J.D. Yau

Vehicle-bridge interaction dynamics: with applications to high-speed railways

The commercial operation of the bullet train in 1964 in Japan marked the beginning of a new era for high-speed railways. Because of the huge amount of kinetic energy carried at high speeds, a train may interact significantly with the bridge and even resonate with it under certain circumstances. Equally important is the riding comfort of the train cars, which relates closely to the maneuverability of the train during its passage over the bridge at high speeds. This book is unique in that it is devoted entirely to the interaction between the supporting bridges and moving trains, the so-called vehicle-bridge interaction (VBI). Finite element procedures have been developed to treat interaction problems of various complexities, while the analytical solutions established for some typical problems are helpful for identifying the key parameters involved. Besides, some field tests were coducted to verify the theories established. This book provides an up-to-date coverage of research conducted on various aspects of the VBI problems. Using the series of VBI elements derived, the authors study a number of frontier problems, including the impact response of bridges with elastic bearings, the dynamic respose of curved beam to moving centrifugal forces, the stability and derailment of trains moving over bridges shaken by earthquakes, the impact response of two trains crossing on a bridge, the steady-state response of trains moving over elevated bridges, and so on.

Extracting bridge frequencies from the dynamic response of a passing vehicle

Abstract The frequencies of vibration of bridges represent a kind of information that is most useful for many purposes. Traditional vibration tests aimed at measuring the bridge frequencies often require on-site installation of the measurement equipment, which is not only costly, but also inconvenient. As a first attempt, the idea of using a vehicle moving over a bridge as a message carrier of the dynamic properties of the bridge is theoretically explored in this paper. In order to identify the key parameters dominating the vehicle–bridge interaction response, while illustrating the key phenomena involved, assumptions that lead to closed-form solutions are adopted in the analytical study. For instance, a vehicle is modelled as a sprung mass, and a bridge as a simply supported beam considering only the first mode of vibration. The concept of extracting bridge frequencies from a passing vehicle, however, is not restricted by the aforementioned assumptions, as will be demonstrated in an independent finite element study, which do not rely on any particular assumptions. Concluding remarks are given concerning the feasibility of extracting the bridge frequencies from the dynamic response of a passing vehicle, along with directions for future research identified.

Vibration reduction for cable-stayed bridges traveled by high-speed trains

The vibration reduction of cable-stayed bridges subjected to the passage of high-speed trains is studied. The train is modeled as a series of sprung masses, the bridge deck and towers by nonlinear beam-column elements, and the stay cables by truss elements with Ernsts equivalent modulus. In particular, the previously derived vehicle-bridge interaction element is employed to simulate the dynamic interaction of the moving vehicles with the bridge. In order to reduce the multiple resonant peaks of the cable-stayed bridge subjected to high-speed trains, a hybrid tuned mass damper system composed of several subsystems is proposed. The mass of each subsystem tuned for one resonant frequency is determined by first minimizing each peak response using Den Hartogs optimal criterion and by enforcing the resonant peaks of concern to be equal. The optimal properties of each subsystem are determined by the minimum-maximum approach. The strategy of vibration reduction proposed herein is simple and robust, which should find applications in areas where multiple resonant peaks are a problem of major concern.

Mechanism of resonance and cancellation for train-induced vibrations on bridges with elastic bearings

In this paper, the mechanism involved in the phenomena of resonance and cancellation in the train-induced vibrations of railway bridges with elastic bearings is explained using an analytical approach. The train is modelled as a sequence of moving loads of constant intervals. The vibration shape of the elastically supported beam is approximated by the combination of a flexural sine mode and a rigid body mode. The present results indicate that under certain conditions, resonances of much higher peaks can be excited on elastically supported beams by moving trains at much lower speeds than those on simply supported beams. The cancellation is a phenomenon more decisive than that of resonance, in that it can suppress the latter even when the condition of resonance is met. Moreover, the speed for cancellation to occur is generally independent of the support stiffness. To verify the analytical results presented herein, a field test was conducted on two adjacent elastically supported bridges in existing railway lines. In the design of railway bridges, it is important that the phenomenon of resonance not be overlooked, as it is harmful not only to the riding comfort of passengers, but to the maintenance of railway tracks.

Vibration reduction of elastically supported beams under moving loads by tuned mass devices

This study is aimed at the physical interpretation of the function of a tuned mass (TM) in suppressing the vibration response of an elastically supported beam to a moving train. The train is simulated as a sequence of moving loads, and the vibration shape of the elastically supported beam is approximated as the combination of a flexural sine mode and a rigid body mode. By distinguishing free vibration from forced vibration, resonance of the beam is identified as the superposition of the free vibrations induced by the moving loads that are in phase. The reverse is also true for the phenomenon of cancellation. Moreover, the mechanism of the TM in reducing the resonant response of the beam to the moving loads can be interpreted using similar concepts. From the parametric study, it is concluded that the use of a mass ratio of 0.01 is most efficient for the TM. To achieve the greatest effect of mitigation, the frequency of the TM should be tuned to that of the elastically supported beam.

SEISMIC RESPONSE OF AN ARCH-BEAM INTERACTING WITH SEQUENTIAL MOVING TRAIN LOADS

Considering the axial-flexural coupling nature of an arch bridge subjected to seismic wave, this paper is aimed at investigation of dynamic response for a train moving over a railway arch-bridge shaken by horizontal ground motions. For analytical formulation, the arch bridge is idealized as a flat-rise parabolic arch with constant sectional properties uniformly distributed along the horizontal span and the train moving over it as a sequence of identical sprung mass units with constant intervals. To perform dynamic analysis of vehicle-bridge system shaken by horizontal earthquakes, an incremental-iterative procedure is proposed in this study. From numerical results, the multiple support motion induced by seismic wave propagation plays a key factor in affecting the dynamic response of the arch-bridge/vehicle system during earthquakes.

A new buckling theory for curved beams of solid cross sections derived from rigid body and force equilibrium considerations

A new method is proposed for deriving the instability potential of initially stressed curved beams based on the rigid body and equilibrium considerations using the updated Lagrangian formulation. Starting from the rigid body rule, the virtual instability potential was derived for a spatially curved beam under real rigid displacements. Next, utilising the equilibrium equations for the boundary forces at the C1 and C2 states, another virtual instability potential was derived for the curved beam under virtual rigid displacements. Comparing the two potentials yields the one in total form for the curved beam. The present approach requires only simple integrations and analogical comparison of related virtual works, thereby avoiding the physically unclear, complicated derivations involved in previous procedures. Based on the first principles of rigid body rule and equilibrium, the derived potential energy is more concise than the conventional approach that requires the consideration of six stress components in the formulation. As an illustration, the present theory was successfully adopted in the buckling analysis of helical curved beams under radial loads.