Deck Vibration Research Articles

Field observation and cause investigation of low-frequency cable vibrations in a cable-stayed bridge

Considerable levels of stay cable vibration in cable-supported bridges pose significant challenges for safety, operation, and maintenance. An accurate understanding of the specific causes and types of vibration is essential for effectively addressing this problem with an optimal design for mitigation measures. This study aims to investigate the cause of an extraordinary low-frequency vibration that occurred at a stay cable by employing comprehensive methodologies. The modal properties and vibrational characteristics of cable vibrations were first obtained through finite element modeling, operational modal analysis, and vision-based displacement measurements. Subsequently, the primary cause of low-frequency vibrations was investigated using field observations and wind tunnel tests. Field-monitoring data revealed that stay cables were excited by small deck vibrations. The critical wind speeds at which deck vibrations occurred in a wind tunnel experiment were aligned with the ranges of wind speeds that produce low-frequency cable vibrations, which confirmed that these two phenomena are manifested under similar wind conditions. A calculated support excitation amplitude, determined via the use of an empirical equation, exhibited consistency with vision-based measured displacement obtained in field experiments. These findings underscore the potential risk of support excitation between minor deck vibrations and cables, which provides valuable insights that could mitigate cable vibrations.

On the energy decay of a coupled nonlinear suspension bridge problem with nonlinear feedback

Abstract In this article, we study a mathematical model for a one-dimensional suspension bridge problem with nonlinear damping. The model takes into consideration the vibration of the bridge deck in the vertical plane and main cable from which the bridge deck is suspended by the suspenders. We use the multiplier method to establish explicit and generalized decay results, without imposing restrictive growth assumption near the origin on the damping terms. Our results substantially improve, extend, and generalize some earlier related results in the literature.

Aerodynamic interference between road vehicles and bridge deck subjected to vortex-induced vibration

An accurate assessment of the driving comfort and safety of road vehicles moving on a long-span bridge subjected to vortex-induced vibration (VIV) is essential for bridge administrators to decide whether the bridge should be closed to traffic. However, previous assessments often ignore the aerodynamic interference between the road vehicles and the bridge deck subjected to VIV. In this study, a specific wind tunnel model is developed to explore the aerodynamic interference between road vehicles and twin-box bridge deck during VIV. The vortex-induced force (VIF) and vortex-induced response (VIR) of the twin-box bridge deck and the aerodynamic forces on the vehicle were simultaneously measured. The influence of the vehicles on the VIV of the deck was investigated, and the influence of the deck vibration on the aerodynamic forces of the vehicle was also explored. The results show that the VIR and VIF of the bridge deck were generally reduced, depending on the type, position, and number of vehicles. The aerodynamic forces of vehicles could be amplified due to the deck vibration. These findings supplement the database of vehicle aerodynamic coefficients for assessing the driving comfort and safety of road vehicles moving on a long-span bridge subjected to VIV.

Random Vibration Analysis of Double Deck Rocking Self-Centering Pier Under Seismic Excitation

This paper investigates nonlinear random vibration of double deck rocking self-centering pier structure subjected to seismic excitation. First of all, a novel type of double deck rocking self-centering pier that offers better resilience is designed. The stochastic dynamical model of the system is then established, in which the seismic excitation is viewed as Kanai–Tajimi filtered white noise and the self-centering restoring force is characterized by classical flag-shaped hysteretic model. Subsequently, the self-centering restoring force is decomposed into equivalent quasi-linear elastic and damping forces by adopting the harmonic balance (HB) scheme. Following this, the stochastic averaging (SA) technique is implemented to derive the averaged Itô equation. The steady-state response probability density with respect to the amplitudes is solved from the averaged Fokker–Planck–Kolmogorov (FPK) equation. Finally, the effects of system parameters on the stochastic response of the double deck rocking self-centering pier structure are performed, and validated by the Monte Carlo simulation (MCS). In addition, with the help of the Laplace transform, the transition function as well as conditional power spectral density are achieved, which are combined with the steady-state probability density to obtain the power spectral density response. This research will contribute to the optimal seismic design of double-deck rocking self-centering piers.

