Deck Motion Research Articles

The effect of sinusoidal rolling ground motion on lifting biomechanics

The objective of this study was to quantify the effects of ground surface motion on the biomechanical responses of a person performing a lifting task. A boat motion simulator (BMS) was built to provide a sinusoidal ground motion (simultaneous vertical linear translation and a roll angular displacement) that simulates the deck motion on a small fishing boat. Sixteen participants performed lifting, lowering and static holding tasks under conditions of two levels of mass (5 and 10 kg) and five ground moving conditions. Each ground moving condition was specified by its ground angular displacement and instantaneous vertical acceleration: A): +6°, −0.54 m/s 2; B): +3°, −0.27 m/s 2; C): 0°, 0 m/s 2; D): −3°, 0.27 m/s 2; and E): −6°, 0.54 m/s 2. As they performed these tasks, trunk kinematics were captured using the lumbar motion monitor and trunk muscle activities were evaluated through surface electromyography. The results showed that peak sagittal plane angular acceleration was significantly higher in Condition A than in Conditions C, D and E (698°/s 2 vs. 612–617°/s 2) while peak sagittal plane angular deceleration during lowering was significantly higher in moving conditions (conditions A and E) than in the stationary condition C (538–542°/s 2 vs. 487°/s 2). The EMG results indicate that the boat motions tend to amplify the effects of the slant of the lifting surface and the external oblique musculature plays an important role in stabilizing the torso during these dynamic lifting tasks.

Dynamic excitation of cables by deck and/or tower motion

Large-amplitude cable vibrations have been observed on many major cable-stayed bridges. One possible source of excitation is movement of the deck and/or tower. Of particular concern is parametric excitation, whereby small deck/tower motion at one frequency can cause large cable motion at half the frequency under certain conditions. More commonly, deck/tower motion causes direct excitation of the cable at the same frequency in the same plane. Since cables have low damping, the response amplitudes can be large and geometric non-linearities can become important. Current design guidelines treat the axial and transverse components of end motion separately, but for an inclined cable subject to vertical deck motion at the lower anchorage and/or in-plane horizontal motion at the upper anchorage, both components occur simultaneously, modifying the behaviour considerably. This paper gives simplified results of non-linear mathematical modelling of inclined cable dynamics, with experimental validation, with the aim of providing more reliable guidelines for use in design. The proposed guidelines are summarised an appendix .

Full-scale measurements of dynamic response of suspension bridge subjected to environmental loads using GPS technology

Nowadays, there are many larger and taller engineering structures than in the past. These structures are commonly designed to be more flexible. Thus, they are sensitive to severe wind gust and earthquake tremor. For the dynamic response prediction, finite element (FE) modal updating and structural health monitoring, the dynamic characteristics of a structure are becoming increasingly important. The aim of this paper is to show an emerging tool-the real time kinematic (RTK) global positioning system (GPS), which is used to measure and monitor the low-frequency vibration of Dalian BeiDa Bridge, a medium span suspension bridge. The modal analysis is firstly performed on the developed three-dimensional FE model according to the original blue prints of the bridge to provide the analytical frequencies and mode shapes. The field ambient vibration tests using the accelerometers on the bridge deck are conducted just prior to the use of the GPS system in order to validate the FE model. And then, the calibration test is done to assess the dynamic displacement measurement accuracy of the GPS in three orthogonal directions. The GPS signal properties, such as the amplitude, standard deviations (STD), power spectral density (PSD), and probability density functions (PDF), are studied in details. After that, a structural health monitoring system based on the GPS is devised and installed on the bridge to provide real-time measurement of deck movement. The output-only modal parameter identification is carried out by using the Periodogram method to investigate the responses of the bridge. The result shows that the spectral densities of the displacements measured by the GPS correspond well with the results by the FEM analysis and the accelerometer vibration test. It is concluded that the GPS method is reliable and useful to clarify the ambient vibration response behaviors of the flexible structures. The integration of the GPS and accelerometer methods results in a hybrid arrangement that can help to eliminate some disadvantages of the two devices used separately.

