正弦行波激励下单层偏心框架结构扭转响应的解析解

文中针对单层偏心框架结构,利用正弦行波激励研究了质量偏心率和激励频率对偏心框架结构行波扭转响应的影响规律.建立了行波激励下单层偏心框架结构的振动方程,采用相对运动法求解给出了正弦行波激励下单层偏心框架结构楼板的质心平动位移和转角位移以及楼板扭矩和柱剪力的解析解.计算了一个钢筋混凝凝土单层偏心框架结构的峰值楼板扭矩和峰值...     

Comparisons between ambient and forced vibration experiments

The ambient and forced vibration techniques for testing full-scale structures are critically compared. Both methods, based on small level excitation, may be used to determine many mode shapes and frequencies of vibration and the corresponding damping values, with adequate accuracy for most purposes. The two techniques give mutually consistent results. The mode amplitudes determined by ambient and forced vibration tests show systematic departure for high modes and near the top levels of buildings tested. This phenomenon is attributed to the participation of all mode shapes and is a consequence of excitation by a concentrated force near the top of a building and at a frequency differing by only a few per cent from a natural frequency of vibrations. A new way of showing the effect of unwanted modes on the response near resonance of the mode being sought is developed. It is particularly useful for the analysis of steady, forced vibration tests of structures using eccentric mass vibration generators.     

Determination of scoured bridge natural frequencies with soil–structure interaction

This study developed a finite element method with the effect of soil–fluid–structure interaction to calculate bridge natural frequencies. The finite element model includes bridge girders, piers, foundations, soil, and water. The effective mass above the soil surface was then used to find the first natural frequency in each direction. A field experiment was performed to validate that the natural frequencies calculated using the proposed finite element method had acceptable accuracy. The calculated natural frequencies with the fluid–structure interaction effect are always smaller than those without this effect. However, the frequency change due to the fluid effect is not obvious, so using the soil–structure interaction model is accurate enough in the bridge natural frequency analysis. The trend of the frequency decreases with the increase of the scour depth, but the curve is not smooth because of non-uniform foundation sections and layered soils. However, when the scour depth is such that pile cap is exposed, the changes in natural frequency with the scour depth are more obvious, and this is useful for measurement of the depth using bridge natural frequencies.     

Vibration tests and analysis of a model arch dam

Vibration tests were conducted on a 1/24-scale model of the North Fork Dam, a double-curvature arch dam, to determine natural frequencies, mode shapes and hydrodynamic pressures. The mode shapes and natural frequencies were determined from tests using two vibrators mounted on the crest of the dam. Hydrodynamic pressures at the dam/reservoir interface were determined from tests in which the vibrator was attached to the downstream foundation of the dam. The hydrodynamic pressures calculated using Westergaard's theory and a theory for arch dams developed by Perumalswami and Kar accurately predicted the measured pressure at frequencies below the first mode frequency of the dam. The differences in the two theories were insignificant. The Structural Analysis Program (SAP), a linear three-dimensional (3-D) finite element code, was used to compute mode shapes and frequencies for the dam with its base fixed and with a foundation. Numerical solution schemes used in the finite element analysis consisted of a Ritz analysis and a subspace iteration method. Calculations were conducted for both full and empty reservoir conditions. The accuracy of the Ritz analysis improved considerably as more nodes in flexible regions of the dam were loaded. However, the lowest eigenvalues were computed using the subspace iteration method. For the full reservoir, the natural frequencies decreased by 20-30 per cent when the foundation was included in the finite element model. The difference was less when the reservoir was empty. The calculations using the subspace iteration scheme and including the foundation agreed closely with experimental mode shapes and corresponding natural frequencies.     

