Effects of False Floors on Vibration Serviceability of Building Floors. I: Modal Properties

This is the first of two papers that present the results of a comprehensive and systematic study into the effects of false flooring on the vibration serviceability of long-span concrete floors. In this paper, advanced modal testing technology was utilized to determine modal properties of long-span concrete floors (natural frequencies, modal damping ratios, and mode shapes) before and after the installation of false flooring. It was found that false flooring had the capacity to change modal properties significantly, particularly modal damping ratios, which had increases of up to 89%. Parametric studies using updated finite element models were also performed, which showed that the false flooring contributed also to floor stiffness. However, changes in modal properties were not consistent across all modes of vibration and it was not possible to predict easily which modes would be affected beneficially by the installation of false flooring.     

Dynamic Field Test, System Identification, and Modal Validation of an RC Minaret: Preprocessing and Postprocessing the Wind-Induced Ambient Vibration Data

The investigation of dynamic response for civil engineering structures largely depends on a detailed understanding of their dynamic characteristics, such as the natural frequencies, mode shapes, and modal damping ratios. Dynamic characteristics of structures may be obtained numerically and experimentally. The finite-element method is widely used to model structural systems numerically. However, there are some uncertainties in numerical models. Material properties and boundary conditions may not be modeled correctly. There may be some microcracks in the structures, and these cracks may directly affect the modeling parameters. Modal testing gives correct uncertain modeling parameters that lead to better predictions of the dynamic behavior of a target structure. Therefore, dynamic behavior of special structures, such as minarets, should be determined with ambient vibration tests. The vibration test results may be used to update numerical models and to detect microcracks distributed along the structure. The operational modal analysis procedure consists of several phases. First, vibration tests are carried out, spectral functions are produced from raw measured acceleration records, dynamic characteristics are determined by analyzing processed spectral functions, and finally analytical models are calibrated or updated depending on experimental analysis results. In this study, an ambient vibration test is conducted on the minaret under natural excitations, such as wind effects and human movement. The dynamic response of the minaret is measured through an array of four trixial force-balanced accelerometers deployed along the whole length of the minaret. The raw measured data obtained from ambient vibration testing are analyzed with the SignalCAD program, which was developed in MATLAB. The employed system identification procedures are based on output-only measurements because the forcing functions are not available during ambient vibration tests. The ModalCAD program developed in MATLAB is used for dynamic characteristic identification. A three-dimensional model of the minaret is constructed, and its modal analysis is performed to obtain analytical frequencies and mode shapes by using the ANSYS finite-element program. The obtained system identification results have very good agreement, thus providing a reliable set of identified modal properties (natural frequencies, damping ratios, and mode shapes) of the structure, which can be used to calibrate finite-element models and as a baseline in health monitoring studies.     

Structural Damage Detection from Modal Strain Energy Change

A structural damage detection method based on modal strain energy (MSE) change before and after damage is presented in this paper. The localization of damage based on MSE of each structural element is briefly presented, and the sensitivity of the MSE with respect to a damage is derived. The sensitivity is not based on any series expansion and is a function of the analytical mode shape changes and the stiffness matrix. Only incomplete measured mode shapes and analytical system matrices are required in this damage localization and quantification approach. Results from a numerical example and an experiment on a single-bay, two-story portal steel frame structure are investigated. The effects of measurement noise and truncated analytical mode shapes are discussed. Results indicate that the proposed approach is noise sensitive, but it can localize single and multiple damages. Damage quantification of two damages is successful with a maximum of 14% error under a 5% measurement noise.     