Impact Pressure Influence of Flood on Bridge Deck under Sediment Deposition Conditions: An Experimental Study

This paper investigates the impact of sediment deposition and inflow conditions on horizontal impact pressure and frequency analysis of bridge deck vibrations during flooding. Flooding-induced pressure and vibrations contribute to bridge collapse, and sediment deposition influences water flow and impact pressure. The study explores the relationship between sediment deposition height and impact pressure, revealing a significant increase as sediment approaches 50% of bridge deck clearance. Sediment amplifies impact pressure response to flow velocity changes. The dimensionless sediment deposition height has a greater influence on impact pressure compared to the inflow Froude number. Two distinct frequencies, dominant and secondary, are identified for impact pressure and water level fluctuations. Dominant frequencies positively correlate with sediment deposition height and Froude number, indicating an increasing trend. Secondary frequencies remain stable (0.31–0.58 Hz). These findings enhance understanding of flow dynamics and bridge–flow interaction in sediment-deposited channels, providing theoretical support for evaluating and managing disasters related to bridges in such environments. Overall, this research contributes to the field of bridge engineering and supports improved design and maintenance practices for bridges exposed to sediment-deposited channels.

Intrinsic Properties of Composite Double Layer Grid Superstructures

This paper examined the opportunities of composite double-layer grid superstructures in short-to-medium span bridge decks. It was empirically shown here that a double-layer grid deck system in composite action with a thin layer of two−way reinforced concrete slab introduced several structural advantages over the conventional composite plate-girder superstructure system. These advantages included improved seismic performance, increased structural rigidity, reduced deck vibration, increased failure capacity, and so on. Optimally proportioned space grid superstructures were found to be less prone to progressive collapse, increasing structural reliability and resilience, while reducing the risk of sudden failure. Through a set of dynamic time-series experiments, considerable enhancement in load transfer efficiency in the transverse direction under dynamic truck loading was gained. Furthermore, the multi-objective generative optimization of the proposed spatial grid bridge (with integral variable depth) using evolutionary optimization methods was examined. Finally, comprehensive discussions were given on: (i) mechanical properties, such as fatigue behavior, corrosion, durability, and behavior in cold environments; (ii) health monitoring aspects, such as ease of inspection, maintenance, and access for the installation of remote monitoring devices; (iii) sustainability considerations, such as reduction of embodied Carbon and energy due to reduced material waste, along with ease of demolition, deconstruction and reuse after lifecycle design; and (iv) lean management aspects, such as support for industrialized construction and mass customization. It was concluded that the proposed spatial grid system shows promise for building essential and sustainable infrastructures of the future.

Modelling of vortex-induced force and prediction of vortex-induced vibration of a bridge deck using method of multiple scales

With the increase of span length, long-span bridges become more flexible and susceptible to vortex-induced vibrations (VIV). Several models for vortex-induced force (VIF) and various methods for predicting VIV have been developed accordingly but without consensus. This paper uses the method of multiple scales, from a different angle of view, to analyze the general polynomial model for VIF and present a concise polynomial model for VIF and a simple method for predicting VIV of a bridge deck. The aeroelastic vibration of a deck section is simulated by the computational fluid dynamics (CFD) and the results are used to verify the concise polynomial model of VIF. The forced vibration of a deck section is also simulated by CFD to yield the simple method for predicting VIV together with the frequency response equation and the critical equation of VIV derived by the method of multiple scales. The results show that the even and cross terms of aerodynamic damping and stiffness in the general polynomial VIF model are small compared with the odd terms and can be thus omitted. The lock-in region and the amplitude of VIV of the deck section can be accurately predicted by the proposed simple method.

