On the coupled torsional and sway vibrations of a class of shear buildings

This paper is concerned with the free vibrations of a restricted class of multi-storey shear buildings in which inertial coupling exists between the torsional and the two sway vibrations. The restrictions imposed are that (a) the shear centres of all storeys lie on a vertical straight line, (b) the principal axes of shear are in the same directions in all storeys, (c) the centres of mass of all floors lie on another vertical straight line, (d) the radius of gyration about the shear centre of every floor mass is the same and (e) the ratios of the two shear stiffnesses to the torsional stiffness do not vary from storey to storey. In consequence of the last restriction it is proved that the 3n natural frequencies, normal modes and generalized masses, where n is the number of storeys, are expressible very simply in terms of products of the three natural frequencies, normal modes and generalized masses of the single-storey, three-dimensional building formed by removing everything above the first floor, with the n natural frequencies, normal modes and generalized masses of a certain n-storey, two-dimensional shear frame. In the special case of a uniform building, a simple closed form solution, valid for any number of storeys, is given.     

基于弯曲弹簧模型的裂纹混凝土梁动力特性分析

利用结构振动波传播理论,将含裂纹混凝土梁以裂纹为界划分为两段连续的波导体,为了表征由裂纹引起的梁中波传播的不连续特性,引入了模拟裂纹的弯曲弹簧模型。通过理论计算得到了裂纹简支梁的特征方程,并以一裂纹混凝土简支梁为例进行数值分析,讨论了裂纹的深度和位置对裂纹梁各阶固有频率的影响。     

Prediction of high-speed train induced ground vibration based on train-track-ground system model

The development of analysis on train-induced ground vibration is briefly summarized. A train-track-ground integrated dynamic model is introduced in the paper to predict the ground vibration induced by high-speed trains. Representative dynamic responses of the train-track-ground system predicted by the model are presented. Some major results measured from two field tests on the ground vibration induced by two high-speed trains are reported. Numerical prediction with the proposed train-track-ground model is validated by the high-speed train running experiments. Research results show that the wheel/rail dynamic interaction caused by track irregularities has a significant influence on the ground acceleration and little influence on the ground displacement. The main frequencies of the ground vibration induced by high-speed trains are usually below 80 Hz. Compared with the ballasted track, the ballastless track structure can produce much larger train-induced ground vibration at frequencies above 40 Hz. The vertical ground vibration is much larger than the lateral and longitudinal components.     

钢筋混凝土框架顶部钢结构加层的抗震性能分析

采用钢结构加层后,结构的整体质量、刚度、周期、阻尼比等都发生较大的变化。仅对加层部分结构进行计算分析是不安全的,应进行结构的整体分析。本文采用有限元软件ANSYS,对某4层钢筋混凝土框架结构办公楼顶部加2层纯钢框架的抗震性能进行分析,并在此基础上讨论了不同加层层数的整体框架模型、不同阻尼比ζ和有侧移及无侧移框架形式对结构整体抗震性能的影响分析。计算表明,由于加层后结构周期加长,整体框架的底层层剪力变化较小。     

Modal identification of structures from ambient vibration,free vibration,and seismic response data via a subspace approach

This work presents a unified procedure for determining the natural frequencies, modal damping ratios and modal shapes of a structure from its ambient vibration, free vibration and earthquake response data. To evaluate the coefficient matrices of a state‐space model, the proposed procedure applies a subspace approach cooperating with an instrumental variable concept. The dynamic characteristics of a structure are determined from the coefficient matrices. The feasibility of the procedure is demonstrated through processing an in situ ambient vibration measurement of a five‐storey steel frame, an impulse response measurement of a three‐span continuous bridge, and simulated earthquake responses of five‐storey steel frames from shaking table tests. The excellent agreement of the results obtained herein with those published previously confirms the feasibility of the present procedure. Copyright © 2001 John Wiley & Sons, Ltd.     

