Cross Correlations of Modal Responses of Tall Buildings in Wind-Induced Lateral-Torsional Motion

Recent trends towards developing increasingly taller and irregularly-shaped buildings imply that these complex structures are potentially more responsive to wind excitation. Making accurate predictions of wind loads and their effects on such structures is therefore a necessary step in the design synthesis process. This paper presents a framework for dynamic analysis of the wind-induced lateral-torsional response of tall buildings with three-dimensional (3D) mode shapes. The cross correlation reflecting the statistical coupling among modal responses under spatiotemporally varying dynamic wind excitations has been investigated in detail. The effects of intermodal correlations on the lateral-torsional response of tall buildings with 3D mode shapes and closely spaced natural frequencies are elucidated and a more accurate method for quantifying intermodal cross correlations is analytically developed. Utilizing the wind tunnel derived synchronous multipressure measurements, a full-scale 60-story asymmetric building of mixed steel and concrete construction is used to illustrate the proposed framework for the coupled dynamic analysis and highlight the intermodal correlation of modal responses on the accurate prediction of coupled building acceleration.     

Dynamic Wind Effects on Buildings with 3D Coupled Modes: Application of High Frequency Force Balance Measurements

Contemporary high-rise buildings with complex geometric profiles and three-dimensional (3D) coupled mode shapes often complicate the use of high frequency force balance (HFFB) technique customarily used in wind tunnel testing for uncoupled buildings. In this study, a comprehensive framework for the coupled building response analysis and the modeling of the associated equivalent static wind loads using the HFFB measurement is presented. This includes modeling of building structural systems whose mass centers at different floors may not be located on a single vertical axis. The building response is separated into the mean, background, and resonant components, which are quantified by modal analysis involving three fundamental modes in two translational and torsional directions. The equivalent static wind load is described in terms of the modal inertial loads. The proposed framework takes into account the cross correlation of wind loads acting in different primary directions and the intermodal coupling of modal responses with closely spaced frequencies. Wind load combination is revisited in the context of modeling of the equivalent static wind loads. A representative tall building with 3D coupled modes and closely spaced frequencies is utilized to demonstrate the proposed framework and to highlight the significance of cross correlation of wind loads and the intermodal coupling of modal responses on the accurate prediction of coupled building response. Additionally, delineation of the proper role of the correlation between integrated loads, modal response, and respective building response components in the evaluation of wind effects on coupled buildings is underscored.     

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.     

Cable Modal Parameter Identification. I: Theory

Cable modal parameters (natural frequencies and damping ratios) that represent the cable inherent dynamic characteristics play an important role in the construction, vibration control, condition assessment, and long-term health monitoring of cable-supported structures. The existing options to identify cable modal parameters through vibration measurements are somewhat limited. For this purpose, a cable dynamic stiffness based method is presented to effectively identify the cable modal parameters. In the first part of this two-part paper, the cable dynamic stiffness is analytically discussed for a viscously damped, uniform, inclined sagging cable supported at the lower end and subjected to a harmonically varying arbitrary angle displacement excitation in an arbitrary angle at the upper end when the cable is assumed to have a parabolic profile at its position of static equilibrium. Special attention is paid to the physical meaning and significance of every part of the frequency-dependent closed-form cable dynamic stiffness. Comprehensive numerical analyses have been carried out and a simplified cable dynamic stiffness is proposed for the purpose of identifying the cable modal parameters with a good accuracy over a wide range of frequencies.     

Hilbert-Huang Based Approach for Structural Damage Detection

When measured data contain damage events of the structure, it is important to extract the information of damage as much as possible from the data. In this paper, two methods are proposed for such a purpose. The first method, based on the empirical mode decomposition (EMD), is intended to extract damage spikes due to a sudden change of structural stiffness from the measured data thereby detecting the damage time instants and damage locations. The second method, based on EMD and Hilbert transform is capable of (1) detecting the damage time instants, and (2) determining the natural frequencies and damping ratios of the structure before and after damage. The two proposed methods are applied to a benchmark problem established by the ASCE Task Group on Structural Health Monitoring. Simulation results demonstrate that the proposed methods provide new and useful tools for the damage detection and evaluation of structures.     

