Jong-Dar Yau

Tamkang University

The advent of railways and especially highspeed railways marks great strides in human transportation history. To guarantee exclusive right-of-way, highspeed railways are often built on equal simply supported beams resting on piers. In this paper, a historical review will be given of the resonance and cancellation phenomena observed for simply suppo...

Moving constant load (MCL) models, which neglect dynamic effects of moving vehicles, are widely adopted for train-induced vibration analysis of railway bridges in current high-speed rail codes, such as Eurocode or UIC code, for simplicity in modeling trainloads to carry out response analysis of bridges. However, for light-weight highspeed railway b...

Train-induced resonance of a railway bridge occurs when the train speed coincides with the primary resonance speed (vbr) of the bridge, from which we can determine the sub-resonance speed as (vbr∕n|n=2,3). The primary resonance speed of a short bridge is generally much higher than the operation speeds of current high-speed trains but the correspond...

Dynamic vehicle–bridge interaction (VBI) plays a crucial role in the train-induced vibrations of a railway bridge for its coupling effects may reduce the bridge response and down-shift the resonant speed. The commonly used nominal theoretical resonant speed (=fbD) of a typical railway bridge, however, is only related to the bridge frequency (fb) an...

The overhead catenary system is a crucial conductor for delivering steady electric power to the trains running on modern electrified railways. The propagation of vibration waves in the catenary system is of interest to railway engineers due to the pantograph-catenary interaction. To explore the wave transmission via the contact wires of a catenary...

In this article, an adjustable frequency device based on curved beam theory is designed to control vertical stiffness of an instrumented vehicle that it can detect dynamic data when moving on a test beam for frequency measurement. The adjustable frequency device consists of a set of two-layer cantilever semi-circular thin-beams to support a lumped...

In this paper, a train–track–bridge (TTB) interaction model that can account for coach-coupler effect is presented for stochastic dynamic analysis of a train traveling over a bridge. Based on the vector form intrinsic finite element (VFIFE) method, both the bridge and non-ballasted track are discretized into a set of mass particles connected by mas...

This paper presents a new Moving Internal Node Element (MINE) method for the dynamic analysis of bridges/beam structure under a moving load/vehicle. By introducing a moving internal node within the standard beam element, the resulting MINE method eliminates the need for interpolation for the dynamic responses at the contact point between the moving...

An optimal control algorithm using a virtual tuned mass damper called virtual TMD to control the levitation force of a magnetic system is developed for resonance suppression of a maglev vehicle moving on multi-span guideway girders. Since the optimal dynamic parameters of a TMD in vibration control are well developed, the optimal tuning gains requi...

This paper is concerned with the dynamic stability and response of an inclined Euler–Bernoulli beam under a moving mass and a moving follower force. The extended Hamilton’s principle is used to derive the governing equation of motion and the boundary conditions for this general moving load/force problem. Considering a simply supported beam, one can...

The pantograph-catenary system is essential to the operation of modern railways. The overhead catenary system serves to deliver steady electric power to the trains running on the railways. The propagation of waves in the catenary system can be significantly affected by its interaction with the pantograph. To investigate the wave transmission via th...

In this study, a nonlinear model of micro arch-beams under the action of electrostatic loadings with an initial air gap is presented. Based on the well-developed 3D beam theory proposed by Yang and Kuo [4], the arch beam is modelled as a series of uniform straight beam elements and the pull-in magnetic force is simulated as an electric-induced forc...

A moving impulse load generated by a heavy cogwheel can be used as a testing excitation for bridges. This novel type of dynamic load acts along the entire driving path, its intensity is adjustable, and it can be very efficient in the case of resonance. Verification tests were performed on a model under laboratory conditions and compared to numerica...

The aim of this article is: (1) to formulate the bridge-induced dual resonance on a moving train with wave transmission; (2) to establish the dispersion relation of wave transmission in periodically linked cars using the Floquet-Bloch theorem; (3) to determine the pass and stop bands of wave transmission from the dispersion relation; and (4) to unv...

Constant moving load models are widely adopted in the dynamic analysis of railway bridges under moving trains. However, the use of this simple model may overestimate the resonant response of simply supported bridges if the vehicle-bridge interaction (VBI) effects are neglected, particularly for short spans. To account for the VBI effects, Eurocode...

A rubber rail-pad is typically inserted between the rail and the sleeper to attenuate wheel/rail vibrations for conventional train-rail-bridge (TRB) system. For mathematical modeling, a rail-fastener with rubber pad is simplified as a spring-dashpot unit, whose spring stiffness is related to the exciting frequency of external loads. To exhibit such...

An analytical study is presented for the slender suspension bridge with inclined wind-resistant ropes (i.e., wind-guys) susceptible to coupled flexural and torsional vibrations. Based on the linearized deflection theory of classical suspension bridges, the modal coupling mechanism of a single-span footbridge is studied analytically. The free vibrat...

In this paper, the modal coupling mechanism is studied of a single-span footbridge consisting of a suspended beam (i.e., bridge deck), two suspension cables (via hangers) and two wind guys (via wind ties). To start, the governing equations for the slender suspended beam are derived based on the linearized deflection theory for classical suspension...

In this paper, the vector form intrinsic finite element (VFIFE) method is presented for analysis the train–bridge systems considering the coach-coupler effect. The bridge is discretized into a group of mass particles linked by massless beam elements and the multi-body coach with suspension systems is simulated as a set of mass particles connected b...

