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.     

Natural frequencies of arch dam reservoir system—by a mapping finite element method

A simple mapping finite element method is used to calculate the coupled natural frequencies and mode shapes of realistic arch dam reservoir systems in which the dam is circular cylindrical with non-uniform cross-section. This method, in which both the dam and the reservoir domains are mapped into geometrically simpler shapes using cylindrical-polar transformations, is found to give accurate results, achieved simply and economically. Results of analysis show that hydrodynamic interaction has a substantial effect on the coupled natural frequencies and mode shapes; also that the effect of water compressibility in the type of dams considered can be ignored without significant loss of accuracy. A simple method is also presented for predicting the water compressibility effect before undertaking detailed response analysis.     

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.     

Ambient vibration measurements on a cable-stayed bridge

An extensive programme of full-scale ambient vibration tests has been conducted to measure the dynamic response of a 542 m (centre span of 274 m) cable-stayed bridge—the Quincy Bayview Bridge in Illinois. A microcomputer-based system was used to collect and analyse the ambient vibration data. A total of 25 modal frequencies and associated mode shapes were identified for the deck structure within the frequency range of 0–2 Hz. Also, estimations were made for damping ratios. The experimental data clearly indicated the occurrence of many closely spaced modal frequencies and spatially complicated mode shapes. Most tower modes were found to be associated with the deck modes, implying a considerable interaction between the deck and tower structure. No detectable levels of motion were evident at the foundation support of the pier. The results of the ambient vibration survey were compared to modal frequencies and mode shapes computed using a three-dimensional finite element model of the bridge. For most modes, the analytic and experimental modal frequencies and mode shapes compare quite well, especially for the vertical modes. Based on the findings of this study, a linear elastic finite element model appears to be capable of capturing much of the complex dynamic behaviour of the bridge with very good accuracy, when compared to the low-level dynamic responses induced by ambient wind and traffic excitations.     

DYNAMIC INVESTIGATION OF A REPAIRED CABLE-STAYED BRIDGE

The theoretical and experimental investigation of a cable-stayed bridge after major repair is described in this paper. Strengthening mainly involved the suspension system (originally with prestressed concrete stays) which was retrofitted by means of external tendons. Full-scale tests were conducted to measure the dynamic response of the repaired system; the experimental program included both traffic-induced and free vibration measurements. A total of 16 vertical frequencies and mode shapes were identified in the frequency range of 0–10 Hz. In the theoretical study, vibration modes involving deck, towers and cables were determined by using finite element models which accounted for the strengthening effects. Two- and three-dimensional models were used so that the importance of three-dimensional modes was estimated as well. The experimental results were compared to natural frequencies and mode shapes computed using theoretical models. For most modes the measured and predicted modal parameters compare well, especially for the vertical modes involving in-phase motion of the stays. © 1997 by John Wiley & Sons, Ltd.     

Modal analysis of a DAM–Foundation system based on an FE–BE method in the time domain

A modal analysis procedure based on an FE–BE method in the time domain is first formulated and then applied to a dam–foundation system. In the application, horizontal and vertical impulsive responses are calculated for the system having six different impedance ratios. Modal characteristics such as natural frequencies, damping ratios and mode shapes are evaluated from the Fourier spectra of the responses. The proposed procedure allows analysis of not only the underdamped but also the overdamped modes. According to the analysis, the radiation damping pertinent to the vertical vibration is half of that pertinent to the horizontal vibration and the interaction effect on the modes is not negligibly small when the impedance ratio exceeds 0·3.     

An experimental investigation of water level effects on the dynamic behaviour of a large arch dam

The need for full‐scale dynamic tests, which are recognized as the most reliable method to evaluate a structure's vibration properties, is increasing as new analysis techniques are developed that take into account the complex interaction phenomenons that occur in dam–reservoir–foundation systems. They are extremely useful to obtain reliable data for the calibration of newly developed numerical methods. The Earthquake Engineering and Structural Dynamics Research Center (CRGP) at the University of Sherbrooke has been developing and applying dynamic testing methods for large structures in the past 10 years. This paper presents the experimental evaluation of the effects of the varying water level on the dynamic response of the 180 m Emosson arch dam in Switzerland. Repeated forced‐vibration tests were carried out on the dam during four different periods of the reservoir's filling cycle during a one‐year span. Acceleration and hydrodynamic pressure frequency responses were obtained at several locations while the dam was subjected to horizontal harmonic loading. The variation of the resonant frequencies as a function of the reservoir level is investigated. A summary of the ongoing numerical correlation phase with a three‐dimensional finite element model for the dam–reservoir–foundation system is also presented. Copyright © 2001 John Wiley & Sons, Ltd.     

大型火力发电厂框排架混合结构主厂房动力特性试验与分析

选取1 000MW大型火力发电厂新型混合结构主厂房体系的三跨三榀进行缩尺比为1/7的空间模型试验研究.采用锤击法测试模型结构的动力特性,得到其自振频率和振型,并根据相似关系换算到原型结构.使用SAP2000软件建立混合结构主厂房模型和原型结构的有限元模型,进行模态分析,得到模型和原型结构的频率和振型,并与试验结果进行对比分析.可为大型火力发电厂新型混合结构主厂房体系的抗震性能研究提供依据.     

