立的近似定量关系模型能够较好地反映不同特性参数、不同周期结构动力响应之间的联系,为工程实践中基于结构特性合理设置地震动特性参数、合成或挑选地震加速度时程提供理论依据.      

TMD结构基于双过滤白噪声随机地震激励的系列响应的简明解

针对既有方法在分析TMD结构基于双过滤白噪声激励下结构响应的解表达式复杂而导致计算效率低的问题,提出了一种简明封闭解法。首先,利用双过滤白噪声谱的滤波方程与TMD结构的地震动方程联立,可将TMD结构基于复杂的双过滤白噪声激励准确的表示为易于求解的运动方程;其次,基于复模态法获得TMD耗能结构位移、层间位移的系列响应的复特征值及复模态参与系数;然后基于随机振动理论获得了TMD结构随机地震动系列响应（相对于地面绝对位移和结构层间位移）的功率谱统一形式的二次正交解,进而获得了TMD结构系列随机响应的0-2阶谱矩和方差的简明封闭解。最后研究了基于首超破坏准、Markov过程假设及串联失效模式的TMD结构的体系动力可靠度。通过一算例分析,表明了本文方法的正确性和高效性。因此,本文方法可用于各类线性结构基于复杂的随机地震动响应的分析及其动力可靠度计算。     

基于新《电力设施抗震设计规范》的地震动随机模型参数研究

根据新《电力设施抗震设计规范》(GB50260-2013)对随机地震动功率谱参数的取值进行分析。介绍新《电力设施抗震设计规范》中设计反应谱,推导设计谱到功率谱的转换过程。选取常用的Clough-Penzien修正过滤白噪声模型作为拟合函数,通过功率谱参数拟合,得到不同场地类别、不同抗震设防烈度下的地震动模型参数。该研究成果可为电力工程抗震设计分析提供参考。     

Impact of seismic excitation characteristics on the efficiency of tuned liquid column dampers

Various types of passive control systems have been used to suppress the seismic response of structures in recent years. Among these systems, Tuned Liquid Column Dampers （TLCDs） dissipate the input earthquake energy by combining the effects of the movement of the liquid mass in the container, the restoring force on the liquid due to the gravity loads and the damping due to the liquid movement through orifices. In this study, the effects of seismic excitation characteristics such as frequency content and soil condition on the seismic performance of TLCDs are investigated using nonlinear time-history analyses. In this regard, among the past earthquake ground motion records of Iran, 16 records with different parameters were selected. In the structural model developed, the attached TLCD is simulated as a Tuned Mass Damper （TMD） having the same vibration period and damping ratio as the original TLCD. The numerical results show that the seismic excitation characteristics have a substantial role on the displacement reduction capability of TLCDs and they should be considered accordingly in the design of TLCDs.     

隔震减震主次结构体系非线性随机地震反应分析

为研究隔震、减震装置非线性恢复力特性对2自由度主次结构体系均方根位移反应的影响规律,以隔震、减震装置微分型恢复力模式的滞回参数为变量,地震地面运动模拟成高斯白噪声过程,利用等效线性化方法得到主体结构和二次结构均方根位移反应的表达式.分析表明,主体结构隔震装置非线性恢复力特征对主、次结构的均方根位移反应的影响占主导地位;隔震、减震装置的恢复力特征产生适度非线性有利于减小主、次结构的均方根位移反应.     

随机地震动作用下的结构振动控制试验设计

研究了随机地震动作用下基于MR阻尼器的结构振动控制振动台试验设计的若干问题。首先,由原型结构按动力相似关系进行了模型结构的设计,基于ANSYS模态分析的结果识别出了其结构参数;其次,基于物理随机地震动模型生成了试验地震动样本,根据试验要求调整了各地震动样本的加速度峰值;然后,基于MATLAB对试验模型进行了随机地震动作用下无控与主动控制数值仿真分析;最后,结合ANSYS弹塑性动力时程分析,研究了试验模型的动力稳定性。介绍的振动控制试验设计方法可供进行类似试验设计的研究人员参考。     

与规范反应谱相对应的Clough-Penzien模型参数研究

根据我国现行抗震规范（GB50011—2001）的反应谱曲线，对Clough—Penzien模型的参数取值进行了具体研究。采用时间包络函数考虑地震动的非平稳性，根据加速度峰值等效原则确定了谱强度因子S0的表达式，表明谱强因子不仅与地面加速度特性、场地类别有关，而且与结构的动力特性（阻尼比、自振周期）有关。最后对谱强度因子计算做了简化处理，为随机抗震计算分析提供了参考依据。     

Simulation of artificial random field considering the temporal-spatial variation

Introduction For the seismic design of special structures such as nuclear power station, marine platform, long-span bridge and dam, generally the time-history response analysis of the structure under seismic excitation is imperative, which was coded in most seismic design codes. The earthquake records suitable for the seismic situation and site condition are necessary to be used as the seismic input in the dynamic analysis of structures. As a result of the limited observational condition of st…