Effect of structural characteristics distribution on strength demand and ductility reduction factor of MDOF systems considering soil-structure interaction

It is known that structural stiffness and strength distributions have an important role in the seismic response of buildings. The effect of using different code-specified lateral load patterns on the seismic performance of fixed-base buildings has been investigated by researchers during the past two decades. However, no investigation has yet been carried out for the case of soil-structure systems. In the present study, through intensive parametric analyses of 21,600 linear and nonlinear MDOF systems and considering five different shear strength and stiffness distribution patterns, including three code-specified patterns as well as uniform and concentric patterns subjected to a group of earthquakes recorded on alluvium and soft soils, the effect of structural characteristics distribution on the strength demand and ductility reduction factor of MDOF fixed-base and soil-structure systems are parametrically investigated. The results of this study show that depending on the level of inelasticity, soil flexibility and number of degrees-of-freedoms (DOFs), structural characteristics distribution can significantly affect the strength demand and ductility reduction factor of MDOF systems. It is also found that at high levels of inelasticity, the ductility reduction factor of low-rise MDOF soil-structure systems could be significantly less than that of fixed-base structures and the reduction is less pronounced as the number of stories increases.

PRESS-based EFOR algorithm for the dynamic parametrical modeling of nonlinear MDOF systems

In response to the identification problem concerning multi-degree of freedom （MDOF） nonlinear systems, this study presents the extended forward orthogonal regression （EFOR） based on predicted residual sums of squares （PRESS） to construct a nonlinear dynamic parametrical model. The proposed parametrical model is based on the non-linear autoregressive with exogenous inputs （NARX） model and aims to explicitly reveal the physical design parameters of the system. The PRESSbased EFOR algorithm is proposed to identify such a model for MDOF systems. By using the algorithm, we built a common-structured model based on the fundamental concept of evaluating its generalization capability through cross-validation. The resulting model aims to prevent over-fitting with poor generalization performance caused by the average error reduction ratio （AERR）-based EFOR algorithm. Then, a functional relationship is established between the coefficients of the terms and the design parameters of the unified model. Moreover, a 5- DOF nonlinear system is taken as a case to illustrate the modeling of the proposed algorithm. Finally, a dynamic parametrical model of a cantilever beam is constructed from experimental data. Results indicate that the dynamic parametrical model of nonlinear systems, which depends on the PRESS-based EFOR, can accurately predict the output response, thus providing a theoretical basis for the optimal design of modeling methods for MDOF nonlinear systems.

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。

基于小波脊的MDOF系统的模态参数识别

将小波理论应用于多自由度(MDOF,multi degree of freedom)系统的模态参数的识别中,首先对MD OF系统的响应函数作基于Morlet小波的时频分解,再由小波系数模的局部极大值求得小波脊,最后求出MDOF系统的各阶模态的固有频率及阻尼比.文中给出了实例,进行了计算说明,结果表明了该方法的有效性.

GIS和MDOF耦合模型下的结构动力计算及评价

结构动力计算是地震工程和结构动力学的重要环节,将地理信息系统(GIS)与多自由度(MDOF)结构动力计算模型耦合,可以实现大范围区域内结构体动力反应的快速计算。GIS平台下,将建筑物结构体抽象为剪切层模型并以2D或者3D实体存储在空间数据库中,通过Jocabi特征值算法求解MDOF振型和Newmark-β算法求解地震的时程反应,并根据位移计算结果实现了建筑物震害破坏等级的分类评价,最终计算结果可以二维图形或者三维可视化的形式在GIS中显示。实例计算结果表明,GIS耦合模型能够高效地实现震灾影响范围内大量MDOF体系的动力反应计算。根据动力反应结果将建筑物地震破坏进行等级划分,并在GIS中可视化计算结果,这将有助于快速预估建筑物结构的破坏程度和分布,为地震应急救援和损失评估提供有力的数据支持。