Examination of occurrence probability of vortex-induced vibration of long-span bridge decks by Fokker–Planck–Kolmogorov equation

Vortex-induced vibration (VIV) is a major concern for long-span bridge decks, which may happen especially for closed-box girders under certain environmental wind conditions. Traditionally, sustained VIV is observed as long as the wind speed falls within the lock-in region in wind tunnel tests. However, structural vibration monitoring of long-span bridges has indicated that frequency of VIV events may exhibit a probabilistic pattern. This paper proposes an analytical framework to evaluate the probability of VIV occurrence. First, a nonlinear aeroelastic model with multi-stability limit cycles is used to simulate the bridge deck VIV response within the VIV-triggering wind conditions. The first structural dynamic equilibrium point is usually unstable; the bridge deck instantaneous oscillation amplitude, which is excited by external environmental loads, must exceed this fixed point to trigger the VIV event. The external environmental excitation applied on bridge can be identified from the deck vibration without VIV occurring, then the VIV occurrence probability can be evaluated by Fokker–Planck–Kolmogorov equation. This study utilizes the field measurement data from the Humen Bridge, on which VIV event occurred the first time after 23-year servicing period, because water-filled barriers were placed along the two edges of bridge deck. Afterwards, VIV occurred frequently for over one month. The bridge deck VIV occurrence probability is evaluated by combining environmental wind information, stochastic deck excitation magnitude and a nonlinear aeroelastic VIV model. The results suggest that the proposed methods can approximate the VIV occurrence probability in comparison with empirical estimations using field measurements.

Experimental and numerical studies on the two “lock-in” regions characteristic of vertical vortex-induced vibration of Π-shaped composite bridge deck

The Π-shaped bridge deck may easily occur vertical vortex-induced vibration, due to the bluff body aerodynamic configuration, which may cause the uncomforting of vehicles and pedestrians on the bridges. The present study mainly focused on the two “lock-in” regions characteristics of vertical vortex-induced vibration (VIV) of Π-shaped bridge deck, which can reveal the aerodynamic mechanism of vibration mitigation countermeasures. The vertical VIV response of original Π-shaped deck and those with different countermeasures are experimentally investigated detailly. Computational fluid dynamics (CFD) method is employed to numerically simulate the surrounding flow field of original girder section and those with different aerodynamic countermeasures. The numerical method is firstly verified through the comparison with the results of corresponding experimental results obtained in wind tunnel test. Afterwards, the flow pattern and vortex structure around the girder section simulated by CFD are utilized to interpret the effects of the mitigation countermeasures. The numerical results show that: (a)The vibration mitigation effect in the first vortex “lock-in” region is not sensitive to the position of the aerodynamic countermeasures, while the vibration mitigation effect in the second “lock-in” region is more sensitive to the position of the aerodynamic countermeasures; (b) The phase of aerodynamic lift and displacement response is close to synchronization in the ascending section of the VIV amplitude, greater than 90° in the descending section, and close to 180° outside the vortex-induced resonance range. The first vertical VIV region is related to the “Karman vortex street” at the trailing edge of the section, while the second vertical VIV region is related to the vortex shedding at the lower edge of the front end of the section and the secondary vortices on the upper surface.

A Code-Type Method to Assess the Running Safety of Railway Vehicles on Bridges Shaken by Earthquakes Including Girder’s Torsional Motion

The safety of railway vehicles running on bridges needs to be evaluated in the seismic design of bridges. This study examined the spectral intensity calculated from the lateral vibration of the bridge deck during earthquakes, a Japanese code-based index to measure bridge vibration’s strength. In addition, the effect of the torsion of the bridge deck on vehicle derailment is investigated using a nonlinear vehicle–track–bridge model. The bridge deck torsion increases the derailment risk, especially for bridges with a low natural frequency. The reason lies in that the lateral and torsional deck motions are highly correlated for bridges with lower frequency. Based on this observation, a code-type formula was proposed to evaluate the vehicle running safety including both lateral and torsional motions of the bridge deck. The accuracy of the proposed formula was demonstrated by comparison with vehicle–track–bridge simulation excited by ground motion records. The new procedure overcomes the non-conservative assessment of derailment caused by ignoring bridge torsion.

