弹性多自由度系统地震输入能量的研究

本文介绍了基于能量抗震设计方法的基本思路和基本概念。根据振型分解法推导了弹性多自由度系统与单自由度系统弹性地震输入能量间的关系。研究表明,N个自由度弹性系统的地震输入能量可表示为N个弹性单自由度系统弹性输入能量的线性组合,组合系数与多自由度系统的振型和质量分布有关。通过时程分析算例,以Eleentro波输入验证了这种方法的正确性。算例结果表明,对于自由度较多的系统,可以只取前几阶振型计算即可得到足够精确的结果。     

基于AEEMD和改进DATA-SSI算法的桥梁结构模态参数自动化识别

模态参数作为桥梁结构最重要的动力参数之一,在实际运用中,可通过监测其变化情况来辨识结构的使用性能,精确地参数识别对保障桥梁健康运营具有十分重要的意义。鉴于此,该文对现阶段常用的振动信号降噪处理算法和模态参数识别算法进行了相应的改进。一方面,提出一种新的信号自适应分解与重构算法,即自适应总体平均经验模态分解算法（AEEMD）,该算法相比总体平均经验模态分解算法（EEMD）而言,能够根据信号的自身特征自动化确定添加白噪声的幅值标准差和集成平均次数|能更好地处理端点效应|同时还能够保证所得本征模态函数之间不存在模态混叠现象|最终实现有效IMF分量的自动化筛选和信号重构。另一方面,将多维数据聚类分析算法引入随机子空间算法中,并以频率值、阻尼比以及振型系数为因子建立判别矩阵,以智能化区分虚假模态和真实模态,最终实现模态参数自动化识别。文章最后分别用模拟信号和实际桥梁测试信号对所提算法的有效性进行验证,结果表明,该文所提算法能运用于实际桥梁结构的模态参数自动化识别。     

Prediction of nonlinear seismic demands of high‐rise rocking wall structures using a simplified modal pushover analysis procedure

This study presents a simplified analysis procedure for the convenient estimation of nonlinear seismic demands of high‐rise rocking wall structures. For this purpose, the displacement modification approach used in the nonlinear static procedure of ASCE/SEI 41‐13 is adopted. However, in the current study, this approach is extended to every significant vibration mode of the structure whereas the displacement modifying coefficients for different modes are calculated using the typical flag‐shaped hysteresis behavior of rocking walls. The parameters of this hysteresis behavior are selected to represent rocking walls with a practical range of energy dissipation capacity and postgap‐opening stiffness. The computed peak inelastic‐to‐elastic displacement ratios are presented as mean spectra, which can be used for the convenient estimation of pushover target displacement for every significant vibration mode. The accuracy of proposed procedure is examined using the seismic demands obtained from the nonlinear response history analysis of a 20‐story case study rocking wall structure. Furthermore, a modal decomposition technique is used to determine the individual modal seismic demands. The proposed procedure is found to predict both the combined and the individual modal demands with a reasonable accuracy and can serve as a convenient analysis option for the design and performance evaluation of high‐rise rocking wall systems.     

Displacement estimation of nonlinear structures using the force analogy method

Significant effort has gone toward developing accurate and efficient displacement estimation procedures for the nonlinear multi‐degree‐of‐freedom (MDOF) system. Although the dynamic nonlinear analysis is capable of providing the high computational precision through the step‐by‐step time integration method, the simplified method is still expected and imperative for seismic design practices. The work presented in this paper focuses on the implementation of using the modal superposition method to estimate displacement responses of the nonlinear MDOF system based on the force analogy method (FAM). The current research demonstrated that the equation of motion for the nonlinear MDOF system can be decoupled, but other two governing equations in the FAM about the internal force, such as the moment and force of structural members, are not decomposable. Thus, the FAM is incorporated with the modal pushover analysis (MPA) method to determine the basic parameters of each mode such that the modal superposition method can be suitable for the solution of the nonlinear MDOF system. The procedure presented here is an approximately estimation method due to the application of MPA method. However, the value and potential for the maximum displacement estimation of the nonlinear MDOF system were demonstrated through the application in a framed structure. Copyright © 2014 John Wiley & Sons, Ltd.     