The vibrational characteristics of a twelve-storey steel frame building

The Ralph M. Parsons World Headquarters building, a twelve-storey steel frame structure, was subjected to a series of forced vibration tests. The natural frequencies, three-dimensional mode shapes and damping coefficients of nine modes of vibration were determined. Other features of this investigation included the study of non-linearities associated with increasing levels of response, detailed measurements of the deformation of the first floor and the ground surrounding the structure, and measurements of strain in one of the columns of the structure during forced excitation. The dynamic characteristics of the building determined by these tests are compared to those predicted by a finite element model of the structure. The properties of primarily translational modes are predicted reasonably well, but adequate prediction of torsional motions is not obtained. The comparison between measured and predicted strains suggests that estimates of stress determined from finite element analyses of buildings might be within 25 per cent of those experienced by the structure for a known excitation.     

Numerical study of characteristics of underground blast induced surface ground motion and their effect on above-ground structures. Part II. Effects on structural responses

Studies of structural responses and damage to high-frequency blast motion are very limited. Current practice uses some empirical allowable ground vibration limits in assessing structural performance. These empirical limits overlook the physical parameters that govern structural response and damage, such as the ground motion characteristics and inherent structural properties. This paper studies the response of RC frame structures to numerically simulated underground blast-induced ground motions. The structural response and damage characteristics of frame structures to ground motions of different frequencies are investigated first. The effects of blast ground motion spatial variations and soil–structure interaction on structural responses are also studied. A suitable discrete model that gives accurate response prediction is determined. A damage index defined based on the accumulated plastic hinge rotation is used to predict structural damage level. Numerical results indicated that both the low structural vibration modes (global modes) and the first elemental vibration mode (local) might govern the dynamic structural responses depending on the ground motion frequency and structural response parameters under consideration. Both ground motion spatial variations and soil–structure interaction effects are prominent. Neglecting them might yield inaccurate structural response prediction. The overall structural response and damage are highly ground motion frequency dependent. Numerical results of structural damage are also compared with some test results obtained in a previous study and with code specifications. Discussions on the adequacy of the code allowable ground vibration limits on RC frame structures are also made.     

Fundamental periods of vibration of RC buildings in Portugal from in-situ experimental and numerical techniques

Since the early nineteen seventies we have been measuring the in-situ dynamic characteristics of the different structures built in Portugal, essentially based on ambient vibration and using expedite techniques. A data-base containing not only the fundamental dynamic characteristics of those structures but also their most important geometric and constructive properties has been created with the aim of setting correlations between construction typologies and fundamental periods or frequencies, and damping characteristics, and calibrate numerical modelling of those structures. This paper presents the main results for circa 197 reinforced concrete (RC) buildings, obtaining the fundamental period as a linear function of height or number of storeys for different typologies and situations, and showing that numerical models, made for a number of illustrative cases, can reproduce with great accuracy the in-situ measurements. The main parameters having remarkable influence on the overall correlation laws are identified and a measure of uncertainty deduced. Comparisons with published formulae for other regions of the world show that we can group these laws by regions with similar expression within each group but with large variations from group to group. Discussion on how to deal with the elongation of the periods of vibration due to moderate and large amplitude motion, causing changes in the seismic behaviour and on appearance of damage, will also be briefly introduced, keeping in mind current code practices.     

Exact dynamic member stiffnesses for a beam on an elastic foundation

This paper gives exact Bernoulli–Euler dynamic flexural member equations for a uniform beam on an elastic foundation. These enable exact results to be obtained when the beam is included in free or sinusoidally forced vibration calculations for a plane or space frame, at any frequency. In addition, information is presented to ensure that no natural frequencies are missed in a free vibration analysis.     