Influence of Early Temperature Rise on Movements and Stress Development in Concrete Decks

The primary focus of this paper is to develop an understanding of temperature changes introduced by hydration heat release in the first few hours after casting in the thermal movements and stresses of the concrete deck and girders. Temperature and strain measurements from a simply supported, single-span, steel girder bridge with a composite concrete deck are presented. It is shown that setting occurs during the temperature rise and partial strain compatibility between steel girder and concrete deck is initiated at the end of the concrete temperature rise. Full strain compatibility between concrete deck and steel girder is achieved at the end of the cooling period following the initial temperature rise. The stresses in the steel girder associated with temperature changes are interpreted using an analytical model. It is shown that the concrete deck gains sufficient stiffness at the end of the temperature rise to restrain the movement of the top flange. Concrete deck movement in the period associated with cooling following the initial temperature rise is restrained, which could potentially produce tensile stress in concrete. The magnitude of tensile stress at the end of the cooling period depends upon the difference in the temperatures of the concrete deck and top flange and on the temperature gradient in the steel girder at the end of the heating period.

An Investigation Into the Relationship of Flexibility, Power, and Strength to Club Head Speed in Male Golfers

The purpose of this study was to investigate the relationship of flexibility, power, and strength to club head speed (CHS) in male golfers. Fifteen golfers (mean age +/- SD: 34.3 +/- 13.6 years) with a handicap of </=8 volunteered for the study. Following a standardized warm-up, subjects proceeded to hit 5 wiffle golf balls with a 5 iron while their CHS was measured. Rotational trunk flexibility was measured on a trunk rotator machine. An index of total body rotational power was measured through a hip toss with a 3-kg medicine ball while an 8-repetition maximum (RM) on a pec deck machine was used to measure chest strength. Pearson correlations were used to assess the magnitude of the relationships between CHS and the measures of flexibility, power, and strength. Partial correlations were then run to assess the effect of handicap on the observed relationships. The only variables that were significantly correlated to CHS were chest strength (r = 0.69, p < 0.05) and total body rotational power (r = 0.54, p < 0.05). These relationships were unchanged when the effect of handicap was controlled for. The results of this study show that strength of the chest in the pec deck motion and total body rotational power significantly correlate with CHS in male golfers. This information can be used by practitioners to develop training programs and field tests for golfers.

A study on aeroelastic forces due to vortex-shedding by reduced frequency response function

The vortex-induced vibration of an <TEX>${\sqcap}$</TEX>-shaped bridge deck sectional model is studied in this paper via the wind tunnel experiment. The vibratory behavior of the model shows that there is a transition of the predominant vibration mode from the vertical to the rotational degree of freedom as the wind speed increases gradually or vice versa as the wind speed decreases gradually. The vertical vibration is, however, much weaker in the latter case than in the former. This is a phenomenon which is difficult to model by existing parametric models for vortex-induced vibrations. In order to characterize the aeroelastic property of the <TEX>${\sqcap}$</TEX>-shaped sectional model, a time domain force identification scheme is proposed to identify the time history of the aeroelastic forces. After the application of the proposed method, the resultant fluid forces are re-sampled in dimensionless time domain so that reduced frequency response function (RFRF) can be obtained to explore the properties of the vortex-induced wind forces in reduced frequency domain. The RFRF model is proven effective to characterize the correlation between the wind forces and bridge deck motions, thus can explain the aeroelastic behavior of the <TEX>${\sqcap}$</TEX>-shaped sectional model.

Numerical and experimental investigation on cable vibration mitigation using shape memory alloy damper

This paper estimates the effectiveness of shape memory alloy (SMA) damper on cable vibration mitigation by numerical simulation and experimental investigation. First, a simplified constitutive law of superelastic SMA and the structure of the SMA damper developed by superelastic SMA wires are presented. Second, based on Hamilton principle and Galerkin method, the vibration equations for a cable–SMA damper system are established, and numerical solutions of which are adopted to obtain the dynamic responses of the system without and with SMA damper using the Newmark-β method. Finally, numerical simulation associated with a practical cable and experiments on a scaled test cable are, respectively, carried out to investigate the effectiveness of SMA damper on the vibration mitigation of the cable subjected to the free and forced vibration. Numerical simulations indicate that the SMA damper developed can clearly shorten the free vibration decay time of the cable and increase the equivalent damping ratios of the cable with the reasonable parameter and location of SMA damper, and that it can decrease the displacement response amplitude when the cable is subjected to white-noise excitations. The experimental results show that the SMA damper can reduce the acceleration response of the test cable under free vibration and forced vibration induced by the deck motion. As a result, the SMA damper developed is very effective for mitigating cable vibration. Copyright © 2009 John Wiley & Sons, Ltd.

