Vibration Control of Railway Bridges under High-Speed Trains Using Multiple Tuned Mass Dampers

In this paper, multiple tuned mass dampers (MTMDs) are considered for suppressing the vibration of railway bridges under high-speed trains. The interaction equations of motion between the vehicle and the bridge with MTMDs have been developed. The effectiveness of MTMDs on suppressing resonant vibration of railway bridges is examined and the optimum parameters of MTMDs for suppressing the resonant vibration are proposed. The results indicate that the use of the MTMD with the optimum parameters reduces the displacement and acceleration responses of railway bridges significantly.     

Tuned Mass Dampers for Dual-Mode Buffeting Control of Bridges

The objective of this paper is to present the idea of control of the dual-mode buffeting response in suspension bridges under service conditions using two tuned mass dampers (TMDs). The bridge is assumed to vibrate in two vertical modes, which are to be controlled using two TMDs. The TMDs’ properties are determined by minimizing the maximum buffeting response of the bridge. By neglecting modal coupling terms, some approximate formulas are derived. A numerical example is used to understand the requirements for the TMDs. The results show that, as compared to using only one TMD, the dual TMDs offer a more pronounced response reduction. The results also reveal some disadvantages of using the TMD system for buffeting vibration control. The major one is that the efficiency of the TMD system declines and the strokes increase significantly as the wind speed increases.     

Pendulum Tuned Mass Dampers for Floor Vibration Control

This paper presents the results of the analytical and experimental studies of a pendulum tuned mass damper (PTMD) to control excessive floor vibrations due to human movements. The PTMD used in this study acts as a passive tuned mass damper. An equivalent single-degree-of-freedom model for the PTMD is developed and used to derive the equations of motion of the coupled PTMD-floor system. The optimal design parameters of the PTMD are found using an optimization algorithm. Effects of off-tuning of the PTMD due to the variations in the floor mass on its response are investigated. Results of the tuning of the PTMD on a laboratory test floor are presented along with the off-tuning effects. These results indicate that a properly tuned PTMD can significantly reduce the excessive floor vibrations. In addition, when subjected to off-tuning due to variations in the floor live load the PTMD may or may not be able to perform effectively depending on the level of human-structure dynamic interactions. Finally, examples of the PTMD already in use to control excessive floor vibrations are presented.     

Natural Frequency of Railway Girder Bridges under Vehicle Loads

To investigate the natural frequency of a railway girder bridge under vehicle loads, two methods are presented. First, the natural frequency of a railway girder bridge under vehicle loads is obtained by solution of the eigenvalue of the vehicle-bridge interaction equation at each step of the numerical integration. Second, based on the vehicle-bridge interaction equation, an approximate formula is developed. The results show that the natural frequency of a railway girder bridge under vehicle loads varies periodically as the vehicles pass over the bridge. The results obtained with the two methods are then compared, showing that a good agreement is achieved. From parametric studies, the effects of the unsprung mass, the sprung mass, and the stiffness of the vehicle suspension are discussed.     

Fatigue Performance of Stringer-to-Floor-Beam Connections in Riveted Railway Bridges

The behavior of double-angle stringer-to-floor-beam connections in riveted railway bridges is examined experimentally. A series of static and fatigue tests were performed on three full-scale bridge parts taken from an old riveted railway bridge. The results of the static tests reveal that the amount of end moment developed in these connections as a result of their rotational stiffness could be considerable. As a result of the cyclic variation in this moment, fatigue damage might develop in these connections. This damage was, however, observed to have a fairly low propagation rate and did not immediately reduce the load-carrying function of the connections.     

Seismic Energy Dissipation of Inelastic Structures with Multiple Tuned Mass Dampers

The ability to use multiple tuned mass dampers (TMDs) in improving inelastic structural performance to dissipate the earthquake input energy is investigated. Inelastic structural behavior is modeled using the force analogy method, which is the backbone of analytically characterizing the plastic energy dissipation in the structure. Both tuning period and placement of the multiple TMDs are studied to give the best structural performance in terms of plastic energy dissipation. Numerical simulations are performed to study the energy responses of structures with and without TMD installed, and the effectiveness of TMDs in the reduction of energy responses is also studied by using tuned mass spectra. Results show that the installation of TMDs gives the structure additional capability of dissipating a large amount of damping energy and at the same time reducing the amount of plastic energy demand and therefore reducing damage in the structure. More important, TMDs have the ability to draw the plastic energy dissipation at the lower stories and release it to the upper stories. This is particularly beneficial for structures that would otherwise suffer more damage at the lower stories than the upper stories. However, the reduction in plastic energy dissipation is quite sensitive to the earthquake vibration characteristics, and TMDs should not be used for structures with weak upper stories.     