Challenges in the Application of Stochastic Modal Identification Methods to a Cable-Stayed Bridge

This paper presents an analysis of the data collected in the ambient vibration test of the International Guadiana cable-stayed Bridge, which links Portugal and Spain, based on different output-only identification techniques: peak-picking, frequency domain decomposition, covariance-driven stochastic subspace identification, and data-driven stochastic subspace identification. The purpose of the analysis is to compare the performance of the four techniques and evaluate their efficiency in dealing with specific challenges involved in the modal identification of the tested cable-stayed bridge, namely the existence of closely spaced modes, the perturbation produced by the local vibration of stay-cables, and the variation of modal damping coefficients with wind velocity. The identified natural frequencies and mode shapes are compared with the corresponding modal parameters provided by a previously developed numerical model. Additionally, the variability of some modal damping coefficients is related with the variation of the wind characteristics and associated with a component of aerodynamic damping.     

桥梁模态频率与运营环境作用的相关性

桥梁模态频率随运营环境作用的变化规律是结构健康监测的研究主题之一.根据东海大桥6 a监测数据的周期变化特性,识别了运营条件下主梁竖弯、侧弯、扭转基频变化的影响因素,采用偏相关系数和周期平均法对比了各因素的影响程度.研究发现,东海大桥的模态频率存在1 a、1周、1 d、12.42 h等变化周期,与结构温度、交通荷载、风荷载、海面高度等的变化周期相吻合;结构温度和交通荷载是引起该桥频率变化的最主要因素,它们在各周期上的相对影响大小不同;周期平均法可有效分离监测数据中的年、周、天周期成分,揭示不同运营环境作用与频率变化的相关性.研究结果有助于加深对桥梁运营期频率变化的理解,从而更准确地评估结构性能.      

Damage Localization and Finite-Element Model Updating Using Multiresponse NDT Data

New techniques for both finite-element model updating and damage localization are presented using multiresponse nondestructive test (NDT) data. A new protocol for combining multiple parameter estimation algorithms for model updating is presented along with an illustrative example. This approach allows for the simultaneous use of both static and modal NDT data to perform model updating at the element level. A new damage index based on multiresponse NDT data is presented for damage localization of structures. This index is based on static and modal strain energy changes in a structure as a result of damage. This method depicts changes in physical properties of each structural element compared to its initial state using NDT data. Deficient or potentially damaged structural elements are then selected as the unknown parameters to be updated by parameter estimation. Error function normalization, error function stacking, and multiresponse parameter estimation methods are proposed for using multiple data types for simultaneous stiffness and mass parameter estimation. Also, multiple sets of measurements with various sizes and missing data points can be utilized. This paper uses a laboratory grid model of a bridge deck built at the University of Cincinnati Infrastructure Institute and the corresponding NDT data for validation of the above damage localization and model updating methods. Multiresponse parameter estimation has been utilized to update the stiffness of bearing pads, and both the stiffness and mass of the connections, using static and dynamic NDT data. The static and modal responses of the updated grid model presented a closer match with the NDT data than the responses from the initial model.     

Implementation of Modal Control for Seismically Excited Structures using Magnetorheological Dampers

This paper proposes an implementation of modal control for seismically excited structures using magnetorheological (MR) dampers. Many control algorithms such as clipped-optimal control, decentralized bang-bang control, and the control algorithms based on Lyapunov stability theory have been adopted for semiactive systems including MR dampers. In spite of good features, some algorithms have drawbacks such as poor performance or difficulties in designing the weighting matrix of the controller. However, modal control reshapes the motion of a structure by merely controlling a few selected vibration modes. Hence a modal control scheme is more convenient to design the controller than other control algorithms. Although modal control has been investigated for several decades, its potential for semiactive control, especially for the MR damper, has not been exploited. Thus, in order to study the effectiveness for a MR damper system, a modal control scheme is implemented to seismically excited structures. A Kalman filter is included in a control scheme to estimate modal states from measurements by sensors. Three cases of the structural measurement are considered by a Kalman filter to verify the effect of each measurement; displacement, velocity, and acceleration, respectively. Moreover, a low-pass filter is applied to eliminate the spillover problem. In a numerical example, a six-story building model with the MR dampers on the bottom two floors is used to verify the proposed modal control scheme. The El Centro earthquake is used to excite the system, and the reduction in the drifts, accelerations, and relative displacements throughout the structure is examined. The performance of the proposed modal control scheme is compared with that of other control algorithms previously studied. The numerical results indicate that the motion of the structure is effectively suppressed by merely controlling a few lowest modes, although resulting responses varied greatly depending on the choice of measurements available and weightings.     