Experimental study of the semi‐active control of building structures using the shaking table

A magnetorheological (MR) damper has been manufactured and tested and a non‐linear model is discussed. The parameters for the model are identified from an identification set of experimental data; these parameters are then used to reconstruct the force vs. displacement and the force vs. velocity hysteresis cycles of the MR damper for the hysteretic model. Then experiments are conducted on a three‐storey frame model using impact excitation, which identifies dynamic parameters of the model equipped with and without the MR damper. Natural frequencies, damping ratios and mode shapes, as well as structural properties, such as the mass, stiffness and damping matrices, are obtained. A semi‐active control method such as a variable structure controller is studied. Based on the ‘reaching law’ method, a feedback controller is presented. In order to evaluate the efficiency of the control system and the effect of earthquake ground motions, both numerical analysis and shaking table tests of the model, with and without the MR damper, have been carried out under three different ground motions: El Centro 1940, Taft 1952, and Ninghe 1976 (Tangshan Earthquake in Chinese). It is found from both the numerical analysis and the shaking table tests that the maximum accelerations and relative displacements for all floors are significantly reduced with the MR damper. A reasonable agreement between the results obtained from the numerical analysis and those from the shaking table tests is also observed. On the other hand, tests conducted at different earthquake excitations and various excitation levels demonstrate the ability of the MR damper to surpass the performance of a comparable passive system in a variety of situations. Copyright © 2003 John Wiley & Sons, Ltd.     

Earthquake‐induced structural response output‐only identification by two different Operational Modal Analysis techniques

Output‐only system identification is developed here towards assessing current modal dynamic properties of buildings under seismic excitation. Earthquake‐induced structural response signals are adopted as input channels for two different Operational Modal Analysis (OMA) techniques, namely, a refined Frequency Domain Decomposition (rFDD) algorithm and an improved Data‐Driven Stochastic Subspace Identification (SSI‐DATA) procedure. Despite that short‐duration, non‐stationary, earthquake‐induced structural response signals shall not fulfil traditional OMA assumptions, these implementations are specifically formulated to operate with seismic responses and simultaneous heavy damping (in terms of identification challenge), for a consistent estimation of natural frequencies, mode shapes, and modal damping ratios. A linear ten‐storey frame structure under a set of ten selected earthquake base‐excitation instances is numerically simulated, by comparing the results from the two identification methods. According to this study, best up‐to‐date, reinterpreted OMA techniques may effectively be used to characterize the current dynamic behaviour of buildings, thus allowing for potential Structural Health Monitoring approaches in the Earthquake Engineering range.     

高温气冷堆核电厂建筑结构采用不同有限元模型的模态分析对比研究

建立有限元模型是核电厂建筑结构模态分析的重要前提。本文以某高温气冷堆核电厂建筑结构为原型，在分析方法相同的前提下，建立2种不同模型（Solid模型和Shell模型），并对这2种模型进行模态分析。重点分析、对比2种模型的自振频率和振型图，计算分析表明:Solid模型与Shell模型相比，计算得到的结构自振频率值较高，但两者的差异很小，前30阶自振频率相对误差小于3.4%；2种模型的计算结构振型基本一致。研究结果可为核电厂抗震性能分析和设计提供参考。     

A method for stochastic seismic response analysis of non-classically damped structures

A method to calculate the stationary random response of a non-classically damped structure is proposed that features clearly-defined physical meaning and simple expression. The method is developed in the frequency domain, The expression of the proposed method consists of three terms, i.e., modal velocity response, modal displacement response, and coupled (between modal velocity and modal displacement response), Numerical results from the parametric study and three example structures reveal that the modal velocity response term and the coupled term are important to structural response estimates only for a dynamic system with a tuned mass damper. In typical cases, the modal displacement term can provide response estimates with satisfactory accuracy by itself, so that the modal velocity term and coupled term may be ignored without loss of accuracy, This is used to simplify the response computation of non-classically damped structures. For the white noise excitation, three modal correlation coefficients in closed form are derived. To consider the modal velocity response term and the coupled term, a simplified approximation based on white noise excitation is developed for the case when the modal velocity response is important to the structural responses. Numerical results show that the approximate expression based on white noise excitation can provide structural responses with satisfactory accuracy~     