MDOFS累积塑性变形能的理论研究与敏感性分析

为了研究多自由度体系(MDOFS)累积塑性变形能的分布规律,基于能量平衡原理和多模态等效单自由度体系(ESDOFS)的概念,推导了MDOFS累积塑性变形能需求量及其沿结构各层的分配系数。在此基础上,综合考虑地震作用下结构局部破坏或损伤情况,进行了16种工况下的敏感性分析,得出结构各层参数对累积塑性变形能分布的敏感性影响规律。结果表明:累积塑性变形能分配系数主要由质量(mi)、屈服剪力系数(αi)、刚度(ki)和累积延性系数(ηi)四个因素决定;顶层参数变化对累积塑性变形能分布无明显影响;逐层递减和中间层薄弱情况下,各层分配的累积塑性变形能与αi和ηi呈正相关,与ki呈反相关;中间薄弱层释放的累积塑性变形能按其相邻两层原累积塑性变形能大小之比进行重新分配。

Mode-based equivalent multi-degree-of-freedom system for one-dimensional viscoelastic response analysis of layered soil deposit

Discrete models such as the lumped parameter model and the finite element model are widely used in the solution of soil amplification of earthquakes. However, neither of the models will accurately estimate the natural frequencies of soil deposit, nor simulate a damping of frequency independence. This research develops a new discrete model for onedimensional viscoelastic response analysis of layered soil deposit based on the mode equivalence method. The new discrete model is a one-dimensional equivalent multi-degree-of-freedom（MDOF） system characterized by a series of concentrated masses, springs and dashpots with a special configuration. The dynamic response of the equivalent MDOF system is analytically derived and the physical parameters are formulated in terms of modal properties. The equivalent MDOF system is verified through a comparison of amplification functions with the available theoretical solutions. The appropriate number of degrees of freedom（DOFs） in the equivalent MDOF system is estimated. A comparative study of the equivalent MDOF system with the existing discrete models is performed. It is shown that the proposed equivalent MDOF system can exactly present the natural frequencies and the hysteretic damping of soil deposits and provide more accurate results with fewer DOFs.

刚度突变MDOF体系动力损伤识别

在结构损伤识别中,损伤发生的时间、损伤定位及损伤程度是三个核心问题。本文利用HHT方法结合经验遗传-单纯形算法分析刚度突变MDOF体系在地震波输入下结构的动力损伤识别问题,并以刚度突变4DOF结构体系在ELCentro地震波输入下结构动力特性识别为例进行了讨论。通过Fourier变换得到了结构损伤后的自振频率,利用HHT方法识别出结构损伤发生的时间,在此基础上运用经验遗传-单纯形算法识别出结构损伤后的刚度,从而确定了损伤的程度。

Dynamic amplification factors for a system with multiple-degrees-of-freedom

It is well-known that the responses of a structure are different when subjected to a static load or a sudden step load.The dynamic amplification factor(DAF),which is defined as the ratio of the amplitude of the vibratory response to the static response,is normally used to depict the dynamic effect.For a single-degree-of-freedom system(SDOF)subjected to a sudden dynamic load,the maximum value of DAF is 2.Many design guidelines therefore use 2 as an upper bound to consider the dynamic effect.For a civil engineering structure,which is normally a multiple-degrees-of-freedom(MDOF)system,the DAF may exceed 2 in certain circumstances.The adoption of 2 as the upper bond as suggested by the design guidelines therefore may lead to unsafe structural design.Very limited studies systematically investigate the DAF of a MDOF sysCorrespondence to:Bi Kaiming,Centre for Infrastructure Monitoring and Protection,School of Civil and Mechanical Engineering,Curtin University,Kent Street,Bentley WA 6102,Australia Tel:(+61)892665139 E-mail:kaiming.bi@curtin.edu.autem.This study theoretically investigates the DAF of a MDOF system when it is subjected to a step load based on the fundamental theory of structural dynamics.The condition on which the DAF may exceed 2 is defined.Two numerical examples and one experimental study of a cable-stayed bridge subjected to sudden cable loss are presented to illustrate the problem.

