基于能量的模态pushover分析方法

提出了一种基于能量的模态pushover分析方法,解决了高阶模态能力曲线失稳的问题。该方法利用基于结构变形吸收能量的等效位移,计算结构在地震作用下的非线性总体变形,替代模态pushover中基于顶点位移的变形解法,采用基于能量原理的等效单自由度体系,结合等强度谱计算目标位移,以目标位移对应的能量指标求出相应的结构性态反应,采用SRSS方法组合得到结构的最大反应。以9层钢框架结构为例对所提出方法进行了验证,结果表明:该方法可以考虑高阶效应,不会出现能力谱折返的失效情况,而且与时程分析法相比,该方法计算效率高且具有较好的精度。     

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.     

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.     

索网结构非线性地震反应分析实用方法

采用现有方法分析索网结构非线性动力反应时,仅能对矩形平面索网结构建立等效单自由度(ESDF)模型,地震作用下,此类结构的响应只能采用时程法进行计算。基于结构整体刚度参数的概念,结合模态推覆分析方法,建立了任意形状索网结构的非线性ESDF模型,该模型刚度特性与Duffing系统相同。采用能量平衡法,导出了索网结构非线性ESDF体系的等效线性刚度ke与位移反应d的关系;结合ESDF体系的等效质量,将加速度-周期(a-T)格式的设计反应谱变换为刚度-位移(k-d)格式;与ke-d关系式联立求解得出ESDF体系的非线性地震反应。该方法在线性设计反应谱的基础上,合理考虑了索网结构的非线性刚化效应。数值算例表明,相对于线性振型叠加反应谱法,该方法具有更好的适用性。     

Approximate modal analysis of multistory symmetrical buildings with restricted inelasticity

Simplified capacity curves are presented for modal decomposition of multistory inelastic cantilever bents. These structural systems are uniform over the height and plasticity is assumed to be restricted into the beams, since significant rotation ductility factors may be attained in these members without loss of strength. The approximate method of modal decomposition of multistory inelastic bents is based on the concept that the total response may be obtained from the contributions of equivalent nonlinear single‐degree‐of‐freedom (SDOF) modal systems, in combination with the technique of modal superposition. In particular, the contribution of the first mode equivalent inelastic SDOF system is examined, since its modal contribution is of higher importance. The response of such SDOF systems basically depends on their capacity curve, which may be formulated by using the dynamic properties (frequency, effective modal mass and mode shape) of the initially elastic bent, as well as the corresponding properties of the bent when the entire set of coupling beams is assumed to be yielded. The procedure is presented for plane cantilever bents, but it can be easily extended to symmetrical structural systems composed of different types of inelastic bents. Its application is illustrated by means of a 10‐story inelastic coupled‐wall bent subject to a strong earthquake motion, equal to 1·5× El Centro N–S ground excitation, and the results compare well with those obtained from a step‐by‐step nonlinear time history analysis of the discrete member model. Copyright © 2007 John Wiley & Sons, Ltd.     

An improved multidimensional modal pushover analysis procedure for seismic evaluation of latticed arch‐type structures under lateral and vertical earthquakes

Pushover methods for seismic assessment of buildings under multidimensional earthquakes have been studied and retrofitted. However, these current methods are not suitable when applied to widely adopted arch‐type structures characterized by strong geometrical nonlinearity and coupling effects. An improved multidimensional modal pushover procedure with two‐stage analyses is proposed for seismic evaluation of latticed arches. Taking overall multidimensional response into consideration, modal stiffness of the equivalent single‐degree‐of‐freedom system is derived, and its capacity curve is determined during the first‐stage analysis. To provide a deformation profile with algebraic signs of response retained, the second‐stage analysis is conducted using the pushover load pattern derived from modal displacement superposition. The objective of the improved procedure is to overcome the drawback of the conventional modal pushover method, which describes the capacity curve resorting to base shear and roof displacement, and that of quadratic combination rules which eliminate the sign reversals of response. To validate its serviceability, nodal displacements and element stresses, as well as the yielding members, of two typical latticed arches are calculated. Through comparative analysis, the results by the improved procedure exhibit good agreement with those by response history analysis. Additionally, this procedure demonstrates great superiority over the conventional method for its satisfying accuracy.     