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.     

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.     

Wind Response Control of Building with Variable Stiffness Tuned Mass Damper Using Empirical Mode Decomposition/Hilbert Transform

The effectiveness of a novel semiactive variable stiffness-tuned mass damper (SAIVS-TMD) for the response control of a wind-excited tall benchmark building is investigated in this study. The benchmark building considered is a proposed 76-story concrete office tower in Melbourne, Australia. It is a slender building 306 m tall with a height to width ratio of 7.3; hence, it is wind sensitive. Across wind load data from wind tunnel tests are used in the present study. The objective of this study is to evaluate the new SAIVS-TMD system, that has the distinct advantage of continuously retuning its frequency due to real time control and is robust to changes in building stiffness and damping. In comparison, the passive tuned mass damper (TMD) can only be tuned to a fixed frequency. A time varying analytical model of the tall building with the SAIVS-TMD is developed. The frequency tuning of the SAIVS-TMD is achieved based on empirical mode decomposition and Hilbert transform instantaneous frequency algorithm developed by the writers. It is shown that the SAIVS-TMD can reduce the structural response substantially, when compared to the uncontrolled case, and it can reduce the response further when compared to the case with TMD. Additionally, it is shown the SAIVS-TMD reduces response even when the building stiffness changes by ±15% and is robust; whereas, the TMD loses its effectiveness under such building stiffness variations. It is also shown that SAIVS-TMD can reduce the response similar to an active TMD; however, with an order of magnitude less power consumption.     

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.     

Considerations of Multimode Structural Response for Near-Field Earthquakes

This paper presents an investigation of multimode effects of tall buildings idealized as a continuous shear-beam model subjected to near-field pulse-like ground motion. The investigation is based on three analytical approaches: a damped wave solution approach, a fundamental-mode approach, and a modal summation approach. In the modal summation approach, all modal damping ratios are assumed to be equal and a set of Green’s functions for the shear strain response is explicitly derived. The multimode effects on the base-level shear strain/force demands are compared by using an effective response spectrum for shear-beam systems. The study results show that the occurrence of major spectral differences is conditioned on the ratio of the fundamental structural period to the duration of the predominant excitation pulse. Seismic analyses for a set of recorded near-field earthquake data indicate a strong correlation between the characteristics of effective response spectra and the ground pulse parameters.     

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.     

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.     

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.     

Modified Cross-Correlation Method for the Blind Identification of Structures

Recently, blind source separation (BSS) methods have gained significant attention in the area of signal processing. Independent component analysis (ICA) and second-order blind identification (SOBI) are two popular BSS methods that have been applied to modal identification of mechanical and structural systems. Published results by several researchers have shown that ICA performs satisfactorily for systems with very low levels of structural damping, for example, for damping ratios of the order of 1% critical. For practical structural applications with higher levels of damping, methods based on SOBI have shown significant improvement over ICA methods. However, traditional SOBI methods suffer when nonstationary sources are present, such as those that occur during earthquakes and other transient excitations. In this paper, a new technique based on SOBI, called the modified cross-correlation method, is proposed to address these shortcomings. The conditions in which the problem of structural system identification can be posed as a BSS problem is also discussed. The results of simulation described in terms of identified natural frequencies, mode shapes, and damping ratios are presented for the cases of synthetic wind and recorded earthquake excitations. The results of identification show that the proposed method achieves better performance over traditional ICA and SOBI methods. Both experimental and large-scale structural simulation results are included to demonstrate the applicability of the newly proposed method to structural identification problems.     