Damping estimation using enhanced virtual dynamic shaker: A web‐enabled framework

Damping estimation from laboratory, full‐scale, or computational simulation is critical in response prediction of structures under wind, waves, or earthquake effects. A virtual dynamic shaker (VDS)‐based scheme was recently developed for system identification (SI) of structures for processing (weakly) stationary responses, that is, frequency and damping features that offers, especially the added advantage of its basic simplicity over other schemes. While the VDS has shown performance, equivalent to other popular SI schemes, it is based on the assumption of the global flatness of the load spectrum (i.e., white noise assumption) like used in most other SI schemes, which may not always be appropriate in practical applications. In addition, it is restricted to data from a single‐degree‐of‐freedom (SDOF) response (or unimodal response) to obtain accurate modal characteristics. To address these potential shortcomings, this study revisits the VDS scheme and offers an enhancement by invoking local flatness assumption (EVDS) to possibly improve the damping estimation with the assumption that the load spectrum is flat only around the natural frequencies of the desired modes. A new formulation involving the effect of the ground motion induced vertical vibrations of a building is also introduced for both the VDS and the EVDS. Extensive examples through numerical simulation and full‐scale data, including a comparison with other popular SI schemes, demonstrate the efficacy of the proposed EVDS scheme. To facilitate expeditious and convenient utilization of the proposed EVDS as well as the VDS, this study has implemented a web‐enabled framework, named VDS‐Damping, for on‐demand and on‐the‐fly applications through user‐friendly input and result interfaces. A recently developed mode decomposition scheme, state space‐based mode decomposition (SSBMD), is implemented in the framework to assist in analyzing output from multiple modes and eliminates restriction of SDOF system. Accordingly, the SSBMD can also serve as a stand‐alone mode decomposition tool to separate response in each mode. This framework enables users to estimate damping on‐the‐fly by uploading with ease their data.     

Probabilistic Approach for Nonlinear Modal Control of MDOF Structures Subjected to Multiple Excitations

Abstract:   A nonlinear control strategy with limited control force is applied to the modal control of the multi-degree-of-freedom (MDOF) structure subjected to multiple excitations. For the modal control of the MDOF structure, a new eigenvalue assignment algorithm that modifies the dynamic characteristics of only the specific mode is proposed. For the probabilistic evaluation of the proposed nonlinear modal control, the joint probability density function (PDF) of the equivalent nonlinearly controlled single-degree-of-freedom (SDOF) system is obtained by the solution of the reduced Fokker–Planck equation for the equivalent nonlinear system. To overcome the difficulty in the application of the joint PDF to the MDOF structure controlled by the hybrid mass damper (HMD) system and subjected to multiple excitations, the equivalent damping ratio is proposed. The results of the analysis indicate that the proposed nonlinear modal control strategy is effective for the control of MDOF structures requiring a significantly smaller peak control force than the linear quadratic Gaussian (LQG) controller to produce a similar control performance level.     

Variational mode decomposition based modal parameter identification in civil engineering

An out-put only modal parameter identification method based on variational mode decomposition (VMD) is developed for civil structure identifications. The recently developed VMD technique is utilized to decompose the free decay response (FDR) of a structure into to modal responses. A novel procedure is developed to calculate the instantaneous modal frequencies and instantaneous modal damping ratios. The proposed identification method can straightforwardly extract the mode shape vectors using the modal responses extracted from the FDRs at all available sensors on the structure. A series of numerical and experimental case studies are conducted to demonstrate the efficiency and highlight the superiority of the proposed method in modal parameter identification using both free vibration and ambient vibration data. The results of the present method are compared with those of the empirical mode decomposition-based method, and the superiorities of the present method are verified. The proposed method is proved to be efficient and accurate in modal parameter identification for both linear and nonlinear civil structures, including structures with closely spaced modes, sudden modal parameter variation, and amplitude-dependent modal parameters, etc.     