Structural Identification and Damage Detection from Noisy Modal Data

In this paper we present a simple, yet powerful, method for the identification of stiffness matrices of structural and mechanical systems from information about some of their measured natural frequencies and corresponding mode shapes of vibration. The method is computationally efficient and is shown to perform remarkably well in the presence of measurement errors in the mode shapes of vibration. It is applied to the identification of the stiffness distribution along the height of a simple vibrating structure. An example illustrating the method’s ability to detect structural damage that could be highly localized in a building structure is also given. The efficiency and accuracy with which the method yields estimates of the system’s stiffness from noisy modal measurement data makes it useful for rapid, on-line damage detection of structures.     

Enhanced Realization∕Identification of Physical Modes

Physical structures are often sufficiently complicated to preclude constructing an accurate mathematical model of the system dynamics from simple analysis using the laws of physics. Consequently, determination of an accurate model requires utilization of (generally noisy) output measurements from dynamic tests. In this paper, we present a robust method for constructing accurate, structural‐dynamic models from discrete time‐domain measurements. The method processes the measurements in order to determine the number of modes present, the damping and frequency of each mode, and the mode shape. The structure may be highly damped. Although the mode‐shape identification is more sensitive to measurement noise than the order, frequency, and damping identification, the method is considerably less sensitive to noise than other leading methods. Accurate detection of the modal parameters and mode shapes is demonstrated for modes with damping ratios exceeding 15%.     

Finite-Element Model Tuning of Global Modes of a Grandstand Structure Using Ambient Vibration Testing

This paper describes the experimental and analytical modal analysis of a full-scale cantilevered grandstand. A 3D finite-element model was successfully updated manually based on the global modes identified from ambient vibration measurements. The ambient vibration testing was effective in capturing the global modes of the large grandstand. A number of global vibration modes of the entire grandstand were reliably identified in the frequency range 0–3.1 Hz, in addition to modes in the same frequency range that engaged primarily the cantilever roof structure. Following a two-stage manual FE model updating process, the correlation between the experimental and analytical results showed good agreement, with physically meaningful updated parameters. It was clearly illustrated that both the roof system and the nonstructural elements contributed significantly to the stiffness and mass of the global modes. Useful and novel lessons are highlighted for efficient and reliable future finite-element modeling of global modes of similar grandstand structures.     

Damage Identification on the Tilff Bridge by Vibration Monitoring Using Optical Fiber Strain Sensors

Vibration testing is a well-known practice for damage identification of civil engineering structures. The real modal parameters of a structure can be determined from the data obtained by tests using system identification methods. By comparing these measured modal parameters with the modal parameters of a numerical model of the same structure in undamaged condition, damage detection, localization, and quantification is possible. This paper presents a real-life application of this technique to assess the structural health of the 50-year old bridge of Tilff, a prestressed three-cell box-girder concrete bridge with variable height. A complete ambient vibration survey comprising both vertical accelerations and axial strains has been carried out. The in situ use of optical fiber strain sensors for the direct measurement of modal strains is an original contribution of this work. It is a big step forward in the exploration of modal curvatures for damage identification because the accuracy in calculating the modal curvatures is substantially improved by directly measuring modal strains rather than deriving the modal curvatures from acceleration measurements. From the ambient vibrations, natural frequencies, damping factors, modal displacements and modal curvatures are extracted by the stochastic subspace identification method. These modal parameters are used for damage identification which is performed by the updating of a finite element model of the intact structure. The obtained results are then compared to the inspections performed on the bridge.     