Evaluation of a Tsunami Wave Load Acting on a Bridge Deck Subjected to Plunging Breaker Bores and Surging Breaker Bores

The giant earthquake of Mw=9.3 and the induced tsunami in December 26, 2004 caused the catastrophic damage of infrastructures such as coastal structures, utilities and transportation facilities. In this study, hydraulic experiments considering similarity laws were carried out to clarify a tsunami wave load to a bridge deck, focusing on the clarification of the dependence of the bridge deck lateral movement on inundation height and wave velocity induced by plunging breaker bores and surging breaker bores. Maximum ratio of the drag force to the deck weight becomes 0.31 to 0.34 when subjected to plunging breaker bores, and becomes 0.43 to 0.48 when subjected to surging breaker bores, that indicates the boundary lateral loads by which the deck movement against static friction force induced between a deck and abutments occurs.

Manual Materials Handling in Simulated Motion Environments

Seafaring occupations have been shown to place operators at an increased risk for injury. The purpose of this study was to understand better the demands of a moving environment on the ability of a person to perform specific lifting tasks. Subjects lifted a 15-kg load under four different lifting conditions. A 6-degree-of-freedom ship motion simulator imposed repeatable deck motions under foot while subjects executed the lifting tasks. Subjects were oriented in three different positions on the simulator floor to inflict different motion profiles. Electromyographic records of four muscles were collected bilaterally, and thoracolumbar kinematics were measured. A repeated-measures ANOVA was employed to assess trunk motions and muscle activities across lifting and motion conditions. The erector spinae muscles showed a trend toward significant differences for motion effects. Maximal sagittal velocities were significantly smaller for all motion states in comparison with the stable condition (p <or= .01), whereas maximum twisting and lateral bending velocities were higher (p <or= .05). Results suggest working in a moving environment will likely increase the operator's risk for overexertion injuries, particularly to the trunk region.

Investigation on the aerodynamic instability of a suspension bridge with a hexagonal cross‐section

The aerodynamic instability of a suspension bridge with a hexagonal cross‐section is investigated systematically based on a two‐dimensional model. Measurements of the dynamic responses of a sectional bridge model in the cross‐wind and torsional directions were firstly carried out in a wind tunnel. The results were used to guide and confirm the execution of parallel numerical simulations. Accordingly, both the experimental and numerical results are used as bases to examine the flow effect as well as the aeroelastic behavior of the bridge in detail. Results show that the numerical predictions of the structural responses agree well with those from the experiments, indicating that the proposed numerical method is capable of predicting the deck motion with good accuracy. Based on the time‐series numerical results, extensive investigations reveal that a hexagonal deck has much better aerodynamic stability performance than a rectangular one. Finally, among the hexagonal decks studied, it is found that one with a 30° side angle leads to the greatest critical flutter speed.

Modeling Helicopter Blade Sailing: Dynamic Formulation in the Planar Case

As part of a research project aimed at simulating rotor dynamic response during shipboard rotor startup and shutdown operations, a dynamic model of the ship–helicopter–rotor system that is appropriate for use in predicting rotor elastic response was developed. This planar model consists of a series of rigid bodies connected by rotational stiffness and damping elements that allow motion in the flapwise direction. The rotors were partitioned into an arbitrary number of rigid beam segments having the inertial and geometrical properties of a typical rotor. Helicopter suspension flexibility and damping were also modeled, although the helicopter was otherwise considered as a rigid body. Lagrange’s equation was used to derive the governing dynamic equations for the helicopter–rotor model. The effect of ship motion on blade deflection was also considered. The ship motion supplied as input to the model included representative frigate flight deck motion in three dimensions corresponding to an actual sea spectrum, ship particulars and ship operating conditions. This paper is intended to detail the dynamic approach adopted for this blade sailing study, and its conceptual validation in the planar case. The methodologies that have been developed lend themselves to easy expansion into three dimensions, and into torsion and lead/lag modeling. The amount of blade motion induced by ship motion on nonrotating helicopter blades is included. Although aerodynamic loads are a major contributor to blade sailing, this paper focuses on the dynamics aspect of the problem, and thus does not include aerodynamic effects.