在用RC框架结构基于位移的抗震性能评估

根据能力谱方法的基本原理 ,建立了在用RC框架结构基于位移抗震性能的评估方法。该方法采用了振型分解法建立的多自由度体系和等效单自由度体系之间的转换关系 ,以及由现行《建筑抗震设计规范》的反应谱曲线建立的结构抗震要求曲线。用本文方法对清华大学主楼 1 0层钢筋混凝土框架结构进行了抗震性能评估 ,同时进行了小震和大震作用下的弹塑性时程分析。本文方法得到的顶点位移角、层间位移角和塑性铰分布与时程分析的结果比较符合     

Modal Identification for High‐Rise Building Structures Using Orthogonality of Filtered Response Vectors

The modal parameters of civil structures (natural frequency, mode shape, and mode damping ratio) are used for structural health monitoring (SHM), damage detection, and updating the finite element model. Long‐term measurement has been necessary to conduct operational modal analysis (OMA) under various loading conditions, requiring hundreds of thousands of discrete data points for estimating the modal parameters. This article proposes an efficient output‐only OMA technique in the form of filtered response vector (frv)‐based modal identification, which does not need complex signal processing and matrix operations such as singular value decomposition (SVD) and lower upper (LU) factorization, thus overcoming the main drawback of the existing OMA technique. The developed OMA technique also simplifies parameters such as window or averaging, which should be designed for signal processing by the OMA operator, under well‐separated frequencies and loading conditions excited by white noise. Using a simulation model and a 4‐story steel frame specimen, the accuracy and applicability were verified by comparing the dynamic properties obtained by the proposed technique and traditional frequency‐domain decomposition (FDD). In addition, the applicability and efficiency of the method were verified by applying the developed OMA to measured data, obtained through a field test on a 55‐story, 214‐m‐tall high‐rise building.     

Estimation of inelastic displacement factor of soil‐shallow‐foundation MDOF systems incorporating higher modes effect

This study attempts to investigate the higher‐mode effects on the constant‐ductility inelastic displacement factors of multi‐degree‐of‐freedom (MDOF) systems considering soil‐structure interaction. These factors were computed for 12,600 two‐dimensional superstructure models of shear buildings and their corresponding equivalent single‐degree‐of‐freedom (ESDOF) systems under 26 ground motions recorded on alluvium and soft soil. An intensive parametric study was carried out for a wide range of non‐dimensional parameters, which completely define the problem. The underlying soil is considered as a homogeneous half‐space based on the concept of cone model. The higher‐mode effects were then investigated through defining the ratio of inelastic displacement factor of MDOF system to that of the corresponding ESDOF one. The influence of soil‐structure interaction key parameters, fundamental period, ductility ratio, the number of stories, and dispersion of the results are evaluated and discussed. Results indicate that as the base becomes very flexible, unlike to the fixed‐base systems, in which the defined ratios are greater than unity, using the inelastic displacement factors of ESDOF models for MDOF ones would result in a remarkable overestimation of maximum inter‐story displacement demand. A new expression is proposed to estimate the ratio of inelastic displacement factor of MDOF soil‐structure systems to that of SDOF counterpart.     

曲率模态法用于网壳结构损伤定位的有效性分析

曲率模态法是针对梁式结构提出的一种损伤识别方法,其用于网壳结构损伤定位的有效性需要进行研究和证实。以一个单层球面网壳为例,对曲率模态法用于该结构的损伤定位进行数值模拟,分析网壳结构模态局部化对损伤定位效果的影响。损伤定位的判断标准为绝对曲率差最大值所对应的节点为损伤位置,指示该节点上的杆件发生了损伤。数值分析的结果表明,对于单杆件损伤,使用损伤前后密集模态的绝对曲率差进行损伤定位,效果很差,而使用损伤前后稀疏模态的绝对曲率差进行损伤定位,效果很好。可见,模态局部化对曲率模态法应用于网壳结构损伤定位的影响很大,因此,只有选择稀疏模态才能较好地避开模态局部化现象,在一定程度上保证曲率模态法用于网壳结构损伤定位的有效性。     