Identification of Parametric Variations of Structures Based on Least Squares Estimation and Adaptive Tracking Technique

An important objective of health monitoring systems for civil infrastructures is to identify the state of the structure and to detect the damage when it occurs. System identification and damage detection, based on measured vibration data, have received considerable attention recently. Frequently, the damage of a structure may be reflected by a change of some parameters in structural elements, such as a degradation of the stiffness. Hence it is important to develop data analysis techniques that are capable of detecting the parametric changes of structural elements during a severe event, such as the earthquake. In this paper, we propose a new adaptive tracking technique, based on the least-squares estimation approach, to identify the time-varying structural parameters. In particular, the new technique proposed is capable of tracking the abrupt changes of system parameters from which the event and the severity of the structural damage may be detected. The proposed technique is applied to linear structures, including the Phase I ASCE structural health monitoring benchmark building, and a nonlinear elastic structure to demonstrate its performance and advantages. Simulation results demonstrate that the proposed technique is capable of tracking the parametric change of structures due to damages.     

Assignment of Geometrical and Physical Parameters for the Confinement of Vibrations in Flexible Structures

A strategy for confinement of flexural vibrations in flexible structures by proper selection of their geometrical and physical parameters is proposed. We first show that the problem of vibration confinement can be formulated as an inverse eigenvalue problem (IEP) where the mode shapes and/or natural frequencies are assumed and the geometrical and physical properties are unknown functions of the space variables. It is required that the assumed modes form a complete and independent set of spatial functions that satisfy the boundary conditions and guarantee confinement within the desired spatial subdomain(s) of the structure. Using simple spatial functions, such as polynomials and exponentials, we determined approximate solutions of the geometrical and physical parameters by applying the orthogonality of the mode shapes with respect to the stiffness and mass density. The order of the selected polynomials or exponentials depends on the number of modes retained in the discretized model. Numerical simulations are presented on a beam and then on a plate to examine convergence of the solution to the IEP. We show that convergence is attained with few assumed mode shapes. The approximated parameters are finally substituted into the forward eigenvalue problem to confirm confinement at the desired locations.     

Experimental and Numerical Study of Damaged Cantilever

The introduction of a crack in a steel structure will cause a local change in the stiffness and damping capacity. The change in stiffness will lead to a change of some of the natural frequencies of the structure and a discontinuity in the associated mode shapes. This paper contains a presentation of the results from experimental and numerical tests with hollow section cantilevers containing fatigue cracks. Two different finite-element (FE) models have been used to estimate the modal parameters numerically. The first FE model consists of beam elements. The second FE model consists of traditional rectangular shell elements and one rectangular shell element with a transverse, internal, open crack. The analytical results from the numerical models are compared with data obtained from experimental tests. The numerical models give good agreements with the experimental data. The beam model takes into account only the first mode of the crack evaluation. In the shell model all three modes of the crack growth are taken into account. Nevertheless, the results obtained for both models are satisfactory because the beam is subjected to bending. It can be concluded that it is sufficient to use crack models for calculating natural frequencies in bending, taking into account the first mode of the crack extension only.     

轴承外圈裂纹损伤的模态参数对比研究

轴承结构的表面损伤对其振动特性具有显著影响。以6307滚动轴承为研究对象,采用有限单元法分析了轴承外圈出现不同尺度的裂纹缺陷后,其固有特性的变化情况。其中,着重探讨了系统固有频率、位移模态以及应变模态参数对外圈损伤的敏感程度。     

Baseline Models for Bridge Performance Monitoring

A baseline model is essential for long-term structural performance monitoring and evaluation. This study represents the first effort in applying a neural network-based system identification technique to establish and update a baseline finite element model of an instrumented highway bridge based on the measurement of its traffic-induced vibrations. The neural network approach is particularly effective in dealing with measurement of a large-scale structure by a limited number of sensors. In this study, sensor systems were installed on two highway bridges and extensive vibration data were collected, based on which modal parameters including natural frequencies and mode shapes of the bridges were extracted using the frequency domain decomposition method as well as the conventional peak picking method. Then an innovative neural network is designed with the input being the modal parameters and the output being the structural parameters of a three-dimensional finite element model of the bridge such as the mass and stiffness elements. After extensively training and testing through finite element analysis, the neural network became capable to identify, with a high level of accuracy, the structural parameter values based on the measured modal parameters, and thus the finite element model of the bridge was successfully updated to a baseline. The neural network developed in this study can be used for future baseline updates as the bridge being monitored periodically over its lifetime.     