时域谱元法的质量特性模型及其构建方法

研究了构建时域谱单元质量特性模型的数学机制,针对时域切比雪夫谱单元和勒让德谱单元建立了一种直接导出谱单元一致质量矩阵和集中质量矩阵的统一数学方法,对比分析两种谱单元质量特性模型的特征,并从物理角度探讨了谱单元质量特性模型的合理性.研究表明,数值积分点与谱单元节点选取是否一致是决定时域谱单元形成一致质量模型或集中质量模型...     

Full-scale dynamic testing and analysis of a reservoir intake tower

Dynamic tests were conducted on a 50 m high intake tower at Wimbleball dam in the U.K. The results were compared against predictions from a corresponding numerical model. The aim of this work was to validate the assumption that the compressibility of the reservoir water is not a significant factor in the seismic analysis of intake towers. Three sets of tests were conducted on different occasions with different water levels in the reservoir. In the first two tests, modal characteristics of the tower were determined from the measured responses under ambient, hammer and human excitation. These results were used in planning the final set of tests where rotating eccentric mass exciters were used to vibrate the tower. Structural accelerations and hydrodynamic pressures were measured over the height of the tower for three important bending modes of vibration. The finite element method was used to develop a numerical model for Wimbleball tower. The tower was discretized with traditional solid elements and the reservoir with incompressible fluid elements. This model was analysed to predict the modal characteristics and harmonic responses of the tower and reservoir under the various conditions imposed during the dynamic tests. Theoretical predictions of the tower's accelerations and hydrodynamic pressures in the reservoir were compared against the test results. Excellent agreement was found for the natural frequencies and mode shapes while predictions of the harmonic responses were only fair. The observed responses of the tower and reservoir support the assumption that reservoir compressibility is not a significant factor in the seismic analysis of towers of this size.     

空间网格结构多维多点随机地震响应分析的高效算法

将林家浩教授提出的“虚拟激励法”进一步推广应用于空间网格结构多维多点非平稳随机地震响应分析,推导了多维虚拟激励随机振动分析方法的理论公式,给出了峰值响应估计方法,并讨论了多维地震动的随机模型及参数选取,通过编制的专用计算机程序分析了网壳结构的随机地震响应。本方法自动包含了参振振型间及各输人地震分量间的相关项,计算精确、快速,非常适合分析频率密集型空间网格结构的随机地震响应,是一种高效的随机振动分析算法。     

Parameter identification of torsionally coupled shear buildings from earthquake response records

This paper presents an efficient procedure to determine the natural frequencies, modal damping ratios and mode shapes for torsionally coupled shear buildings using earthquake response records. It is shown that the responses recorded at the top and first floor levels are sufficient to identify the dominant modal properties of a multistoried torsionally coupled shear building with uniform mass and constant eccentricity even when the input excitation is not known. The procedure applies eigenrealization algorithm to generate the state‐space model of the structure using the cross‐correlations among the measured responses. The dynamic characteristics of the structure are determined from the state‐space realization matrices. Since the mode shapes are obtained only at the instrumented floor (top and first floors) levels, a new mode shape interpolation technique has been proposed to estimate the mode shape coefficients at the remaining floor levels. The application of the procedure has been demonstrated through a numerical experiment on an eight‐storied torsionally coupled shear building subjected to earthquake base excitation. The results show that the proposed parameter identification technique is capable of identifying dominant modal parameters and responses even with significant noise contamination of the response records. Copyright © 2008 John Wiley & Sons, Ltd.     