Analytical modelling of multi‐mass flexible rocking structures

This paper presents a new analytical model for describing the large rocking response of an elastic multi‐mass structure resting on ideally rigid ground. Using the experimental results from a rocking steel column, the ability of the proposed analytical model to estimate the rocking and translational acceleration response under free vibration, pulse and earthquake excitations is evaluated. It is observed that the classical treatment of impact may result in an unrealistically large transfer of energy to vibrations. Therefore a new Dirac‐delta type impact model that spreads the effects of impact over time and space is proposed. The use of a Dirac‐delta model and accurate restitution factors play a pivotal role in prediction of rocking and acceleration responses. In order to characterize the nonlinear response better, a modal analysis of the linearized system is proposed. With this approach, the vibration mode frequencies and shapes during rocking action were determined. A comparison of analytical and experimental modal estimations suggests good agreement. The results emphasize that the vibration characteristics of several vibration modes are affected by rocking action, and these modes may be excited at impact. Copyright © 2016 John Wiley & Sons, Ltd.     

全埋入单桩基础横向振动模态正交性研究

采用Timoshenko梁模型作为挠曲波在全埋入单桩基础中的传播模型,根据频域中全埋入单桩基础横向振动时的运动微分方程,结合各节点的力平衡、位移协调方程及局部对偶坐标系中内力及位移的对偶变换关系,严格推导全埋入单桩基础横向振动的模态正交性条件。以回传射线矩阵法为基础,求解全埋入单桩基础横向振动的自振频率、衰减系数及不同自振频率所对应的模态,并通过具体算例验证全埋入单桩基础横向振动模态的正交性条件公式推导的正确性。     

基于褶积原理和改进广义S变换的震动波衰减补偿试验研究

为了恢复震动波能量在传播过程中产生的衰减损耗,提出基于褶积原理求取品质因子Q的方法与改进广义S变换相结合的反Q滤波法。通过震动波衰减补偿模型试验,对试验数据进行改进广义S变换的时频特性分析,得出了信号的能量分布情况以及时间频率对应关系;采用基于褶积原理求取品质因子的方法,得到时变Q值;对试验数据进行反Q滤波处理,使震动波能量得到了补偿。结果表明本文提出的反Q滤波法提高了对震动波能量衰减补偿的效果,拓宽了地震资料的频带,提高了地震资料分辨率,有利于进行高分辨率地震勘探、深部信号增强和油气藏预测工作的开展。     

Frequency analysis of coupled shear wall assemblies

The finite strip procedure is used to predict the free vibration response of both planar and non-planar coupled shear wall assemblies. The solid walls are considered as vertical cantilever strips and a comparison is made between modelling the spandrel beams as discrete beams and as an equivalent continuum with orthotropic plate properties. It is shown that both approaches lead to essentially the same frequencies. The effects of vertical inertial forces and shear deflection are included, and structures considered may have properties that vary with height. The method presented appears to be more versatile than previously published techniques and numerical comparisons with existing methods indicate the predicted results to be accurate.     

Free vibration of asymmetric shear wall-frame buildings

The Galerkin method of weighted residuals is used to determine the frequencies and associated mode shapes of asymmetric shear wall-frame structures. The governing equations are formulated using the continuum approach by idealizing the structure as a shear-flexure beam. Varying properties along the height of the building are considered. The effect of translational, rocking and torsional flexibilities of the foundation on the natural frequencies is also investigated. The method presented herein utilizes polynomial and transcendental displacement functions, and is found to be simple, versatile and efficient.     

Soil–pile–structure interaction under SH wave excitation

A continuum model for the interaction analysis of a fully coupled soil–pile–structure system under seismic excitation is presented in this paper. Only horizontal shaking induced by harmonic SH waves is considered so that the soil–pile–structure system is under anti‐plane deformation. The soil mass, pile and superstructure were all considered as elastic with hysteretic damping, while geometrically both pile and structures were simplified as a beam model. Buildings of various heights in Hong Kong designed to resist wind load were analysed using the present model. It was discovered that the acceleration of the piled‐structures at ground level can, in general, be larger than that of a free‐field shaking of the soil site, depending on the excitation frequency. For typical piled‐structures in Hong Kong, the amplification factor of shaking at the ground level does not show simple trends with the number of storeys of the superstructure, the thickness and the stiffness of soil, and the stiffness of the superstructure if number of storeys is fixed. The effect of pile stiffness on the amplification factor of shaking is, however, insignificant. Thus, simply increasing the pile size or the superstructure stiffness does not necessarily improve the seismic resistance of the soil–pile–structure system; on the contrary, it may lead to excessive amplification of shaking for the whole system. Copyright © 2003 John Wiley & Sons, Ltd.     