Nonlinear Identification of Lumped-Mass Buildings Using Empirical Mode Decomposition and Incomplete Measurement

Most structures exhibit some degrees of nonlinearity such as hysteretic behavior especially under damage. It is necessary to develop applicable methods that can be used to characterize these nonlinear behaviors in structures. In this paper, one such method based on the empirical mode decomposition (EMD) technique is proposed for identifying and quantifying nonlinearity in damaged structures using incomplete measurement. The method expresses nonlinear restoring forces in semireduced-order models in which a modal coordinate approach is used for the linear part while a physical coordinate representation is retained for the nonlinear part. The method allows the identification of parameters from nonlinear models through linear least-squares. It has been shown that the intrinsic mode functions (IMFs) obtained from the EMD of a response measured from a nonlinear structure are numerically close to its nonlinear modal responses. Hence, these IMFs can be used as modal coordinates as well as provide estimates for responses at unmeasured locations if the mode shapes of the structure are known. Two procedures are developed for identifying nonlinear damage in the form of nonhysteresis and hysteresis in a structure. A numerical study on a seven-story shear-beam building model with cubic stiffness and hysteretic nonlinearity and an experimental study on a three-story building model with frictional magnetoreological dampers are performed to illustrate the proposed method. Results show that the method can quite accurately identify the presence as well as the severity of different types of nonlinearity in the structure.     

Aerodynamic Coupling Effects on Flutter and Buffeting of Bridges

The effects of aerodynamic coupling among modes of vibration on the flutter and buffeting response of long-span bridges are investigated. By introducing the unsteady, self-excited aerodynamic forces in terms of rational function approximations, the equations of motion in generalized modal coordinates are transformed into a frequency-independent state-space format. The frequencies, damping ratios, and complex mode shapes at a prescribed wind velocity, and the critical flutter conditions, are identified by solving a complex eigenvalue problem. A significant feature of this approach is that an iterative solution for determining the flutter conditions is not necessary, because the equations of motion are independent of frequency. The energy increase in each flutter motion cycle is examined using the work done by the generalized aerodynamic forces or by the self-excited forces along the bridge axis. Accordingly, their contribution to the aerodynamic damping can be clearly identified. The multimode flutter generation mechanism and the roles of flutter derivatives are investigated. Finally, the coupling effects on the buffeting response due to self-excited forces are also discussed.     

Damping of Vibration by Actively Controlled Initial Distortions

A concept for the artificial damping of free vibration by means of actively controlled initial distortions imposed on the structure is presented. Two formulations for active control are presented: The first simulates the natural damping properties of structures, while the second uses a more sophisticated modal strategy of control (but with a faster damping process). The general idea of damping by actively forced distortions is explained and followed by a simple example for a one‐degree‐of‐freedom system. Then, the simulation of natural damping (which is a particular case of active control) and the possibility of accelerating the damping process by the modal optimal strategy are discussed and demonstrated with some examples for a two‐degree‐of‐freedom system. Finally, the vibration control of a four‐degree‐of‐freedom system is presented to demonstrate the efficiency of the proposed method. The method of active damping is described for truss structures, but it can be easily generalized to include frame structures as well.     

Equivalent Modal Damping of Short-Span Bridges Subjected to Strong Motion

In this paper four different methods are investigated for estimating the equivalent modal damping ratios of a short-span bridge under strong ground motion by considering the energy dissipation at the boundary. The Painter Street Overcrossing (PSO) is investigated because of seismic data availability. Computed responses using the response-spectrum method with the equivalent damping ratios estimates are compared with the recorded responses. The results show that the four methods provide reasonable estimation of equivalent modal damping ratios and that neglecting off-diagonal elements in the damping matrix is the most efficient and practical method. The equivalent damping ratio of the PSO was nearly 25% under an earthquake with peak ground acceleration of 0.55g, which is much higher than the conventional assumption of 5%.     

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.     

Ambient Vibration of Long-Span Cable-Stayed Bridge

The investigation of dynamic response for long-span cable-stayed bridges largely depends on a detailed understanding of their dynamic characteristics, such as the natural frequencies, mode shapes, and modal damping ratios. In this paper, the dynamic characteristics of a fairly long cable-stayed bridge in Hong Kong are studied using finite-element analysis and ambient vibration measurements. A three-dimensional finite-element model is first established for the bridge based on design drawings. The dynamic characteristics are then analyzed from the statically deformed configuration. Ambient vibration measurements are also conducted to obtain the dynamic characteristics of the bridge. Comparison between these two results shows that, for the most part, a total of 31 modes can be correlated with a reasonable agreement. However, the frequency differences of the higher modes can range between 15 and 30%. This implies that, if the measurement is more reliable, a finite-element model updating is necessary in order to achieve better correlation between these two results.