测定堆石体密度的附加质量法理论分析研究

附加质量法是一种新兴的堆石体密度检测方法,它具有方便、无损等优点,近年来有较为广泛的应用,但该方法的应用效果会受到震源、雨水、双峰频谱等因素的影响.本文则考虑堆石体系统振动的阻尼因素,以及附加质量块与堆石体之间的非刚性连接,分别基于质弹阻模型以及双自由度-质弹阻模型对这些因素的影响进行了理论分析.结果表明,质弹阻模型可以解释主频随震源频率和雨水而变化的现象;而双自由度-质弹阻模型则可以解释主频随质量块偏移距和触地面积而变化的现象.在此基础上,本文对附加质量法的测试过程提出了几点改进建议.     

多源频率域地空系统三维电磁响应分析

地空电磁法已经成为深部资源勘探的重要地球物理方法,但对频率域地空系统的三维多源电磁响应特征研究较少.本文设计了多种激励源组合方式,采用非结构化有限元数值模拟方法,对三维地电模型的空中垂直磁场的响应特征进行了研究.首先推导了基于电场的双旋度公式及其变分形式,加入罚项以减少伪解的影响.接着把有限元稀疏矩阵方程转换为频率的函数,采用Krylov子空间投影方法,通过模型降阶算法降低稀疏矩阵的阶数,实现多频点的快速计算.建立了三维低阻体模型、高阻体模型以及两个相邻低阻体模型,分别采用单源、双源、三源和四源激励模式,从垂直磁场的总场、二次场响应和全域视电阻率等方面进行分析比较.结果表明:多源地空电磁法不仅可以增加总场的强度,而且可以改变异常体的二次电磁响应分布规律.各电偶源延长线呈正三角形分布的三源和矩形分布的四源激励模式在增强信号强度以及削弱异常体的边界效应方面具有一定的优势,是一种优化的多源激励方式.     

Seismic analysis of the fatih sultan mehmet (second Bosporus) suspension bridge

Theoretical dynamic characteristics of the Fatih Bridge in terms of natural frequencies and mode shapes of free vibration were obtained using a range of finite element models. Based on this free-vibration data, separate analyses of the asynchronous response of the bridge to earthquake excitation in three orthogonal axes with different speeds of wave propagation, and of stochastic response to vertical excitation were used to estimate levels of dynamic response due to seismic loading. Fatih is the third of three modern European long-span box-girder suspension bridges that have been investigated and the relationship of the different design features and the dynamic responses of this type of bridge is reviewed. The main conclusion is that where seismic response is an important consideration, the effects of asynchronous excitation can be significant and must be considered.     

A response spectrum method for random vibration analysis of mdf systems

A response spectrum method for stationary random vibration analysis of linear, multi-degree-of-freedom systems is developed. The method is based on the assumption that the input excitation is a wide-band, stationary Gaussian process and the response is stationary. However, it can also be used as a good approximation for the response to a transient stationary Gaussian input with a duration several times longer than the fundamental period of the system. Various response quantities, including the mean-squares of the response and its time derivative, the response mean frequency, and the cumulative distribution and the mean and variance of the peak response are obtained in terms of the ordinates of the mean response spectrum of the input excitation and the modal properties of the system. The formulation includes the cross-correlation between modal responses, which is shown to be significant for modes with closely spaced natural frequencies. The proposed procedure is demonstrated for an example structure that is subjected to an ensemble of earthquake-induced base excitations. Computed results based on the response spectrum method are in close agreement with simulation results obtained from time-history dynamic analysis. The significance of closely spaced modes and the error associated with a conventional method that neglects the modal correlations are also demonstrated.     

Dimensional analysis of the earthquake‐induced pounding between adjacent structures