Errors in response calculations for extensional vibrations of bars

The transient extensional vibrations of a slender and uniform bar, which is clamped at one end and is subjected to an axial force at the other free end, are investigated by applying three methods: the Laplace transform method, the normal mode and Newmark β methods in conjunction with the finite element method (FEM); the errors caused by the spatial discretization of the FEM and the direct integration of the Newmark β method are studied and compared with those of the previous paper where the flexural vibrations of a cantilever beam were considered. The reason why the extensional vibration problem is investigated here is that the condition seems to be severe due to the closeness of adjacent natural frequencies, the larger values of natural frequencies and the smaller number of nodal variables of the FEM in comparison with those of the flexural vibration problem. The numerical results show that the errors in response of the extensional vibration problem are large. However, if one follows the criterion proposed in this paper, accurate response is obtainable by the Newmark β method, which requires less computer time than either of the other methods mentioned above.     

Finite element analysis of structure-borne vibration from high-speed train

Finite element analyses were used to investigate the behavior of the building vibration induced by high-speed trains moving on bridges. The model includes the bridge, nearby building, soil and train. Finite element results indicate that trainload frequencies are more important than the natural frequencies of bridges and trains for building vibrations. If the building natural frequencies approach to the trainload frequencies, which equal an integer times the train speed over the compartment length, the resonance occurs and the building vibration will be large. Moreover, the vibration shape is similar to the mode shape of the resonance building frequency. To isolate the building vibration induced by moving trains, this paper investigates three common types of foundations, which include the extension of retaining walls, pile foundation and soil improvement around the building. Soil improvement around the building is the best way to reduce the building vibration both in horizontal and vertical directions.     

强非线性杜芬系统随机振动的等效化研究

以相对穿阈率为评估指标，探讨了强非线性杜芬系统稳态随机振动的等效化问题。结果表明，在不同位移阈值条件下，随着系统振动非线性的增强，立方恢复力等效模型预测精度逐步提高。该等效模型对强非线性杜芬系统具有良好的适用性。     

Optimum absorber parameters for various combinations of response and excitation parameters

In recent papers the author has shown that when determining optimum parameters for an absorber which minimizes the vibration response of a complex system, the latter may be treated as an equivalent single degree-of-freedom system if its natural frequencies are well separated. Emphasis was on minimizing the displacement response when the excitation was a harmonic force. In the present paper simple expressions for optimum absorber parameters are derived for undamped one degree-of-freedom main systems for harmonic and white noise random excitations with force and frame acceleration as input and minimization of various response parameters. These expressions can be used to obtain optimum parameters for absorbers attached to complex systems provided that optimization is with respect to an absolute, rather than a relative, quantity. The requirement that the natural frequencies should be well separated is investigated numerically for the different cases. The effect of damping in the main system on optimum absorber parameters is investigated also.     

单级弹簧主动隔振系统建模与分析

主动隔振系统具有隔振频带宽,能够在低频处取得较好隔振效果的优点,因而成为研究的热点。基于单级弹簧主动隔振系统建立数学模型,着重分析了系统位移反馈、速度反馈和加速度反馈3种反馈量对系统隔振性能的影响。结果表明:位移反馈使系统固有角频率提高,低频处隔振效果增强,而高频处隔振效果略有降低;速度反馈使系统在固有角频率附近的隔振效果有很好的改善,但是在其他频段的隔振效果基本没有变化;加速度反馈使得系统固有角频率减小,并且在高频段的隔振效果增加。这对主动隔振系统控制器的设计具有实际指导意义。