Identification of Fei-Tsui arch dam from both ambient and seismic response data

This purpose of this paper is to study the dynamic characteristics of the Fei-Tsui arch dam using the seismic response data and the ambient vibration data. For the identification of dam properties from seismic response data, the multiple inputs from the abutment of the dam to represent the nonuniform excitations of seismic input motion are considered, and the ARX model is applied using the discrete-time linear filtering approach with least-squares approximation to identify the dynamic characteristics of the dam. The system modal dampings, natural frequencies and frequency response functions are identified. A comparison of the identified modal parameters is made among different seismic events. Post-earthquake safety evaluation of the dam can be made based on the identified model. Finally, the ambient vibration test of the dam is performed to identify the mode shapes along the dam crest.     

Dynamic characteristics of a base isolated building from ambient vibration measurements and low level earthquake shaking

Ambient vibration tests were conducted on a base-isolated apartment building in Takamatsu, Japan, to determine the mode shapes and the associated natural frequencies and damping ratios at very low levels of excitation. The latest developments in signal analysis for modal decomposition are used to analyze the ambient response data. A finite element model of the building and isolators was calibrated and refined using the experimental results from the ambient vibration tests. This model was then used to simulate the recorded response of the building under excitation from a small earthquake. The finite element model, calibrated by ambient vibration data and the low level of earthquake shaking, provides the starting point for modelling the non-linear response of the building when subjected to strong shaking.     

Full-scale experimental modal analysis of an arch dam: The first experience in Iran

Forced vibration field tests and finite-element studies were conducted on the Shahid Rajaee concrete arch dam in Northern Iran to determine the dynamic properties of the dam–reservoir–foundation system. The first forced vibration tests on the dam were performed with two different types of exciter units, with a limited maximum force, bolted on the dam crest for alternative in-phase and out-of-phase sequencing. Because of an insufficient number of recording sensors, two arrangements of sensors were used to cover sufficient points on the dam crest and one gallery during tests. Two kinds of vibration tests, on–off and frequency sweeping, were carried out on the dam. The primary natural frequencies of the coupled system for both symmetric and anti-symmetric vibration modes were approximated during on–off tests in two types of sequencing of exciters, in phase and out-of-phase, with a maximum frequency of 14 Hz. The principal forced vibration tests were performed at precise resonant frequencies based on the results of the on–off tests in which sweeping around the approximated frequencies at 0.1 Hz increments was performed. Baseline correction and suitable bandpass filtering were applied to the test records and then signal processing was carried out to compute the auto power, cross power and coherence spectra. Nine middle modes of vibration of the coupled system and corresponding damping ratios were estimated. The empirical results are compared against the results from calibrated finite-element modeling of the system using former ambient vibration tests, considering the dam–reservoir–foundation interaction effects. Good agreement is obtained between experimental and numerical results for eight middle modes of the dam–reservoir–foundation system.     

Ambient vibration studies for system identification of tall buildings

The performance of a building under wind and seismic loads depends on stiffness and mass distribution, and may be estimated using finite element codes. Experience has, however, shown that such finite element models often fail to predict accurately the fundamental natural frequencies. Usually the frequencies will be underestimated, that is the building will turn out to be stiffer than anticipated, meaning the design would usually be conservative. On the other hand, effects like torsional eccentricity and foundation compliance may not be correctly modelled, which could be less desirable. A full understanding of linear performance under lateral loads can be obtained through experimental evaluation of the vibration modes. Traditionally only a limited range of modal analysis procedures and software has been applied to civil applications and the ‘special case’ where no input forces can be measured has been the usual situation for large civil structures. Recent developments in system identification, which is the set of procedures to build mathematical models of the dynamic structural systems based on measured data, have added significantly to the potential of ambient vibration or ‘output only’ testing. The aim of the research reported here has been to apply and evaluate the procedures on typical buildings. The procedures are briefly explained and two experimental programmes are then described; a long‐term tremor monitoring exercise on a 280m office tower and an ambient vibration survey of a smaller office block. The different forms of response data are examined to study the performance of the analysis procedures and expose benefits and limitations in their use. There is a growing interest in output‐only modal analysis procedures in civil engineering. The experience reported in this paper has shown that quick and reliable estimation of mode shapes and frequencies can be obtained, even with small amounts of data. Judgement of modal participation and damping ratios requires more detailed study yet the results are at least as convincing as existing and relatively limited frequency domain methods. Copyright © 2002 John Wiley & Sons, Ltd.     

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。     

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.     