A Novel Method for Vibration Mitigation of Complex Mechanical Systems

Taking the complex mechanical systems as the research project,a theoretical multi-degree-of-freedom(MDOF)model was established.Based on the vibration characteristics analysis of this system,a novel method of vibration mitigation was proposed,which can be applied to most of the complex mechanical systems.Through this method,limited grounding stiffness was made use of and added to certain degree of freedom(DOF)discretely.Thus,the root-meansquare(RMS)of the systems amplitude can be reduced to ideal level.The MATLAB code based on this method was attached,which was tested on the theoretical model.Consider that complex mechanical systems are nonlinear and uncertain,theoretically the optimal solution of vibration mitigation is inaccessible.However,this method can always provide a relatively effective solution.

A New Method of Shock Dynamic Analysis of Multi-degree-of-freedom Systems

A new method is presented to analyze multi-degree-of-freedom (MDOF) dynamic systems subjected to an external shock excitation. A two-degree-of-freedom theoretical system with linear characteristics is exemplified to illustrate the procedure of this method. The equations of motion of the dynamic system are established via matrix method. The dynamic responses of the dynamic system under an external shock excitation of a half-sine type are obtained by MATLAB and ANSYS. It is proved that the new method is helpful to analyze MDOF dynamic systems.

A highly-efficient method for stationary response of multi-degree-of-freedom nonlinear stochastic systems

Analytical and numerical studies of multi-degree-of-freedom(MDOF) nonlinear stochastic or deterministic dynamic systems have long been a technical challenge.This paper presents a highly-efficient method for determining the stationary probability density functions(PDFs) of MDOF nonlinear systems subjected to both additive and multiplicative Gaussian white noises. The proposed method takes advantages of the sufficient conditions of the reduced Fokker-Planck-Kolmogorov(FPK) equation when constructing the trial solution. The assumed solution consists of the analytically constructed trial solutions satisfying the sufficient conditions and an exponential polynomial of the state variables, and delivers a high accuracy of the solution because the analytically constructed trial solutions capture the main characteristics of the nonlinear system. We also make use of the concept from the data-science and propose a symbolic integration over a hypercube to replace the numerical integrations in a higher-dimensional space, which has been regarded as the insurmountable difficulty in the classical method of weighted residuals or stochastic averaging for high-dimensional dynamic systems. Three illustrative examples of MDOF nonlinear systems are analyzed in detail. The accuracy of the numerical results is validated by comparison with the Monte Carlo simulation(MCS) or the available exact solution. Furthermore, we also show the substantial gain in the computational efficiency of the proposed method compared with the MCS.

Ideal Drift Response Curve for Robust Optimal Damper Design for Elastic-Plastic MDOF Structures under Multi-Level Earthquakes Dedicated to Professor Karl S.Pister for his 95th birthday

A new method of robust damper design is presented for elastic-plastic multi-degree-of-freedom(MDOF)building structures under multi-level ground motions(GMs).This method realizes a design that is effective for various levels of GMs.The robustness of a design is measured by an incremental dynamic analysis(IDA)curve and an ideal drift response curve(IDRC).The IDRC is a plot of the optimized maximum deformation under a constraint on the total damper quantity vs.the design level of the GMs.The total damper quantity corresponds to the total cost of the added dampers.First,a problem of generation of IDRCs is stated.Then,its solution algorithm,which consists of the sensitivity-based algorithm(SBA)and a local search method,is proposed.In the application of the SBA,the passive added dampers are removed sequentially under the specified-level GMs.On the other hand,the proposed local search method can search the optimal solutions for a constant total damper quantity under GMs’increased levels.In this way,combining these two algorithms enables the comprehensive search of the optimal solutions for various conditions of the status of the GMs and the total damper quantity.The influence of selecting the type of added dampers(oil,hysteretic,and so on)and the selection of the input GMs on the IDRCs are investigated.Finally,a robust optimal design problem is formulated,and a simple local search-based algorithm is proposed.A simple index using the IDRC and the IDA curve of the model is used as the objective function.It is demonstrated that the proposed algorithm works well in spite of its simplicity.

Elastic and Inelastic Response of Structural Systems in Seismic Pounding

The present paper addresses the comparative study of three adjacent single-degree-of freedom structures for elastic and inelastic system with and without pounding under seismic excitations. For the gap between three adjacent structures, the simulation is done by using linear spring element without damping. The entire numerical simulation is done in time domain by considering the inputs of four real ground motions. The results of the study show that the response of elastic system is much different to that of response of inelastic system in the absence and presence of pounding, especially in lighter or more flexible structures. Elastic structures show much severe pounding response than inelastic structures. Modeling of colliding structures behaving inelastically is really needed in order to obtain the accurate structural pounding involved response under seismic excitation.