Double Sub-Resonance Mechanism in Torsional–Flexural Vibrations of a Double-Track Short Bridge Under a Moving Train

Train-induced resonance of a railway bridge occurs when the train speed coincides with the primary resonance speed ([Formula: see text]) of the bridge, from which we can determine the sub-resonance speed as ([Formula: see text]). The primary resonance speed of a short bridge is generally much higher than the operation speeds of current high-speed trains but the corresponding sub-resonance speeds probably lie in the operation speed range. Such a resonance scenario can be observed from the vibration of a double-track bridge subjected to an eccentrically moving train, in which the deck vibration is combined by the vertical-flexural and torsional vibration modes of the bridge. Once the two modal sub-resonance speeds coincide with each other, a double sub-resonance will be developed on the bridge. In this study, an iteration-based train–bridge interaction finite element procedure will be presented to demonstrate the double resonance phenomenon. As expected, the double resonance may bring about a dramatic amplification on deck vibration. Such an excessive vibration is harmful to ballast stability and track maintenance of railway bridges.

Extraction of aerodynamic damping and prediction of vortex-induced vibration of bridge deck using CFD simulation of forced vibration

This study presents computational fluid dynamics (CFD) simulation of forced vibration of a bridge deck for extraction of amplitude-dependent aerodynamic damping in the vicinity of vortex lock-in region. The coordinate system fixed on the oscillating body is used to bypass the requirement of mesh updating. The three-dimensional flow around the vibrating deck is assumed to be homogeneous in spanwise direction and simulated using the efficient high-order spectral element/Fourier method. The aerodynamic damping is extracted from the simulated lift and then used to estimate the steady-state vortex-induced vibration (VIV) amplitude for given wind velocity and structural parameters. A good match of VIV amplitudes between simulations and wind tunnel tests validates the accuracy of simulation. The VIV mechanisms are discussed from the vortex shedding modes, distributions of dynamic pressure and energy transfer from flow to bridge deck. The leading-edge vortex shedding rather than Karman vortex shedding is identified to be responsible for the VIV. The hysteresis of VIV is observed which is related to the mode change of impinging leading-edge vortex and leading-edge vortex shedding. Finally, a novel forced vibration technique with a varying amplitude is proposed that permits extraction of aerodynamic damping by a single CFD run with improved efficiency.

Dynamic response and time-variant reliability analysis of an eight-rod shock isolator

The operation of a warship is commonly affected by shock loads in different directions during sailing in a rough sea, which can decrease the precision of the shipboard equipment. To improve the shock resistance performance of the shipboard equipment, an isolator is usually installed to isolate it from the vibration of the ship deck. The paper proposes a method for dynamic response and time-variant reliability analysis of an eight-rod shock isolator (ERSI). ERSI has a novel symmetrical structure, which can improve the utilization of the isolation rods compared with the classical parallel mechanism. The isolator is modeled using Denavit-Hartenberg (D-H) convention and screw theory. Then, Duhamel integral is employed to derive the dynamic response to the isolator after decoupling the governing equation using the modal analysis method. Considering impacts of uncertain factors, this paper also presents a practical method for time-variant reliability analysis of ERSI. Finally, a discussion of the practical example of this method along with a detailed analysis to evaluate the efficiency of the proposed method is presented.

Mathematical Description and Study of the Vibration Deck of a Grain Sorting Machine

This article presents the results of a study of the vibrations of the deck of a pneumatic sorting machine. The purpose of this work is to describe the design and technological parameters of the soundboard for the implementation of a mathematical model of the technological process of the grain sorting machine. A kinematic study of the flat hinge mechanism of the deck of a grain sorting machine has been carried out, for which all geometric dimensions are known and the laws of motion of the leading link-the electric drive of the deck based on an asynchronous electric motor – have been determined. As a result, the following were determined: kinematic modes of deck vibrations under various technological conditions; the laws of motion of all links of the deck mechanism, displacement, speed and acceleration of the driven links; a mathematical model of the kinematic scheme of the deck of a grain sorting machine driven by an asynchronous electric motor has been developed.