An experimental assessment of the added mass of some plates vibrating in water

A reservoir of water is contained by a concrete valley block, a ferrocement wall and a steel plate. Both wall and plate contain an array of pressure transducer sockets (Figures 1 and 2). Using the M.A.M.A.¹ equipment pure modes of vibration are excited. Frequency and mode shape are measured with the reservoir empty. When the reservoir is full hydrodynamic pressure is also measured. These hydrodynamic pressures are compared with Chopra's² two-dimensional, series solution, which includes compressibility of water, and with two- and three-dimensional finite element solutions of Laplace's equation, which do not include compressibility. Chopra's solution is unsatisfactory for modes which contain a vertical node line. The best agreement between experimental and theoretical hydrodynamic pressure is obtained when the latter is obtained from three-dimensional solutions of Laplace's equations, indicating that compressibility does not play a significant rǒle. This conclusion is supported by agreement between experimental frequencies (reservoir full) and those calculated using added mass obtained from the Laplace solution. Similar conclusions were reached from tests on a floating steel plate, suspended in the surface of the reservoir by a soft spring. Here, dynamic pressure measurements were not made, reliance being placed on agreement between calculated and measured frequencies and mode shapes.     

大跨度预应力混凝土连续刚构桥的动力特性分析

介绍了福建泉州后渚大桥——大跨度预应力混凝土连续刚构桥的现场环境振动实验．并利用频域中的单模态识别法(SDOFI)、峰值法(PP)和时域中的随机子空间识别法(SSI)分别进行桥梁动力特性识别。利用ANSYS建立了全桥三维有限元模型并进行了理论模态分析,基于参数分析和环境振动测试结果对有限元模型进行了标定,建立了该桥的基准有限元模型,该模型可服务于桥梁长期健康监测与状态评估。     

Ambient vibration testing of two masonry monuments in Cyprus

The current study investigates the dynamic characteristics of two historical monuments in Cyprus, the St. Nicholas Cathedral in Famagusta and the St. Mamas Church in Morphou. The testing was performed using the ambient vibration survey approach and the output-only method for both structures, to obtain the frequencies and mode shapes of the lower modes. These results contributed in the updating of the finite element models and in the planning of the monitoring strategy that was implemented for these structures, as well as the study for their seismic vulnerability. Comparisons are made between the measured and finite element model dynamic characteristics, and conclusions are drawn.     

Earthquake analysis of gravity dams including hydrodynamic interaction

A general procedure for analysis of the response of gravity dams, including hydrodynamic interaction and compressibility of water, to the transverse horizontal and vertical components of earthquake ground motion is presented. The problem is reduced to one in two dimensions considering the transverse vibration of a monolith of a dam, and the material behaviour is assumed to be linearly elastic The complete system is considered as composed of two substructures—the dam, represented as a finite element system, and the reservoir, as a continuum of infinite length in the upstream direction governed by the wave equation. The structural displacements of the dam (including effects of water) are expressed as a linear combination of the modes of vibration of the dam with the reservoir empty. The effectiveness of this analytical formulation lies in its being able to produce excellent results by considering only the first few modes. The complex frequency response for the modal displacements are obtained first. The responses to arbitrary ground motion are subsequently obtained with the aid of the Fast Fourier Transform algorithm An example analysis is presented to illustrate results obtained from this method. It is concluded that the method is very effective and efficient and is capable of producing results to any desired degree of accuracy by including the necessary number of modes of vibration of the dam.     

Automatic modal parameter identification of high arch dams: feasibility verification

Modal parameters, including fundamental frequencies, damping ratios, and mode shapes, could be used to evaluate the health condition of structures. Automatic modal parameter identification, which plays an essential role in realtime structural health monitoring, has become a popular topic in recent years. In this study, an automatic modal parameter identification procedure for high arch dams is proposed. The proposed procedure is implemented by combining the density-based spatial clustering of applications with noise (DBSCAN) algorithm and the stochastic subspace identification (SSI). The 210-m-high Dagangshan Dam is investigated as an example to verify the feasibility of the procedure. The results show that the DBSCAN algorithm is robust enough to interpret the stabilization diagram from SSI and may avoid outline modes. This leads to the proposed procedure obtaining a better performance than the partitioned clustering and hierarchical clustering algorithms. In addition, the errors of the identified frequencies of the arch dam are within 4%, and the identified mode shapes are in agreement with those obtained from the finite element model, which implies that the proposed procedure is accurate enough to use in modal parameter identification. The procedure is feasible for online modal parameter identification and modal tracking of arch dams.

     

CFRP composite retrofitting effect on the dynamic characteristics of arch dams

The purpose of this study is to investigate the effect of retrofitting dynamic characteristics of a damaged laboratory arch dam model, subsequently repaired with high-strength structural mortar and strengthened with composite carbon fiber reinforced polymer. This study constructed in laboratory conditions is a prototype arch dam–reservoir–foundation model. Five test cases of ambient vibration on the arch dam model illustrate the changes in dynamic characteristics: natural frequency, mode shape, and damping ratio, before and after retrofitting. The ambient vibration tests collected data from the dam body during vibrations by natural excitations which provided small impacts and response signals from sensitivity accelerometers placed at crest points. Enhanced Frequency Domain Decomposition Method in the frequency domain extracts the experimental dynamic characteristics. At the end of the study, experimentally identified dynamic characteristics obtained from all test cases have been compared with each other. Apparently, after the retrofitting, the natural frequencies of the dam body increased considerably, demonstrating that the retrofitting, including repairing and strengthening is very effective on the flashback of initial dynamic characteristics.