Effective wind actions on ideal and real structures

Gust buffeting of structures is analyzed by Double Modal Transformation, a method consisting in the joint transformation into principal components of structural displacements (modal analysis) and of wind loading (proper orthogonal decomposition). It commonly occurs that modal truncation applies to both the series of structural and loading modes; besides, many loading modes are almost orthogonal respect the dominant structural modes, so they do not contribute to structural response. This set of conditions allows the introduction of an effective action, defined as the loading process reconstructed retaining only those loading modes that excite the structure. This paper discusses this method and the related concepts by analyzing a set of simple ideal structures in closed form; this approach allows the formulation of general criteria aimed at defining the effective wind action as a function of non-dimensional structural and wind parameters. The numerical analysis of a real structure confirms the tendencies pointed out by the analytical solutions.     

结构运营模态测-辨相和理论

运营模态是表征实际工程结构动力特性的重要参数。从结构动力学基本理论出发,阐释了振动测试与模态识别的动力学互馈本质,指出传统模态测试精度不高的根本原因在于两者的割裂操作,提出“振动测试正向服务模态辨识、模态辨识逆向指导振动测试”的动力学统一范畴,建立了结构运营模态测 辨相和理论,给出由响应强度、识别误差和重构精度三大系列评价准则构成的理论体系框架,以健康监测基准模型模拟数据和某大跨径桥梁实测数据为例,共同印证该理论可有效解决以往振动测试的盲目性和模态识别的被动性。文末,总结并展望了结构运营模态测 辨相和理论的发展趋势。     

Strength reduction factor for MDOF soil–structure systems

In most of the seismic design provision, the concept of strength reduction factor has been developed to account for inelastic behavior of structures under seismic excitations. Most recent studies considered soil–structure interaction (SSI) in inelastic response analysis are mainly based on idealized structural models of single degree‐of‐freedom (SDOF) systems. However, an SDOF system might not be able to well capture the SSI and structural response characteristics of real multiple degrees‐of‐freedom (MDOF) systems. In this paper, through a comprehensive parametric study of 21600 MDOF and its equivalent SDOF (E‐SDOF) systems subjected to an ensemble of 30 earthquake ground motions recorded on alluvium and soft soils, effects of SSI on strength reduction factor of MDOF systems have been intensively investigated. It is concluded that generally, SSI reduces the strength reduction factor of both MDOF and more intensively SDOF systems. However, depending on the number of stories, soil flexibility, aspect ratio and inelastic range of vibration, the strength reduction factor of MDOF systems could be significantly different from that of E‐SDOF systems. A new simplified equation, which is a function of fixed‐base fundamental period, ductility ratio, the number of stories, structure slenderness ratio and dimensionless frequency, is proposed to estimate strength reduction factors for MDOF soil–structure systems. Copyright © 2012 John Wiley & Sons, Ltd.     

Modal parameter identification for closely spaced modes of civil structures based on an upgraded stochastic subspace methodology

Based on a recently developed stochastic subspace identification methodology equipped with an alternative stabilization diagram and a hierarchical sifting process, this research aims to improve this approach for more efficiently identifying the modal parameters of civil structures with closely spaced modes. The concept of a doubly folded stabilization diagram is proposed to combine the advantages of both the conventional and alternative stabilization diagrams for achieving better computational efficiency. In addition, the hierarchical sifting process is further refined to more properly handle closely spaced modes. The investigated cases for the occurrence of extremely close modes in civil engineering structures include axially symmetric stay cables, a symmetric cable-stayed bridge with respect to the pylon, and a uniformly arranged office building. Applying the upgraded SSI methodology established in this study, it is demonstrated that the modal parameter identification of civil engineering structures with extremely close modes can be elevated to an advanced level with a frequency space index at the order of 0.1%. Such an accurate identification and distinction is particularly important in the practical applications of structural health monitoring to prevent the false alarms resulting from the confusion of two extremely close modes. Furthermore, this approach also performs well in the determination of mode shape vectors for closely spaced modes to provide an excellent tool for observing their corresponding orthogonality property and high sensitivity.     