Modal Interaction-Induced Parametric Resonance of Stayed Cable: A Combined Theoretical and Experimental Investigation

The cable-stayed bridge is widely used due to its strong spanning capacity and navigability. However, flexible cables parametrically resonated by external excitation may result in instability or even damage to the bridge. To prevent such undesirable resonance, this paper discusses an in-plane modal interaction-induced parametric resonance of the stayed cable excited by the bridge deck vibration via nonlinear dynamic analysis. Based on the nonlinear distributed model, two modal governing equations of the cable are established via the Galerkin method. A certain working condition, when the external excitation frequency is close to the second-order natural frequency of the stay cable while nearly twice the first-order natural frequency, is theoretically and experimentally investigated. Specifically, the frequency response equations are obtained by the multiscale method, and the stability of solutions is examined through the Routh Hurwitz criterion. Theoretical and experimental results show that bridge deck vibration can induce not only the primary and superharmonic resonance of the cable but also the principal parametric resonance. Parametric resonance-induced bifurcations are also observed in the system. Particularly, the energy exchange from second-order primary resonance to first-order principal parametric resonance is found, which can induce the parametric resonance with the response amplitude one to three times higher than that of the primary resonance. This paper also validates the superiority of the present modal interaction model over the traditional single-mode model in practical engineering applications.

Seismic Analysis of Double Deck Floating Roofs of Siraf Storage Tanks with Condensate, Light and Heavy Crude Oils

Seismic vibration of double deck floating roof of Siraf storage tanks located in southern Iran has been studied. Condensate of Nar and Kagan gas field in south of Iran as a very light hydrocarbon, Lavan as light and Soroosh as heavy crude oil content have been chosen. In addition to fluid-structure interaction, intermediate stiffeners, foam seal with nonlinear radial compression behavior and contact friction between the seal and the inner side of the wall are also considered. Under the above conditions, modal and time history analysis has been performed. For time history analysis, Sarpol-e Zahab and Shonbeh earthquakes in Zagros seismotectonic province of Iran and Sakaria as an earthquake near Iran were selected. Dominant natural frequencies, mode shapes of the roof parts and damping ratios of the first and second natural frequencies in addition to overall and spectral behavior of the roof in each liquid cases were obtained and discussed. Changing condensate to Soroosh oil made about 17% hydroelastic natural frequency decrement and about 10% damping ratio decrease for the first natural frequency. The results showed that dominant natural frequencies and the relevant damping ratios decrease with moving from light to heavy liquid. Vibration of the roof fundamentally depends on the frequency content of earthquake in relation to such natural frequencies. Also, floating roof in heavier liquid is more vulnerable to vibration according to the scaling method and steady state amplitude.

Static behavior of partially earth-anchored cable-stayed bridge of different side-to-main span ratios: super-long span system with crossing cables

This article presents a study to evaluate the structural response of a cable-stayed bridge under a novelsystem, partially earth-anchored system with crossing cables at the main span.Six side-to-main span ratios, ranging from 0.24to 0.39in increments of 0.03,aretested for differentbridge response parameters for both the superstructure and substructure. The loads considered in theanalysis are the dead load and traffic load. Three-dimensional finite element models of the bridge are developed using structural analysis software SAP2000 and arevalidated based on the data available in the literature.From this study, it is found that the side-to-main span ratios have a significant effect on girder axial force and anchorage forces while having a very minor effect on cable axial forces. The results also show that the ratio does not affect the bending moment of the main span, but that when a small ratio is considered particular attention needs to be paid to the pier farther from the pylon to avoid uplifting. Deck vibration and longitudinal movement, as well as pylon longitudinal displacement, are not to be an issue for this super-long bridge.

