Yeong-Bin Yang

Vibration of simple beams due to trains moving at high speeds

To investigate the vibration of simple beams subjected to the passage of high speed trains, a train is modeled as the composition of two subsystems of wheel loads of constant intervals, with one consisting of all the front wheel assemblies and the other the rear assemblies. By an analytical approach, the key parameters that govern the dynamic responses of the beams are identified, using the moving load assumption. To evaluate the inertia effect of moving vehicles, numerical solutions are obtained using Newmarks β method. Based on the condition of resonance and the condition of cancellation for the waves generated by continuously moving loads on the beam, optimal design criteria that are effective for suppressing the resonant responses are proposed. In designing a high speed railway bridge, such criteria should be considered in selecting the span length and cross-section of the beam, given the car length, axle distance and operating speed of the train.

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.

Train-induced wave propagation in layered soils using finite/infinite element simulation

In this paper, the transmissibility of soils for vibrations induced by trains moving at different speeds is studied. The 2.5 D finite/infinite element approach adopted herein allows us to consider the load-moving effect of the train in the direction normal to the two-dimensional profile of the soils considered, and, therefore, to obtain three-dimensional responses for the soils using only plane elements. The moving train is simulated by a sequence of moving wheel loads that may vibrate with certain frequency. Two train speeds are considered, one is smaller and the other is greater than the Rayleigh wave speed of the layered soils, to represent the effects of speed in the sub-critical and super-critical ranges. In order to evaluate the effect of each parameter on the ground response induced by moving trains, parametric studies are conducted for the following parameters: the shear wave speed, damping ratio and stratum depth of the supporting soils, and the moving speed and vibration frequency of the traveling trains. Conclusions concerning the mechanism of wave propagation in layered soils are drawn from the parametric studies, which should prove useful to practicing engineers.

A versatile element for analyzing vehicle-bridge interaction response

Abstract In this paper, a versatile element that is capable of treating various vehicle–bridge interaction (VBI) effects is derived. Central to the present formulation is the use of Newmarks finite difference scheme to discretize the vehicle equations of motion. This enables us to relate first the contact forces to the wheel displacements. Through use of the no-jump condition for vehicles, the contact forces can then be related to the contact displacements of the bridge. As such, a VBI element that considers all of the interaction effects can be derived from the bridge equations, which enables us to compute the vehicle response, contact forces and bridge response with no iterations required. The present procedure is versatile in that it allows us to deal with vehicle models of various complexities, ranging from the moving load, moving mass, sprung mass, to suspended rigid bar, and so on. The capability of the present procedure is demonstrated in the study of various VBI phenomena, including those caused by vehicles in braking.

A PARAMETRIC STUDY OF WAVE BARRIERS FOR REDUCTION OF TRAIN-INDUCED VIBRATIONS

In this paper, a finite/infinite element scheme developed previously by the authors is employed to investigate the effectiveness of three different wave barriers, i.e., the open trench, in-filled trench, and elastic foundation, in reducing the ground vibrations caused by the passage of trains. The mathematical model adopted herein is the two-dimensional profile that contains the cross-section of the railway, barrier and underlying soils, with the moving train loads simulated as a vertical harmonic line load. Concerning the effect of isolation, the geometric and material parameters of the three barriers investigated include the distance to rail, depth, width and thickness, damping ratio, shear modulus, mass density, Poissons ratio, elastic modulus, etc. Also examined is the effectiveness of the three barriers with respect to different exciting frequencies. Conclusions are made regarding the selection of optimal parameter values for the three barriers in isolating the train-induced ground vibrations.

Steady-state response and riding comfort of trains moving over a series of simply supported bridges

Abstract This paper deals with the 2D steady-state response and riding comfort of a train moving over a series of simply supported railway bridges, together with the impact response of the rails and bridges. The dynamic response of the vehicle-rails-bridge interaction system is solved by a condensation technique developed previously. For the moving train to achieve the steady-state response, a bridge segment consisting of a minimal number of units should be considered. Track irregularity with random nature is considered through use of a power spectral density (PSD) function. The steady-state response of the train, rails and bridges, together with the fast Fourier transform (FFT) of the response, are computed and discussed. The impact responses of the rails and bridges under different train speeds are investigated using the impact factors. The maximum response of the train caused by the train-rail-bridge resonance is identified. Finally, the riding comfort of the trains moving over tracks of different classes of irregularities is assessed using Sperling’s ride index.

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.

Impact response of high speed rail bridges and riding comfort of rail cars

The vibration of simple and three-span continuous beams traveled by trains moving at high speeds is studied in this paper. Central to this study is the adoption of a dimensionless speed parameter S, defined as the ratio of the exciting frequency of the moving vehicles to the fundamental frequency of the beam. The numerical studies indicate that the moving load model is generally accurate for simulating the bridge response. However, the use of the sprung mass model is necessary whenever the riding comfort of rail cars is of concern. If the characteristic length, rather than the span length, is used for the continuous beam, then both the simple and continuous beams will reach their peak responses at the same critical speed S, when traveled by wheel loads of constant intervals. The rail irregularity, ballast stiffness, suspension stiffness and suspension damping can drastically affect the riding comfort of rail cars traveling over simple beams. Their effects are comparatively small for continuous beams. In conclusion, the design of a high speed rail bridge is governed primarily by the conditions of serviceability, rather than by strength.

Three-Dimensional Analysis of Train-Rail-Bridge Interaction Problems

A vehicle-rail-bridge interaction (VRBI) model for analysing the 3D dynamic interaction between the moving trains and railway bridge was developed. By the dynamic condensation scheme, three types of vehicle-rail interaction (VRI) elements were derived, by which the vehicle and bridge responses, as well as the wheel / rail contact forces, can be computed. Track irregularity of random nature was taken into account. The results indicate that resonance can occur in both the lateral and torsional vibrations of the bridge, as well as in the vertical vibration. Under the crossing of two face-to-face moving trains, the vertical vibration of the bridge is greatly intensified, while the lateral and torsional responses may be increased or reduced, depending on how the two trains cross each other. Finally, two common indices are used to assess the possibility of derailment for trains passing over the bridge at different speeds.