Performance study of a bridge involving sliding decks and pounded abutment during a violent earthquake

This paper presents a case study on the sliding of bridge decks and pounding at abutment-backfill. It involves a multi-span concrete bridge supported on simple rubber bearings, subjected to longitudinal as well as vertical ground motions from the 1999 Chi-Chi earthquake. To account for soil–structure interaction, the stiffness and strength constants of backfill soils are determined by relating the tilting movement of the abutment to the bearing pressure of backfill soils. In order to evaluate the performance of the bridge, incremental time history analyses are conducted on a number of discrete mass-spring models to simulate various nonlinear behaviors of the bridge including frictional sliding at bearings, pounding among decks/abutments and elasto-plastic compression of backfill soils. Major parameters in the models are varied in ranges, which include gaps at expansion joints, friction coefficients at bearings, and strength limits in soils. Simulation results demonstrate that frictional sliding on bearing pads together with plastic deformation in backfill soils are essential to preventing deck fall-off disaster during large earthquakes. In the case the friction coefficient at bearings rises from 0.1 to 0.2, the maximum abutment tilting by pounding is reduced by ten times. Even if the soil strength were down by half, the maximum deck movement would be less than doubled. In any case, deck fall-off is very unlikely.

Numerical predictions on the dynamic response of a suspension bridge with a trapezoidal cross‐section

A numerical method is developed to predict the dynamic behavior of a suspension bridge under wind action in a two dimensional sense. In particular, the behavior of a vibrating deck with a trapezoidal cross‐section is examined. The simulations contain two parts of computations, which are performed alternatively during the calculation process. The solutions of the instantaneous flow field and the deck motions are considered the basis to analyze the problem of deck instability. Wind tunnel measurements are conducted in parallel to measure the response of a sectional bridge model. The vertical and torsional deflections of the model are measured under various wind speeds with several selected attack angles. The results are used to confirm the accuracy of the numerical predictions. Results show that the numerical predictions of the structural response agree well with those from the experiments, indicating that the proposed method is capable of predicting the deck motion with good accuracy. Based on the time‐series numerical results, finally, the interactive behavior of the vibrating trapezoidal deck is examined extensively.

Application of the Real-Time Kinematic Global Positioning System in Bridge Safety Monitoring

A real-time kinematic (RTK) global positioning system (GPS) has been developed and installed on the Humen Bridge (China) for on-line monitoring of bridge deck movement, which may occur as a result of seismic activity, traffic load, and such environmental elements as temperature and wind. This paper presents the main features of the on-line GPS RTK system and its value for on-line safety monitoring.

Measurements of dynamic properties of a medium span suspension bridge by using the wavelet transforms

The aim of this paper is to show the capabilities of the real-time kinematic (RTK) global positioning network system (GPS) to measure the low-frequency vibration of a medium span suspension bridge. In particular, this paper presents the results of studies conducted on the identification of modal parameters including natural frequencies, damping coefficients and mode shapes of a suspension bridge using ambient excitation loads. A real-time kinematic (RTK) global positioning system (GPS) was designed and installed on the Nottingham Wilford Bridge to provide long-term and real-time measurement of bridge deck movement. An approach to estimate modal parameters, from only output data in the time domain using the wavelet transform, is presented. Displacements responses of the bridge are used in the wavelet transform to identify its dynamic characteristics. The modal properties were extracted using a two-step methodology. In the first step, the random decrement method was used to transform random signals in free vibration responses. Secondly, a wavelets-based technique was used to extract natural frequencies and to determine the mode shapes of the structure. This method was compared with the well-established techniques eigensystem realisation algorithm showing a difference of 1% in the estimated first natural frequency. The efficiency of RTK–GPS was demonstrated in the full-scale measurement. In particular, the results showed that the RTK–GPS data can be used for extracting modal properties from in-service-loads induced low-frequency vibration (<5 Hz) by processing the signal with the wavelets transform.

