Cable Modal Parameter Identification. II: Modal Tests

The cable dynamic stiffness describes the load–deformation behavior that reflects the cable intrinsic dynamic characteristics. It is defined as a ratio of response to excitation and represents a very similar frequency response property to the frequency response function (FRF). Therefore, by fitting both analytical cable dynamic stiffness and measured frequency response function, the modal parameters of cables can be identified. Based on the simplified cable dynamic stiffness proposed in the first part of the two-part paper, this paper presents a cable dynamic stiffness based procedure to identify the cable modal parameters (natural frequencies and damping ratios) by modal tests. To carry out the curve fitting, a nonlinear least-squares approach is used. A numerical simulation example is first introduced to illustrate the feasibility of the proposed method. Further, a series of cable modal tests are conducted in the laboratory with different cable tensions and the frequency response functions are measured accordingly. A number of issues related to the cable modal tests have been discussed, such as accelerometer arrangement and excitation placement, frequency resolution, windowing, and averaging. It is demonstrated that the cable modal parameters can be effectively identified by using the proposed method through the cable modal tests.     

Damping of Cables by a Transverse Force

A general asymptotic format is presented for the effect on the modal vibrations of a transverse damper close to the end of a cable. Complete locking of the damper leads to an increase of the natural frequencies, and it is demonstrated that the maximum attainable damping is a certain fraction of the relative frequency increase, depending on the type of damping device. The asymptotic format only includes a real and a complex nondimensional parameter, and it is demonstrated how these parameters can be determined from the frequency increase by locking and from an energy balance on the undamped natural vibration modes. It is shown how the asymptotic format can incorporate sag of the cable, and specific results are presented for viscous damping, the effect of stiffness and mass, fractional viscous damping, and a nonlinear viscous damper. The relation of the stiffness component to active and semiactive damping is discussed.     

Vibration Control of Stay Cables of the Shandong Binzhou Yellow River Highway Bridge Using Magnetorheological Fluid Dampers

The Shandong Binzhou Yellow River Highway Bridge is a three-tower, cable-stayed bridge in Shandong Province, China. Because the stay cables are prone to vibration, 40 magnetorheological (MR) fluid dampers were attached to the 20 longest cables of this bridge to suppress possible vibration. An innovative control algorithm for active and semiactive control of mass-distributed dynamic systems, e.g., stay cables, was proposed. The frequencies and modal damping ratios of the unimpeded tested cable were identified through an ambient vibration test and free vibration tests, respectively. Subsequently, a series of field tests were carried out to investigate the control efficacy of the free cable vibrations achieved by semiactive MR dampers, “Passive-off” MR dampers and “Passive-on” MR dampers. The first three modal damping ratios of the cable incorporated with the MR dampers were also identified from the in situ experiments. The field experiment results indicated that the semiactive MR dampers can provide significantly greater supplemental damping for the cable than either the Passive-off or the Passive-on MR dampers because of the pseudonegative stiffness generated by the semiactive MR dampers.     

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.     

Design of Mechanical Viscous Dampers for Stay Cables

External dampers have been utilized in a number of cable-stayed bridges to suppress transverse cable vibrations. However, simple and accurate damper design recommendations that concurrently consider all important cable parameters are lacking. Previous efforts have been based on the idealization of cables as taut strings. In this paper, the governing differential equation for vibration of cables containing a viscous damper was first converted to a complex eigenvalue problem containing nondimensional cable parameters. Then, a parametric study was conducted involving repeated solutions of the eigenvalue problem for a wide range of nondimensional parameters. Based on the results of the parametric study, the effects of dampers on first mode vibration frequencies and first mode cable damping ratios were presented in nondimensional format. It is shown that for the range of parameters involved in most stay cables, the influence of cable sag is insignificant, whereas the cable bending stiffness can have a significant influence on the resulting cable damping ratios. Simplified nondimensional relationships are proposed for calculating damper-induced changes in the first mode cable damping ratios. Results of laboratory tests on a scaled model cable are compared with the estimated values using the formulation presented. Finally, example problems are presented for comparison with other relationships, and for the design of mechanical viscous dampers for suppression of cable vibrations including rain-wind induced vibrations.     