In this paper the dynamic response of two and three pounding oscillators subjected to pulse‐type excitations is revisited with dimensional analysis. Using Buckingham's Π‐theorem the number of variables that govern the response of the system is reduced by three. When the response is presented in the dimensionless Π‐terms remarkable order emerges. It is shown that regardless of the acceleration level and duration of the pulse all response spectra become self‐similar and follow a single master curve. This is true despite the realization of finite duration contacts with increasing durations as the excitation level increases. All physically realizable contacts (impacts, continuous contacts, and detachments) are captured via a linear complementarity approach. The study confirms the existence of three spectral regions. The response of the most flexible among the two oscillators amplifies in the low range of the frequency spectrum (flexible structures); whereas, the response of the most stiff among the two oscillators amplifies at the upper range of the frequency spectrum (stiff structures). Most importantly, the study shows that pounding structures such as colliding buildings or interacting bridge segments may be most vulnerable for excitations with frequencies very different from their natural eigenfrequencies. Finally, by applying the concept of intermediate asymptotics, the study unveils that the dimensionless response of two pounding oscillators follows a scaling law with respect to the mass ratio, or in mathematical terms, that the response exhibits an incomplete self‐similarity or self‐similarity of the second kind with respect to the mass ratio. Copyright © 2008 John Wiley & Sons, Ltd.     

Sensitivity analysis of pounding between adjacent structures

This article deals with sensitivity of the response of pounding buildings with respect to structural and earthquake excitation parameters. A comprehensive sensitivity analysis is carried out by means of Monte Carlo simulations of adjacent single degree of freedom impacting oscillators. This sensitivity analysis, based on Sobol's method, computes sensitivity indexes which provide a consistent measure of the relative importance of parameters such as the dimensionless main excitation frequency, the mass and frequency ratios of the structures, and the coefficient of restitution. Moreover, the influence of nonlinear behavior of the impacting structures is also considered. The consequences of pounding on the structures themselves are analyzed in terms of maximum force and nonlinear demand amplification compared with the case without pounding. As for the influence of pounding on the floor response spectra, the quantity of interest is the maximum impact impulse. The overall conclusions of this analysis are that the frequency ratio is the most important parameter as far as the maximum force and nonlinear demand are concerned. Regarding the maximum impact impulse, the mass and frequency ratios are, in general, the most influential parameters, the mass ratio being predominant for low frequencies of the oscillator of interest.     

A RATE-DEPENDENT ISOTROPIC DAMAGE MODEL FOR THE SEISMIC ANALYSIS OF CONCRETE DAMS

In this paper a rate-dependent isotropic damage model developed for the numerical analysis of concrete dams subjected to seismic excitation is presented. The model is shown to incorporate two features essential for seismic analysis: stiffness degradation and stiffness recovery upon load reversals and strain-rate sensitivity. The issue of mesh objectivity is addressed using the concept of the ‘characteristic length’ of the fracture zone, to show that both the softening modulus and the fluidity parameter must depend on it to provide consistent results as the computational mesh is refined. Some aspects of the numerical implementation of the model are also treated, to show that the model can be easily incorporated in any standard non-linear finite element code. The application of the proposed model to the seismic analysis of a large gravity concrete dam shows that the structural response may vary significantly in terms of the development of damage. The inclusion of rate sensitivity is able to reproduce the experimental observation that the tensile peak strength of concrete can be increased up to 50 percent for the range of strain rates that appear in a structural safety analysis of a dam subjected to severe seismic actions.     

Coupled hydrodynamic response of concrete gravity dams using finite and infinite elements

This paper presents the application of the finite element method for analysing the two-dimensional response of reservoir-dam systems subjected to horizontal ground motion. The interaction between the dam and the reservoir as well as the compressibility of water has been taken into account. The complete system has been considered to be composed of two substructures, namely the reservoir and the dam. To take into account the large extent of the reservoir, it has been idealized using specially developed infinite elements coupled with standard finite elements while the dam is represented using finite elements alone. Structural damping of the dam and radiation damping in the fluid phase have been accounted for in the analysis. It is concluded that the effect of radiation damping is considerable at high frequencies of excitation. The coupled response of the system is significantly large at and near the fundamental natural frequency of the system in comparison to the uncoupled responses. The method is computationally quite economical, capable of taking into account the arbitrary geometry of the system and is recommended for practical application. Further applications and extensions of the approach to three dimensional analyses are possible.