Effect of Hanger Flexibility on Dynamic Response of Suspension Bridges

Linearized continuum models of a suspended span with unloaded backstays and of a symmetric three-span suspension bridge are used to study the effects of the flexibility of the hangers on the vertical vibrations of suspension bridges. The models include elastic parabolic cables, flexible distributed hangers with variable length, and a stiffening girder represented by an elastic beam. It is shown that the free vibrations of a suspended span with unloaded backstays are controlled by five dimensionless parameters, while six dimensionless parameters control the response of a symmetric three-span suspension bridge. The results indicate that the flexibility of the hangers has a significant effect on the natural frequencies of the higher modes only when the relative stiffness of the girder is very high. The effects of hanger flexibility on the response of a suspension bridge to localized impulsive loads are also found to be small. These findings confirm the traditional, albeit previously untested, assumption of inextensible hangers. Finally, the threshold amplitudes of free vibrations that would result in the incipient slackening of the hangers are determined.     

Three-Dimensional Analyses of Wave Barriers for Reduction of Train-Induced Vibrations

This paper explores the use of a three-dimensional finite-element analysis to model soil vibrations due to high-speed trains on bridges. Finite-element meshes include the bridge superstructure, bridge foundations, nearby building foundations, and piles. Wheel elements represented by appropriate mass, damping and stiffness factors were used to simulate a moving high-speed train. Along the mesh boundaries, absorbing boundary conditions were employed to avoid fictitious wave reflections. Isolation methods to reduce soil vibrations were investigated including construction of open and infilled trenches and soil improvement. Vibration isolation effects due to building foundations and piles were also studied. The finite-element results indicate that suitable axial stiffness between two simple beams can reduce vibration significantly, especially at a near-resonance condition. Operating with an appropriate train velocity to avoid resonance can be another way to reduce vibrations. Suitable mat foundations can significantly reduce soil horizontal vibration, but cannot isolate vertical vibration. Soil improvements near the bridge do not effectively attenuate low-frequency vibrations. Infilled and open trenches can isolate soil vertical vibration; however, their efficiency seems disproportionate to their cost.     

Isolation System for Vibration Control of Stay Cables

Rain-wind induced cable vibration can cause serious problems in cable-stayed bridges. Externally attached dampers have been used to provide an effective means to suppress the vibration of relatively short stay cables. For very long stay cables, however, such damper systems are rendered ineffective, as the dampers need be attached near the end of the cables for aesthetic reasons. This paper investigates a new stay-cable isolation system to mitigate the cable vibration. The proposed isolation system, which consists of a laminated rubber bearing and an internal damper, may be installed inside of the cable anchorage. A simple analytical model of the cable-damper system is developed first based on the taut string representation of the cable. The response of a cable with the proposed isolation system is obtained and then compared to those of the cable with and without an external passive damper. The proposed stay-cable isolation system is shown to perform better than the optimal passive viscous damper, thereby demonstrating its applicability in large cable-stayed bridges.     

Dynamic Analysis of Metallic Arch Railway Bridge

This work describes some of the most interesting aspects of the experimental and numerical dynamic analyses of the Luiz I Bridge, an old arch double-deck iron bridge, when subjected to the moving loads of the new light metro of Porto. Presented are the methodology and computational tools developed, as well as some of the most significant results obtained from numerical simulations conducted on the basis of an experimentally calibrated finite-element model, both in terms of structural safety and of the comfort of pedestrians and train passengers.     

Dynamic Stress Analysis of Long Suspension Bridges under Wind, Railway, and Highway Loadings

Computation of the dynamic stress of long suspension bridges under multiloadings is essential for either the strength or fatigue assessment of the bridge. This paper presents a framework for dynamic stress analysis of long suspension bridges under wind, railway, and highway loadings. The bridge, trains, and road vehicles are respectively modeled using the finite-element method (FEM). The connections between the bridge and trains and between the bridge and road vehicles are respectively considered in terms of wheel-rail and tire-road surface contact conditions. The spatial distributions of both buffeting forces and self-excited forces over the bridge deck surface are considered. The Tsing Ma suspension bridge and the field measurement data recorded by a wind and structural health monitoring system (WASHMS) installed in the bridge are utilized as a case study to examine the proposed framework. The information on the concerned loadings measured by the WASHMS is taken as inputs for the computation simulation, and the computed stress responses are compared with the measured ones. The results show that running trains play a predominant role in bridge stress responses compared with running road vehicles and fluctuating wind loading.     

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.     

Dynamic Analysis of Curved Continuous Multiple-Box Girder Bridges

The use of horizontally curved composite multiple-box girder bridges in modern highway systems is quite suitable in resisting torsional and warping effects induced by highway curvatures. Bridge users react adversely to vibrations of a bridge and especially where torsional modes dominate. In this paper, continuous curved composite multiple-box girder bridges are analyzed, using the finite-element method, to evaluate their natural frequencies and mode shapes. Experimental tests are conducted on two continuous twin-box girder bridge models of different curvatures to verify and substantiate the finite-element model. Empirical expressions are deduced from these results to evaluate the fundamental frequency for such bridges. The parameters considered herein are the span length, number of lanes, number of boxes, span-to-radius of curvature ratio, span-to-depth ratio, end-diaphragm thickness, number of cross bracings, and number of spans.     