A study on the accuracy of force analogy method in nonlinear static analysis

In this paper, the accuracy of the force analogy method (FAM) for nonlinear static (pushover) analysis is investigated. Hence, after explanation of the concept of FAM by a new approach, 12 2D steel special moment resisting frames with different configurations were derived from two different 3D archetypes and modeled using four various methods of capturing nonlinearity including SAP2000 super elements, OpenSees force‐based and displacement‐based fiber method, and FAM. In addition, a MATLAB code was developed for modeling and analyzing the frames by FAM. The accuracy of FAM in predictions of pushover curves, base shear forces, and plastic rotation of the critical hinges was investigated. The results indicated that in general, the predictions obtained using the FAM had a good agreement and compatibility with those from other methods of analysis currently used in practice for seismic performance assessment of structures.     

Damage Identification for Hysteretic Structures Using a Mode Decomposition Method

This article investigates structural health monitoring (SHM) of multidegree of freedom (MDOF) structures after major seismic or environmental events. A recently developed hysteresis loop analysis (HLA) SHM technique has performed robustly for single degree of freedom (SDOF) and single mode dominant MDOF structures. However, strong ground motions can trigger higher vibration modes, resulting in irregular hysteresis loops and making this otherwise robust identification difficult. This study presents a new filtering tool, enabling reconstruction of single mode dominant restoring force‐displacement loops which can be readily used for HLA. The proposed filtering tool is based on a classic modal decomposition using optimized mode shape coefficients. The optimization process is carried out in a modal space and is based on decoupling frequency response spectra of interfering modes. Application of modal decomposition using the optimized mode shape coefficients allows for reconstruction of single‐mode dominant hysteresis loops, which can be effectively identified using HLA. The proposed filtering tool is validated on the reconstruction of hysteresis loops on an experimental bridge pier test structure with notable contributions from at least two modes. The results show the method eliminates the influence of all higher modes that contain significant energy content and yields the reconstruction of “smooth” single mode dominant hysteresis loops. The resulting SHM analysis on the reconstructed experimental hysteresis loops identified degradation in the elastic stiffness profiles, indicating damage within the structure and matching prior published results based on physical inspection of damage. The overall method presented increases the breadth of potential application of the HLA method and can be readily generalized to a range of MDOF structures.     

改进分析过程的模态pushover分析

Chopra的模态pushover分析需要求解各振型等效单自由度体系动力方程,以得到结构对应振型pushover分析的终止目标位移,进而求解对应多自由度体系的各阶振型下楼层的位移。本文对Chopra的模态pushover分析过程进行了改进,通过振型pushover曲线与弹塑性反应谱相交的性能点来求解对应多自由度体系各阶振型下的楼层位移,以考虑高阶振型对静力弹塑性分析方法的影响。并通过SAP2000实现改进模态pushover分析过程,计算结果表明改进的模态pushover分析可以有效的考虑高阶振型影响。     

Reduction of inelastic seismic demands in a mid‐rise rocking wall structure designed using the displacement‐based design procedure

Precast post‐tensioned rocking wall structural system has been developed in the recent past as a damage‐avoidance structural system for seismic regions. For a widespread use of this structural system, suitable design procedures are required to ensure a reliable and well‐predicted performance under different levels of seismic hazard. In the current study, a mid‐rise 20‐story rocking wall structure is selected and designed using the displacement‐based design procedure. Furthermore, two different capacity design procedures are used to predict the increased force demands due to higher mode effects. The time history results against moderate and severe level of seismic hazards show the effectiveness of displacement‐based design procedure in predicting and controlling the displacement and drift demands, while the simplified procedure and the modified modal superposition procedure for the capacity design are found to be unconservative and conservative, respectively. To further investigate the seismic demands, modal decomposition of inelastic seismic responses is carried out, and the contribution of different modes in the total responses is calculated. Based on this improved understanding, a mitigation technique of dual gap opening is employed. A detailed discussion about the location and design strength of the extra gap‐opening is carried out by considering different performance parameters. Copyright © 2016 John Wiley & Sons, Ltd.     

弹塑性MDOF系统地震输入能量研究

基于地震作用下弹塑性SDOF(Single Degree of Freedom)和弹性MDOF(Multi-degree of Freedom)系统能量输入研究,本文分析了弹塑性MDOF系统能量输入规律。以实测地震记录为输入,采用弹塑性时程分析方法,计算了一阶初始周期≤3s的5、10、20、30层双线性滞回剪切层模型,不同阻尼比、承载力降低系数情况下4800个结构和一阶初始周期>3s的40层结构能量输入,与弹塑性SDOF系统的输入能量谱进行对比。研究表明:一阶周期在3s以内的弹塑性MDOF系统输入能量EI可用相同阻尼比、初始周期、承载力降低系数的弹塑性SDOF系统计算结果近似确定;一阶周期大于3s的弹塑性MDOF系统,可采用MPA方法等效为多个弹塑性SDOF系统,按照振型叠加法计算总输入能。     