On the parametric excitation of some nonlinear aeroelastic oscillators

In this paper the parametric excitation of two one-degree-of-freedom nonlinear aeroelastic oscillators in cross-flow is considered. This is for example relevant for the understanding of aeroelastic oscillations of bridge stay cables induced by bridge deck motion. In particular the parametric excitation for a plunge oscillator and a seesaw oscillator are discussed. The following model equation for the parametric excitation of the aeroelastic oscillators is considered: z ̈ +2β z ̇ +[1−κ cos(ωt)]z=F(z, z ̇ ,U) . Here, for the plunge oscillator, z denotes the vertical displacement of a mass-spring-damper system, and for the seesaw oscillator, z denotes the rotation of a seesaw structure around the hinge axis. F represents the nonlinear aeroelastic force which depends on z, ż and wind velocity U. Assuming F, the coefficients of parametric excitation κ and structural damping β to be small, the averaging method can be applied to study the equation that equation. Note that it is a nonlinear Mathieu equation. Without the parametric excitation one typically finds an aerodynamic instability for a critical wind velocity above which finite amplitude, periodic oscillations result. The parametric excitation complicates this simple picture, especially for the seesaw oscillator. Depending on the ratio of κ and β a critical wind velocity may still exist. For some cases though, increasing the wind velocity above the critical velocity re-stabilizes the trivial solution. Next to the familiar periodic constant amplitude solutions also solutions with periodically modulated amplitudes and phases are obtained. Criteria for the stability of the trivial solution, the existence and the stability of various nontrivial (periodic) solutions and their bifurcations are given.

피딩데크 운동을 고려한 광픽업 액추에이터의 동특성 해석

피딩데크 운동을 고려한 광픽업 액추에이터의 동특성 해석

On the wind loading mechanism of long-span bridge deck box sections

Box girders have been used in the last 35 years to stiffen suspension and cable-stayed bridge decks, as an alternative to truss and plate girders. Their good performance, both from the structural and from the aerodynamic points of view has been widely recognised. More recently, an improved version of the box girder, the multi-box girder has been developed, which is presently considered the state-of-the-art in terms of bridge deck aerodynamics. Nevertheless, the older truss and plate girders are still in use, and are often preferred to box girders, especially in North America and in eastern Asia. The aerodynamic behaviour of bridge deck box sections is examined in this paper. The mechanism of the wind excitation is investigated through the analysis of the mean and fluctuating deck pressure distributions, and their relation to the characteristics of the deck motion.

Modeling of cable vibration effects of cable-stayed bridges

The analysis of dynamic responses of cable-stayed bridges subjected to wind and earthquake loads generally considers only the motions of the bridge deck and pylons. The influence of the stay cable vibration on the responses of the bridge is either ignored or considered by approximate procedures. The transverse vibration of the stay cables, which can be significant in some cases, are usually neglected in previous research. In the present study, a new three-node cable element has been developed to model the transverse motions of the cables. The interactions between the cable behavior and the other parts of the bridge superstructure are considered by the concept of dynamic stiffness. The nonlinear effect of the cable caused by its self-weight is included in the formulation. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed model. The impact of cable vibration behavior on the dynamic characteristics of cable-stayed bridges is discussed.

TIME–FREQUENCY ANALYSIS OF A SUSPENSION BRIDGE BASED ON GPS

This paper describes the results obtained from full-scale measurements of Humen bridge, which is the second longest suspension bridge in China. A real-time kinematic (RTK) global positioning system (GPS) has been developed and installed on the Humen bridge for on-line monitoring of bridge deck movements. The field wind-induced vibration data were measured by this monitoring system. Three system identification techniques are then adopted in the modal analysis of the wind-induced vibration response: the time–frequency Wigner distribution (WD) technique, the frequency-domain fast Fourier transform (FFT) technique and the time-domain auto-regressive moving average vector (ARMAV) technique. The WD technique can recognize close modal coupling and non-stationary response. The FFT technique can on site verify the quality of the measurements, but its frequency resolution is low and damping estimates are unreliable. The ARMAV method allows for gaining high-frequency resolution. However, it is strictly related to the stationary hypothesis. It is a general conclusion that we can improve the quality of the analysis and get more precise characteristics of the signal by these three methods. In addition, the WD combined with ARMAV seems to be the best case in quantitative analysis of fast-changing vibration signals.