结构抗震分析用地震动强度指标的研究

随着基于性能结构抗震设计方法的推广应用,结构弹塑性时程分析逐渐成为主要的分析方法,但该方法所面临主要困难是缺乏对地震波选择的统一标准。由于影响地震动的参数很多,且不同参数对结构弹塑性地震响应的影响规律又十分复杂,因此能综合反映各种地震动参数对结构弹塑性地震响应影响的地震动强度指标成为基于性能结构抗震设计方法研究中的一个基本问题。本文参考已有学者的研究成果,总结归纳了现有主要的33个地震动强度指标,基于弹塑性SDOF和MD-OF系统的代表性地震响应指标,分析了不同地震动强度指标与不同结构地震响应指标之间的相关性,研究了不同地震动指标的适用范围和优缺点,给出了结构抗震分析用地震强度指标的建议。

结构静力弹塑性分析方法的研究和改进

在对结构静力弹塑性分析方法的物理意义进行了有益的探讨之后,指出了该方法存在的一些局限,考虑了结构第二、第三两阶振型对结构地震反应的影响,并在把MDOF体系转换为SDOF体系和进行等效SDOF体系的动力时程分析时,将结构视为两个不同的结构。数值结果表明:采用本文的改进方法以后,计算精度明显提高。

试件特性对地震模拟振动台控制性能影响研究(Ⅱ)——对地震记录再现精度的影响及实时补偿

常规振动台系统共振频率为20 Hz,而试验试件1阶频率最大为8 Hz,在进行地震模拟振动台控制系统设计时将试件视为刚性体,二者存在较大差异.因此,振动控制系统控制频带窄、稳定性差,降低了地震记录再现精度.本文通过系统建模分析了试件质量、频率、阻尼等因素对振动台控制性能的影响.结果表明:试件各阶频率周围频带的输入波再现精度很低,出现不同程度的放大与削弱,最大可达3倍.针对这一问题设计了实时反力补偿算法以修正试件与台面相互作用对控制系统性能的影响,在保证系统稳定性的前提下提高了地震记录的再现精度.

结构地震反应Pushover位移形状向量的选取

对结构静力弹塑性分析方法的物理意义进行了探讨,指出了该方法存在的一些局限,提出由结构前三阶振型的线性加权组合确定结构位移形状向量或将前三阶振型分别确定为前三个位移形状向量,并在把MDOF体系转换为等效SDOF体系和进行等效SDOF体系的动力时程分析时,将结构区分为屈服前和屈服后两种不同的状态.数值结果表明:采用改进的方法以后,目标位移计算精度明显提高,对结构的损伤评估结果与试验观测结果吻合.

多自由度无阻尼动力吸振器的理论研究

讨论了将简谐激振下无阻尼单自由度主系统的动力消振原理推广到多频谐波激励下无阻尼多自由度主系统的情况 ,通过选择一个合适的多自由度无阻尼动力吸振从系统 ,即从系统的固定频率正好是所有的激振力的频率 ,可以完全消除多频谐波激励下无阻尼多自由度主系统中某质点的振动响应。还讨论了根据给定弹簧 -质量系统的特征值及对该系统进行小的、已知的修正后所得系统的特征值 。

复阻尼多自由度系统动力分析的模态叠加法

工程实际中,复阻尼多自由度系统的瞬态响应过去一直是通过频域方法求解的。频域方法的一个突出问题是求传递函数矩阵的计算工作量过大。本文给出一种有效而实用的时域解法———实模态叠加法,此外还介绍了复模态叠加法。实模态叠加法是基于一个事实,即n维复向量空间中的复向量可以在n维实向量空间中的一组线性无关的实向量构成的基下表出;另外,就此方法还讨论了复阻尼多自由度系统初始运动条件的给出和转换问题。复模态叠加法则是通过变量替换的方法,变其中的复特征值问题为形式上的一个实特征值问题来解决的。