Dynamic Characteristics of Chilean Bridges with Seismic Protection

A new highway system is being constructed in Chile including many bridges. Due to the high seismic risk in the country, high damping rubber bearings, friction bearings, and passive energy dissipation devices have been considered in the design of the majority of the new moderate and large span bridges. Their design follows American Association of State Highway guidelines and technical specifications from the Chilean Ministry of Public Works. Experimental and analytical studies have been performed in three of these structures: (1) a 383 m long continuous beam bridge supported on high damping rubber bearings; (2) a 268 m long continuous beam bridge supported on friction bearing with additional viscous dampers; and (3) a five-span simply supported beam bridge resting on neoprene bearings. Predominant periods and damping characteristics for small amplitude vibrations have been determined from output-only nonparametric analyses. Comparison with standard analytical structural models indicates that the models normally used for analysis yield comparable predominant periods and mode shapes but the damping values typically recommended are larger than the ones observed from ambient vibrations, even when additional energy dissipation elements are present.     

Effects of Seismically Induced Pounding at Expansion Joints of Concrete Bridges

This paper presents the result of a study on the effect of pounding at expansion joints on concrete bridge response to earthquake ground motions. An engineering approach, rather than continuum mechanics approach, is emphasized. First, the dynamic behavior of a damped multidegree-of-freedom bridge system separated by an expansion joint involving an impact is examined by means of the finite element method. Second, the sensitivity analysis of the stiffness in gap elements is performed. Third, usefulness of the analysis method for simulation of pounding phenomena is demonstrated and the effect of pounding on the ductility demands measured in terms of the rotation of column ends is investigated. Two-dimensional finite element analysis using a bilinear hysterestic model for bridge substructure joints and a nonlinear gap element for the expansion joint is performed on a realistic bridge with an expansion joint. The effects of the primary factors on the ductility demand such as gap sizes and characteristics of earthquake ground motion are investigated through a parametric study. The major conclusions are (1) the effect of impact most directly depends on the size of momentum (or pounding magnitude); and (2) the pounding effect is generally found to be negligible on the ductility demand for wide practical ranges of gap size and peak ground acceleration, but is potentially significant at the locations of impact.     

Influence of Haunches on Performance of Precast-Concrete, Short-Span, Skewed Bridges with Integral Abutment Walls

Precast-concrete, skewed bridges with integral abutment walls are, typically, designed as simplified plane rigid portal frames, neglecting the degrading effects of the skew angle, the influence of haunches between the abutment walls and the deck, and laterally unsymmetrical vertical loading. This practice produces underdesigned bridges for certain aspect ratios. It is well known that the higher shear and torsional moments near the obtuse corners cause cracking and local deterioration. To evaluate the limitations of this practice, an experimental and analytical study was carried out for the live load response at the linear service level. It has been observed that for certain bridge configurations, both the positive and negative moment stresses are higher than the stresses given by plane frame analysis. The presented qualitative results enable comparison of performance characteristics.     

Free Vibration of Three-Dimensional Orthotropic Uniform Shear Beam-Columns with Generalized End Conditions

The free vibration analysis of asymmetrical three-dimensional (3D) uniform shear beam-columns with generalized boundary conditions (semirigid flexural and torsional restraints, lateral bracings, and lumped masses at both ends) subjected to an eccentric end axial load in addition to a linearly distributed eccentric axial load along its span is presented in a classic manner. The five coupled governing equations of dynamic equilibrium (i.e., two shear equations, two bending moment equations, and the pure torsion moment equation) are sufficient to determine the natural frequencies and modal shapes. The proposed model which is an extension of a 2D model presented previously by the writer includes the simultaneous 3D coupling effects among the lateral deflections, deformations of the cross section along the member (shear, torsional and rotational), the translational, rotational and torsional inertias of all masses considered, an eccentric end axial load in addition to a linearly distributed axial load along its span, and the end restraints. Deformations caused by shear forces and pure torsion are considered. The effects of axial deformations, warping torsion and torsional stability are not included. The proposed model shows that the dynamic behavior of 3D shear beam-columns is highly sensitive to the coupling effects just mentioned, particularly in members with both ends free to rotate. Analytical results indicate that except for doubly symmetric members with concentric axial loads and with perfectly clamped ends, the natural frequencies and modal shapes of 3D shear beam-columns are determined from the eigenvalues of a full 8×8 matrix, rather than from the uncoupled equations of transverse (or shear-wave equations) and torsional moment equilibrium. Two comprehensive examples are presented that show the effectiveness of the proposed method.