Three-to-one internal resonance analysis for a suspension bridge with spatial cable through a continuum model

Nonlinear vibration of suspension bridge is a topic requiring comprehensive investigation. This study is focused on the internal resonance of the suspension bridge consisting of spatially inclined main cables and hangers by proposing a mathematic full bridge model. The vertical vibration of the bridge deck is studied. Specifically, the dynamic governing functions of this model can consider the geometric non-linearity of cables and deck. Firstly, the modal property of the continuum model is investigated, and the scenarios of modal frequency ratio between different modes equals to 3:1 are obtained. Then, the 3:1 internal resonances between two lowest symmetric or asymmetric modes with the external harmonic excitation are investigated by the Multiple Scales Method. The corresponding modulation equations explaining the internal resonance of two modes are obtained and solved by pseudo-arc-length method for exploring the nonlinear dynamic behaviors. The internal resonance is discussed with various detuning parameters. Some novel and interesting conclusions have been made. Knowledge of such possible occurrences can be beneficial in the design of the bridge structure.

Experimental study on suppression of vortex-induced vibration of bridge deck using vertical stabilizer plates

Despite the wind-resistant design performed during the design stage, an existing bridge may still experience severe vortex-induced vibrations (VIVs) because of the installation of new affiliated facilities during its operation period. Therefore, it is necessary to apply control measures to suppress the VIV induced by such changes in configuration. In this study, the VIV performance of a streamlined box girder bridge during the installation of new auxiliary piping system was investigated through a series of sectional model tests and flow visualization tests. Severe vertical VIVs of the bridge used in this study were observed at lower wind speed ranges during wind tunnel tests. Based on the flow pattern around the sectional model, it was inferred that the flow across the deck bottom surface was entirely separated by the new pipelines, which resulted in the periodic generation of shedding vortices in the wake zone and induced deck vibration. Twin downward vertical stabilizer plates (TDVS) were found to be an effective aerodynamic countermeasure for improving the VIV performance of the bridge and could significantly decrease the amplitude of the vertical VIV motion. Additional flow visualization investigations showed that after the TDVS were installed, the vortex shedding in the wake was mitigated, and the location of the vortex shedding was further away from the deck, and hence, considerably suppressed the vertical VIVs. It was found that the effectiveness of the TDVS in improving the aerodynamic performance was significantly dependent on the TDVS parameters, i.e., the plate height and spacing between plate elements. The optimal values of these parameters were correspondingly identified for the bridge deck used in this study after a comprehensive evaluation.

Nonlinear Parametric Resonance Behavior of Cables in a Long Cantilever Bridge for Sightseeing Platform

In order to study the parametric vibration of stayed cables in a long cantilever bridge for a sightseeing platform, nonlinear parametric vibration equations of the stayed cables excited by the vibration of bridge deck and tower are derived. Then, a second‐order differential equation is transformed into a first‐order ordinary differential equation, which is solved by using the Runge–Kutta method. A finite element model of cables was also built to verify the solution of the Runge–Kutta method. Then, the inherent dynamic characteristics of the full structure and all the cables with different lengths were analyzed to discuss the potential risk of parametric vibration. The longest and shortest cables were taken as examples to explore their nonlinear vibration performance. The effects of damping ratio, excitation position, and amplitude on cables’ nonlinear vibration performance were investigated. The results show that it will be more efficient and convenient to use the Runge–Kutta method to calculate cables’ nonlinear vibration amplitude without loss of accuracy. In addition, short cables have more resonance zones compared to long cables. Especially, with the cable length shortening, the dominant frequencies of the dynamic response and its amplitude increase significantly, and the number of resonance zones also increases. However, excessive excitation amplitude will also cause multiple resonance zones in the cable. The parametric analysis results show that it is effective and efficient to mitigate the nonlinear vibration by adjusting the frequency relationship between the bridge and the cables, rather than by increasing the damping ratio.