Research on mode localization of reticulated shell structures

Reticulated shell structures (RSSs) are characterized as cyclically periodic structures. Mistuning of RSSs will induce structural mode localization. Mode localization has the following two features: some modal vectors of the structure change remarkably when the values of its physical parameters (mass or stiffness) have a slight change; and the vibration of some modes is mainly restricted in some local areas of the structure. In this paper, two quantitative assessment indexes are introduced that correspond to these two features. The first feature is studied through a numerical example of a RSS, and its induced causes are analyzed by using the perturbation theory. The analysis showed that internally, mode localization is closely related to structural frequencies and externally, slight changes of the physical parameters of the structure cause instability to the RSS. A scaled model experiment to examine mode localization was carried out on a Kiewit single-layer spherical RSS,and both features of mode localization are studied. Eight tests that measured the changes of the physical parameters were carried out in the experiment. Since many modes make their contribution in structural dynamic response, six strong vibration modes were tested at random in the experimental analysis. The change and localization of the six modes are analyzed for each test. The results show that slight changes to the physical parameters are likely to induce remarkable changes and localization of some modal vectors in the RSSs.     

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.     

Finite-Element Analysis and Vibration Testing of a Two-Span Masonry Arch Bridge

This paper presents the analytical modeling, modal testing, and finite-element model updating for a two-span masonry arch bridge. An Ottoman masonry arch bridge built in the 19th century and located at Camlihemsin, Rize, Turkey is selected as an example. Analytical modal analysis is performed on the developed 3D finite-element model of the bridge to obtain dynamic characteristics. The ambient vibration tests are conducted under natural excitation such as human walking. The operational modal analysis is carried out using peak picking method in the frequency domain and stochastic subspace identification method in the time domain, and dynamic characteristics (natural frequencies, mode shapes, and damping ratios) are determined experimentally. Finite-element model of the bridge is updated to minimize the differences between analytically and experimentally estimated dynamic characteristics by changing boundary conditions. At the end of the study, maximum differences in the natural frequencies are reduced on average from 18 to 7% and a good agreement is found between analytical and experimental dynamic characteristics after finite-element model updating.     

Wavelet-Galerkin Method for Free Vibrations of Elastic Cable

The wavelet-Galerkin method is applied to study the free vibration of a horizontally suspended catenary cable. Antiderivatives of the Daubechies compactly supported wavelets have been used with multilevel representations. Comparison between wavelet and Fourier methods is presented for natural frequencies, mode shapes, and dynamic tension of the cable. Both methods showed that they are converging fast in obtaining the natural frequencies and mode shapes. However, as the dynamic tension is obtained, the Fourier solution shows many oscillations and the existence of the Gibbs phenomenon at the cable supports, whereas, these oscillations do not appear in the wavelet solutions. Comparison is also made with the linear theory of cable vibration. Due to the inclusion of the inertia term of the longitudinal component in our solution, new modes have been found. Those modes are reverting but swapping modes in which the longitudinal displacement component is larger than the transverse displacement component.     

Identification of Natural Frequencies and Dampings of In Situ Tall Buildings Using Ambient Wind Vibration Data

An accurate prediction for the response of tall buildings subject to strong wind gusts or earthquakes requires the information of in situ dynamic properties of the building, including natural frequencies and damping ratios. This paper presents a method of identifying natural frequencies and damping ratios of in situ tall buildings using ambient wind vibration data. Our approach is based on the empirical mode decomposition (EMD) method, the random decrement technique (RDT), and the Hilbert–Huang transform. Our method requires only one acceleration sensor. The noisy measurement of the building acceleration is first processed through the EMD method to determine the response of each mode. Then, RDT is used to obtain the free vibration modal response. Finally, the Hilbert transform is applied to each free vibration modal response to identify natural frequencies and damping ratios of in situ tall buildings. The application of the proposed methodology is demonstrated in detail using simulated response data of a 76-story benchmark building polluted by noise. Both the along-wind and across-wind vibration measurements have been illustrated. Simulation results demonstrate that the accuracy of the proposed method in identifying natural frequencies and damping ratios is remarkable. The methodology proposed herein provides a new and effective tool for the parametric identification of in situ tall buildings.     