基于拟力法的纤维梁有限元非线性分析方法

以拟力法中的弹塑性分解思路和纤维梁理论为基础,将梁单元的截面变形分解为弹性变形和塑性变形,并引入塑性自由度,在材料层面建立了基于拟力法的纤维梁有限元非线性分析方法。该方法可以保持结构整体刚度矩阵不变,其非线性状态通过局部塑性矩阵加以体现,在迭代计算时避免了结构整体刚度矩阵的实时更新与分解,且塑性矩阵相比于结构整体刚度矩阵规模小,提高了计算效率。通过数值算例,将文中方法与采用有限元软件ABAQUS的分析结果进行对比,两者吻合较好,证明了该方法的有效性。     

Identification of modal damping ratios of four‐flue chimney of a thermoelectrical plant using pseudo‐inverse matrix method

Some computational issues related to the identification of modal parameters of structures are presented in this paper. Optimal estimation of modal parameters often requires the solution of an overdetermined linear system of equations. Hence the computation of a pseudo‐inverse matrix is involved. In this paper the numerical performance of different algorithms for Moore–Penrose pseudo‐inverse computation have been tested for modal analysis of a four‐flue chimney of a thermoelectrical plant. The computational scheme herein adopted for parameter identification is based on well‐known modal properties and has a fast rate of convergence to solution. The computation of the Rayleigh damping coefficients a and b is an important step in the area of the modal superposition technique. The proposed approach can accurately predict damping ratios and all the eigenvectors without evaluating mass and stiffness matrices. Copyright © 2007 John Wiley & Sons, Ltd.     

地震作用下悬臂类结构的模态截断方法

为估计模态叠加法中模态截断对结构地震作用下位移、速度、加速度反应的影响，对比分析了累积振型参与质量误差、静荷载参与比误差、质量相关荷载作用下的位移误差、累积振型贡献系数误差、累积振型加速度贡献系数误差和单位阵误差等模态截断指标随模态数目增加的变化规律。以一个5层剪切框架、一个单向不对称的4层框架和一个框架支撑结构的地震反应为例，讨论了结构位移、速度和加速度反应的模态截断误差与模态截断指标的关系。算例分析结果表明，静荷载参与比误差高估了低阶模态的影响而使模态截断数目偏少；质量相关荷载作用下的位移误差所得模态数目不稳定，这两个指标不适合作为模态截断的依据。对于悬臂类结构，模态截断所产生的累积误差以加速度的最大，速度的次之，位移的最小；对于位移反应，首层平动位移的累积振型贡献系数误差和累积振型参与质量误差可作为位移反应模态截断的依据；高阶模态对结构加速度反应的贡献大于对位移反应的贡献，应采用累积振型加速度贡献系数误差作为加速度反应模态截断的依据。     

Simplified multi‐degree‐of‐freedom model for estimation of seismic response of regular wall‐frame structures

A simplified multi‐degree‐of‐freedom (MDOF) model is developed for estimation of seismic response of tall wall‐frame structures. By using the continuum technique for the structure and adopting the bilinear hysteretic model for material properties, procedure for the development of the simplified MDOF model is derived. The numerical study for a 20‐storey reinforced concrete (RC) wall‐frame structure is conducted to investigate the accuracy of seismic response predicted by the proposed model. Results from the nonlinear response history analyses based on the proposed MDOF model and the detailed structural model with member‐by‐member representation are compared and show very good agreement. The proposed simplified MDOF model is shown to provide a simple, efficient and accurate method for estimation of seismic performance of tall wall‐frame structures. Copyright © 2009 John Wiley & Sons, Ltd.     

时域载荷识别法在海洋结构中的应用

动载荷识别的时域法是利用结构的模态参数建立结构系统在时域内的逆向模型,进而通过系统的动态响应识别输入动态载荷的过程。分析了采用时域方法对离散系统进行动载荷识别的方法,它是用正分析的方法来求解反问题。根据渤海某平台的测厚报告用ANSYS软件建立了该平台的有限元模型,采用理论分析和计算机仿真的方法相结合,将时域正演方法应用在海洋平台这种大型结构的载荷识别中,结果表明,只要实测信息准确,该方法在理论上具有较高的精度。     

An alternative approach for assessing eccentricities in asymmetric multistory buildings. 2. Inelastic systems