基于试验模态参数的索-拱铁路桥的改进有限元模型

介绍基于模态参数的索-拱铁路桥的校准数值模型。基于扩大的频域分解法,采用只输出技术,通过扰动测试来确定自振频率,桥梁振动的整体和局部模态对应的振型及阻尼系数。采用一种遗传算法对数值模型进行改进,该算法可以在数值模型的15个参数中得到最优解。为了与模态匹配,采用了一种基于模态应变能计算的新技术。考虑到不同的初始种群,大量参数的稳定性证明了数值模型在优化范围内所采用优化算法的鲁棒性。通过一个混凝土的变形模量的特征试验和铁路运输下的动力试验,对改进的数值模型进行了验证。结果显示数值模拟结果与试验结果吻合较好。     

Identifying the Modal Parameters of a Structure from Ambient Vibration Data via the Stationary Wavelet Packet

Ambient vibration tests are conducted widely to estimate the modal parameters of a structure. The work proposes an efficient wavelet‐based approach to determine the modal parameters of a structure from its ambient vibration responses. The proposed approach integrates the time series autoregressive (AR) model with the stationary wavelet packet transform. In addition to providing a richer decomposition and allowing for an improved time–frequency localization of signals over that of the discrete wavelet transform, the stationary wavelet packet transform also has significantly higher computational efficiency than the wavelet packet transform in terms of decomposing time‐shifted signals because the former has a time‐invariance property. The correlation matrices needed in determining the coefficient matrices in an AR model are established in subspaces expanded by stationary wavelet packets. The formulation for estimating the correlation matrices is shown for the first time. Because different subspaces contain signals with different frequency subbands, the fine filtering property enhances the ability of the proposed approach to identify not only the modes with strong modal interference, but also many modes from the responses of very few measured degrees of freedom. The proposed approach is validated by processing the numerically simulated responses of a seven‐floor shear building, which has closely spaced modes, with considering the effects of noise and incomplete measurements. Furthermore, the present approach is employed to process the velocity responses of an eight‐storey steel frame subjected to white noise input in a shaking table test and ambient vibration responses of a cable‐stayed bridge.     

A framework for reliability-based system assessment based on structural health monitoring

The safety and usability of transport infrastructures is of great importance for the entire society, because disturbances of traffic networks can have significant consequences for the economy and the environment. Especially today, when bad news about deteriorated structures and shortened public budgets are omnipresent, this must not be forgotten. Structural health monitoring (SHM) can help to ensure the safety of deteriorated structures. SHM is expensive and therefore the investigation of optimized inspection and monitoring strategies is an active field of research. The Collaborative Research Centre (CRC) 477 at the Braunschweig University of Technology investigates innovative methods for SHM. In project field A1, a framework for the probabilistic safety assessment of structures has been developed using data from SHM. The current paper describes and explains the methodology of the framework and shows its application using a substitute structure, which was built for the CRC 477.     

基于Matlab数值方法的结构地震反应分析

通过Matlab语言编写了3个时程分析程序,分别采用Duhamel积分法、Newmark-beta法及Rong-kuta法。在求解多自由度结构体系时,采用振型分解法将多自由度结构体系问题转化为多个广义单自由度结构体系问题,然后对所得计算结果按一定准则进行叠加,求出结构地震反应。首先,对某3层钢筋混凝土框架结构进行时程分析,计算结果与已有文献吻合较好,证明了所编程序的正确性;其次,通过对计算时间的分析对比,表明Rong-kuta法效率最高。论文可为相关工程及设计人员在选择计算方法时提供参考。     

复杂结构的模态选取方法及在连体结构中的应用

针对复杂结构的各阶模态在地震反应中贡献悬殊,提出了基于模态参与因子的模态分析方法,以便于分析结构的动力特性和采用反应谱方法时结构反应的分析计算。通过动力特性分析和地震反应计算,验证了该方法的可靠性,并指出连体结构模态耦合复杂,高阶模态参与的反应较大,同时指出,增加连接层数可以使薄弱单体的结构性能得到较好的改善。