Roebling Suspension Bridge. I: Finite-Element Model and Free Vibration Response

This first part of a two-part paper on the John A. Roebling suspension bridge (1867) across the Ohio River is an analytical investigation, whereas Part II focuses on the experimental investigation of the bridge. The primary objectives of the investigation are to assess the bridge’s load-carrying capacity and compare this capacity with current standards of safety. Dynamics-based evaluation is used, which requires combining finite-element bridge analysis and field testing. A 3D finite-element model is developed to represent the bridge and to establish its deformed equilibrium configuration due to dead loading. Starting from the deformed configuration, a modal analysis is performed to provide the frequencies and mode shapes. Transverse vibration modes dominate the low-frequency response. It is demonstrated that cable stress stiffening plays an important role in both the static and dynamic responses of the bridge. Inclusion of large deflection behavior is shown to have a limited effect on the member forces and bridge deflections. Parametric studies are performed using the developed finite-element model. The outcome of the investigation is to provide structural information that will assist in the preservation of the historic John A. Roebling suspension bridge, though the developed methodology could be applied to a wide range of cable-supported bridges.     

Stiffness Evaluation and Damage Detection of Ceramic Candle Filters

This paper presents a nondestructive evaluation method to identify the structural stiffness of ceramic candle filters. A ceramic candle filter is a hollow cylindrical structure made of a porous ceramic material used in advanced, coal-fired power generation systems. The candle filters need to sustain an extreme thermal and chemical environment over a great period of time to protect the gas turbine components from exposure to particulate matter. A total of 92 new candle filters and 29 used candle filters have been tested nondestructively using a dynamic characterization technique. All filters were subjected to an excitation force, and the response was picked up by an accelerometer in a free-free boundary condition. The frequency response function and vibration mode shapes of each filter were evaluated. Beam vibration equations and finite-element models were built to calculate the filter's dynamic response. Results indicate that the vibration signatures can be used as an index to quantify the structural properties of ceramic candle filters. The results also show estimations of the overall bending stiffness values for four different types of candle filters. The used filters show a trend of stiffness degradation, which was related to the filter's exposure time. Damage detection procedures using modal strain energy and finite-element simulation were studied for detection of a localized damage in the candle filter. The location and the size of the damaged section can be identified using the measured model strain energy.     

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.     

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.     

Vibration Testing at Meazza Stadium: Reliability of Operational Modal Analysis to Health Monitoring Purposes

In the last years an increasing interest has been devoted to all the topics related to the security and safety of people. Particular attention has been paid to health monitoring of large civil structures hosting many people, such as high-rise buildings and stadiums. Some extraordinary events, such as the Millennium Bridge oscillations in London, excited by pedestrians, or the Bruce Springsteen concert at the Ullevi Stadium in which coordinated jumps from the crowd caused serious damage to the structure, and drew attention toward a deeper and more careful study of all those problems related to the dynamic behavior of civil structures and their interaction with crowds. Research on these topics is also aimed, among others, at developing techniques allowing for a continuous monitoring of the structure, starting from a set of measurements that can be performed continuously, 24?h a day, without the need to stop the structure's functionality. The vast scientific literature confirms the possibility of relating structural health to the evolution of modal parameters, often reaching the aim of localizing any eventual damage, a task otherwise impossible with different techniques. This paper shows part of a long lasting project involving Politecnico di Milano in the setting up of a permanent health monitoring system at the G. Meazza Stadium in Milan. The aim of this project was the evaluation of the actual health state of the structures constituting the stands of the stadium and the deployment of a permanent monitoring system to record the vibration levels reached in all substructures during each event. Evaluation of the actual structure condition was performed by the use of ambient vibration, which was also checked against traditional experimental modal analysis, performed by using an inertial force given by a hydraulic actuator and a detailed measurement mesh. This offered the chance to exploit all possible information concerning natural frequencies, modal shapes, and damping factors. This task is extremely time consuming and expensive, therefore, it cannot be repeated very often. The possibility of using the data coming from the permanent monitoring system, which is about to be installed, is then an attractive perspective to improve structural diagnosis. It is expected that using operational modal analysis techniques will mean knowledge of the excitation applied to the structure will not be required. The parameter estimation obtained by this technique is usually affected by a spread, given both by the uncertainty of the adopted identification techniques and the influence of external parameters, such as crowd loading or temperature. As damage identification is related to changes of the modal parameters, the evaluation of their normal spread is fundamental to fix a threshold in order to identify possible worrysome situations. This paper deals with the identification of the spread in the modal parameter estimation of one of the grandstands of the so-called 3° ring of the G. Meazza Stadium in Milan, performed analyzing data collected over more than one year. Vibration data have been recorded during different events, such as soccer matches and concerts. The considered data came from a set of sensors similar to that which is to be installed for the permanent monitoring system, to check about the possibility to use the monitoring system as a diagnostic tool for the structure. A study was also carried out to identify critical aspects in the sensors’ choice and their placement, in order to provide useful information about the design of the permanent monitoring system. The presented results can be used to determine confidence intervals out of which changes in the modal properties can be considered anomalous, and so, worthy of being deeply investigated to assess structural integrity.     