Modal Testing, Finite-Element Model Updating, and Dynamic Analysis of an Arch Type Steel Footbridge

This paper describes an arch type steel footbridge, its analytical modeling, modal testing, finite-element model updating, and dynamic analysis. A modern steel footbridge which has an arch type structural system and is located on the Karadeniz coast road in Trabzon, Turkey is selected as an application. An analytical modal analysis is performed on the developed three-dimensional finite-element model of footbridge to provide analytical frequencies and mode shapes. Field ambient vibration tests on the footbridge deck under natural excitation such as human walking and traffic loads are conducted. The output-only modal parameter identification is carried out by using peak picking of the average normalized power spectral densities in the frequency domain and stochastic subspace identification in the time domain, and dynamic characteristics such as natural frequencies, mode shapes, and damping ratios are determined. The finite-element model of the footbridge is updated to minimize the differences between analytically and experimentally estimated modal properties by changing some uncertain modeling parameters such as material properties. Dynamic analyses of the footbridge before and after finite-element model updating are performed using the 1992 Erzincan earthquake record. At the end of the study, maximum differences in the natural frequencies are reduced from 22 to only 5% and good agreement is found between analytical and experimental dynamic characteristics such as natural frequencies and mode shapes by model updating. Also, maximum displacements and principal stresses before and after model updating are compared with each other.     

工艺参数对热轧机振动固有特性影响分析

 某钢厂热连轧生产线F2机架在轧制薄规格产品时发生了强烈的振动现象。为了更好地识别轧机振动的类型,抑制轧机振动,需对轧机系统的固有特性进行全面分析。考虑水平、扭转和垂直系统的振动,并考虑带钢和轧机系统的耦合作用建立热轧机11自由度振动模型,分析轧机系统在无带钢下的固有特性,并分析各阶模态对惯性参数和弹性参数的灵敏度。同时分析带钢和轧机耦合作用下前后张力、入口厚度、出口厚度、摩擦因数、变形抗力等工艺参数对轧机系统固有特性的影响。研究结果表明,带钢和轧机相耦合成一种变结构系统,系统固有特性随着工艺参数的变化而变化,工艺参数主要通过改变第4阶模态和第10阶模态来影响系统固有特性。不同的工艺参数对轧机系统固有特性的影响程度不同,入口厚度影响最为显著,可以通过改变工艺参数来改善系统固有频率。可以为轧机振动类型的识别和振动的抑制提供指导。     

Free Vibrations of Cylindrical Storage Tanks: Finite-Element Analysis and Experiments

This note summarizes a theoretical and experimental study undertaken to provide a deeper understanding of the effect of different parameters on the coupled modal characteristics of circular cylindrical tanks. First, the most common case of clamped-free tanks resting on rigid foundations is investigated by using finite-element (FE) modeling and holographic experiments. A good agreement between experimental and numerical results is a basis to draw a number of conclusions. For both tank geometries investigated, the frequencies for modes of circumferential parameter n = 1 (the “beam” modes) are found to be reduced most significantly by the presence of liquid. Very significant dependence of the radial shell mode shapes on the filling ratio is confirmed both by the FE and experimental results. In addition, nonclassical vibration patterns for radial shell modes were extracted numerically and recorded experimentally. Special attention is paid to the pairs of shell modes. Second, the effects of a flexible foundation and axial compression are investigated using holographic interferometry. The modal responses of this shell–liquid system are found to be different from those of the existing theoretical models.