The approximate method, presented in the companion paper, for assessing modal eccentricities of elastic multistory buildings with simple eccentricity is extended in systems composed by elastoplastic resisting bents. Following the technique of the aforementioned paper for computing modal properties of such buildings by means of an equivalent single‐story system composed of elastic elements, modal capacity curves of these systems may also be drawn when the resisting elements are defined by a bilinear force–displacement (characteristic) curve. The procedure for constructing element‐characteristic curves is based on the methodology presented by the author in an earlier paper, and modal capacity curves of the equivalent single‐story system may be drawn by performing a non‐linear pushover analysis using the inertia force eccentricity of each mode of this system. Therefore, base shears and their eccentricities for the first two modes of vibration of multistory inelastic buildings can be determined as in real one‐story non‐linear systems. The method is illustrated in a 10‐story partial symmetric building, having along the direction of the ground motion three identical, inelastic, coupled wall bents. The structure is analyzed for a strong ground motion, equal to 1·5 × El Centro earthquake excitation, and the results are compared with those obtained from a step‐by‐step non‐linear time history analysis of the discrete member model. Copyright © 2007 John Wiley & Sons, Ltd.     

框架——剪力墙结构的静力弹塑性分析研究

静力弹塑性方法作为一种评价结构抗震性能和计算结构弹塑性变形的简化方法,近年来得到了广泛应用。但由于传统的定侧力模式的静力弹塑性方法只考虑第一振型,无法反映高层建筑结构的高阶振型影响。为考虑高阶振型的影响,Chopra在振型分解反应谱组合法的基础上,提出了MPA方法。本文首先讨论了应用MPA方法需注意的问题,然后用一个18层钢筋混凝土框架—剪力墙结构为算例,以逐步增量弹塑性时程分析结果为基准,对传统定侧力模式静力弹塑性方法和MPA方法的分析结果进行了对比研究。结果表明,相比于定侧力模式静力弹塑性分析结果,MPA方法的分析结果更接近弹塑性时程分析结果。     

New method for modal identification of super high‐rise building structures using discretized synchrosqueezed wavelet and Hilbert transforms

Measured signals obtained by sensors during dynamic events such as earthquake, wind, and wave contain nonlinear, nonstationary, and noisy properties. In this paper, a new approach is presented for modal parameter identification of structures particularly suitable for very large real‐life structures such as super high‐rise building structures based on the integration of discretized synchrosqueezed wavelet transform, the Hilbert transform, and the linear least‐square fit. Its effectiveness is demonstrated first by application to a two‐dimensional frames from the literature, and then to the 123‐story Lotte World Tower (LWT) under construction in Seoul, Korea. The LWT measurements are very low‐amplitude ambient vibrations. Extracting the natural frequencies and damping ratios from such low‐amplitude signals are known to be very challenging. Further, the new methodology was compared with the empirical mode decomposition. It is demonstrated that the new method is capable of extracting both natural frequencies and damping rations from low‐amplitude signals effectively and with a higher accuracy compared with the empirical mode decomposition approach. The results of this research indicate a super high‐rise building like LWT has a damping ratio in the range 0.7–3.4%. The new method is quite promising for practical implementations of health monitoring of large real‐life structures.     

Alternative approach to compute shear amplification in high‐rise reinforced concrete core wall buildings using uncoupled modal response history analysis procedure

The seismic response of the high‐rise reinforced concrete (RC) wall structures is really complicated as several vibration modes other than the fundamental mode normally contribute significantly to the response—commonly recognized as ‘higher mode effects’. Response spectrum analysis (RSA) procedure, which can account for higher mode effects, is usually employed to compute the seismic design demand for the high‐rise structures. Recent studies show that the inelastic seismic force demands obtained from the rigorous nonlinear response history analysis procedure are much larger than the seismic force design demands obtained from the code‐based RSA procedure for the high‐rise RC wall structures. Though, the nonlinear response history analysis procedure is widely accepted for its ability to provide the most accurate estimate of nonlinear seismic responses, the obtained responses are generally so complex that it is quite difficult for engineers to grasp the overall picture of the responses and gain some insight into them and use them to understand the cause of high seismic demands. Another important issue related to the nonlinear seismic response prediction of the high‐rise RC wall structures is the realistic and accurate numerical modeling of RC walls. In this study, a simplified but reasonably accurate procedure called the uncoupled modal response history analysis procedure is used to interpret the complex nonlinear behavior of high‐rise RC wall structures. Moreover, a finite element model based on modified compression field theory is employed for accurate numerical modeling of RC walls by incorporating the axial‐flexure‐shear interaction. This study, by making use of a better computer modeling approach and an in‐depth analysis by modal decomposition, aims to resolve some of the unanswered questions regarding realistic prediction of nonlinear seismic demands of high‐rise structures.