Combined Damping Effect of Two Dampers on a Stay Cable

The combined effect of two dampers, either on the same end or opposite ends of a stay cable, is analytically studied in this paper. By considering small distances of the dampers from the anchorages, an asymptotic formula for the modal damping ratio of the cable is derived from which the total damping effect is presented in an explicit form. It is shown that when two dampers are installed at opposite ends of the cable, the total damping effect is asymptotically the sum of the contributions from single dampers. On the contrast, if two dampers are at the same end, there is no advantage of increasing the maximum modal damping in the cable over the use of a single damper.     

Free Vibrations of Taut Cable with Attached Damper. I: Linear Viscous Damper

Free vibrations of a taut cable with an attached linear viscous damper are investigated in detail using an analytical formulation of the complex eigenvalue problem. This problem is of considerable practical interest in the context of stay-cable vibration suppression in bridges. An expression for the eigenvalues is derived that is independent of the damper coefficient, giving the range of attainable modal damping ratios and corresponding oscillation frequencies in every mode for a given damper location without approximation. This formulation reveals the importance of damper-induced frequency shifts in characterizing the response of the system. New regimes of behavior are observed when these frequency shifts are large, as is the case in higher modes and for damper locations further from the end of the cable. For a damper located sufficiently near the antinode in a given mode, a regime of solutions is identified for which the damping approaches critical as the damper coefficient approaches a critical value. A regime diagram is developed to indicate the type of behavior in each mode for any given damper location.     

General Realization Algorithm for Modal Identification of Linear Dynamic Systems

The general realization algorithm (GRA) is developed to identify modal parameters of linear multi-degree-of-freedom dynamic systems subjected to measured (known) arbitrary dynamic loading from known initial conditions. The GRA extends the well known eigensystem realization algorithm (ERA) based on Hankel matrix decomposition by allowing an arbitrary input signal in the realization algorithm. This generalization is obtained by performing a weighted Hankel matrix decomposition, where the weighting is determined by the loading. The state-space matrices are identified in a two-step procedure that includes a state reconstruction followed by a least-squares optimization to get the minimum prediction error for the response. The statistical properties (i.e., bias, variance, and robustness to added output noise introduced to model measurement noise and modeling errors) of the modal parameter estimators provided by the GRA are investigated through numerical simulation based on a benchmark problem with nonclassical damping.     

Overview of Vibrational Structural Health Monitoring with Representative Case Studies

In the field of nondestructive evaluation and damage detection, there is continued interest in the utilization of vibrational techniques. Structural damage will result in permanent changes in the distribution of structural stiffness. These changes may be detected through structural monitoring. Because of the direct relationship of stiffness, mass, and damping of a multi-degree-of-freedom system to the natural frequencies, mode shapes, and modal damping values, many studies have been directed at using these dynamic properties for the purpose of structural health monitoring. The use of vibrational monitoring is a developing field of structural analysis and is capable of assisting in both detecting and locating structural damage. Vibrational data have been shown to be most useful when used in conjunction with other monitoring systems if a remote and robust damage detection scheme is desired. This paper includes a literature review that summarizes the basic approaches to vibrational monitoring, suggested guidelines for sensor selection and monitoring, and concludes with three example case studies.     

Vibration Analysis of an Elastic Beam Subjected to a Moving Beam with Flexible Connections

The vibration problem of a simply supported beam subjected to a moving elastic structure is investigated. The model consists of two Euler-Bernoulli beams which are assumed to be connected by flexible springs at two discrete points. The dynamic response of the simply supported beam subjected to the moving elastic beam at a constant speed is studied by the modal superposition method. The elastic stiffness and the inertial effect of the moving beam are included in the analysis. By solving the ordinary differential equations governing the motion of the model, some approximate analytical results are derived and influence factors on the dynamic response of the simply supported beam are discussed in details, including the stiffness ratio, which is defined as the stiffness of the moving beam to that of the simply supported beam, the moving velocity and the connection spring stiffness between the two beams. Results of the study imply that the connection stiffness has an apparent influence on the dynamic behavior of the simply supported beam.