In order to investigate the structure-borne noise of trough-girder beam and its influence factors, a 30.0 m simply-supported concrete trough-girder beam is simulated by a means of hybrid FEM-IBEM method. Firstly, the combination of SIMPACK and ANSYS simulation method is adopted to obtain the wheel/rail exciting force. Then, we can calculate the vib...

Based on the coupling nature of a vehicle moving on a bridge, Yang et al. [3] proposed an indirect bridge frequency approach, in which the bridge response can be recorded by the passing vehicle. Then the bridge frequencies can be detected from the dynamic response of the moving test vehicle. According to this concept, in this study an experimental...

For a train car moving over a multi-span continuous beam of identical span length L at constant speed v, it may encounter repetitive excitations transmitted from the sustaining beam of frequency v∕L excited by the previous passing cars. If the exciting frequency v∕L coincides with the vehicle frequency f c , namely v∕L = f c , resonance will be dev...

For a train composed of a number of identical cars moving over a bridge at high speeds, train-induced resonance on the bridge may occur when any of the frequencies of the bridge coincides with any of those implied by the wheel loads. On the other hand, for a vehicle moving over a series of bridges with identical spans at constant speeds, bridge-ind...

The wavelength characteristic is a useful clue for locating and assessing the severity of slope discontinuity in beams. In this study, the slope discontinuity of a beam is represented by an internal hinge restrained by elastic springs, and the wavelength of the beam is calculated indirectly from the vertical response of a test vehicle during its tr...

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 propert...

Vehicle response is served as a reference to evaluate riding comfort of passengers and running safety of moving carriages for high speed trains. In analyzing the vehicle-bridge interaction (VBI) problems, two sets of coupled equations of motion for running vehicles and bridge need to be solved and the VBI system matrices must be updated and factori...

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, utilisi...

As a seismic wave travels along the separate supports of an extended structure, the structure is subjected to multiple-support excitation due to seismic wave propagation. Considering the seismic wave passage effect, this paper describes seismic analysis of a maglev vehicle moving on a multiply supported gudieway. The guideway system is modeled as a...

The objective of this study is to investigate the resonance and sub-resonance acceleration response of a two-span continuous railway bridge under the passage of moving train loadings. The continuous bridge is modeled as a Bernoulli–Euler beam with uniform span length and the moving train is simulated as a series of equidistant two degrees-of-freedo...

An efficient time-integration algorithm for nonlinear dynamic analysis of structures is presented. By adopting the temporal discretization for time finite element approximation, very large time steps can be used by the algorithm. With an accuracy of fourth order, this technique requires only displacements and velocities to be made available at the...

This paper presents a study of reducing multiple resonant peaks of high-speed trains traveling over a two-span continuous railway bridge using visco-elastic (VE) dampers. The moving train is modeled as a series of two-degree-of-freedom (2 DOF) moving oscillators with identical intervals and the two-span continuous bridge as a Bernoulli-Euler beam w...

Conventionally, only three components of stress, i.e., the membrane stresses (1σ xx , 1σ yy , 1σ xy ) in x-y plane along span directions, are considered in deriving the buckling equations of thin plates using energy approaches. Of particular interest in this study is to take all the six components of stress into account in formulating the potential...

This paper presents a framework of nonlinear dynamic analysis of a low-speed moving maglev (magnetically levitated) vehicle subjected to cross winds and controlled using a clipped-LQR actuator with time delay compensation. A four degrees-of-freedom (4-DOFs) maglev-vehicle equipped with an onboard PID (Proportional-Integral-Derivative) controller tr...

Using conventional virtual work method to derive geometric stiffness of a thin-walled beam element, researchers usually have to deal with nonlinear strains with high order terms and the induced moments caused by cross sectional stress results under rotations. To simplify the laborious procedure, this study decomposes an I-beam element into three na...

Very small time steps are usually needed in numerical computation as conventional time integration methods are used to compute the response of a structure subjected to a dynamic loading with rapid changes or load discontinuity. To overcome this drawback, this study proposed a fast, fourth-order accurate step-by-step time integration (FASSTI) algori...

This paper presents an iterative interacting method for analyzing the dynamic response of a maglev train traveling on an elevated guideway supported by piers embedded in soil. The maglev train is idealized as a row of 2D rigid beams each suspended by levitation forces and controlled by onboard PID controllers. The guideway is modeled as a series of...

This paper intends to present a computational framework of aerodynamic analysis for a maglev (magnetically levitated) vehicle traveling over flexible guideways under oncoming wind loads. The guideway unit is simulated as a series of simple beams with identical span and the maglev vehicle as a rigid car body supported by levitation forces. To carry...

This paper is intended to present a preliminary framework for dynamic interaction analysis of a maglev (magnetically levitated) vehicle running on a two-span guideway using a comprehensive iterative approach. A maglev vehicle with electrodynamic suspension (EDS) system is simplified as a two degrees-of-freedom (2-DOF) maglev oscillator tuned by a P...

Geometric non-linearity becomes an issue of great concern that cannot be overlooked in the analysis of cable-supported structures since their material properties may be in an elastic range but they exhibit nonlinear behavior when loaded. This study intends to present an analytical approach for analyzing the large deflection behavior of a guyed colu...

In this paper, an efficient and accurate step-by-step time integration algorithm with unconditional stability for dynamic analysis is presented. For a dynamic system under impulsive loadings with load discontinuities, a very small time step is usually required to provide acceptable levels of accuracy in performing time history analysis. To improve...

In this paper, an efficient and accurate step-by-step time integration algorithm with unconditional stability for dynamic analysis is presented. For a dynamic system under impulsive loadings with load discontinuities, a very small time step is usually required to provide acceptable levels of accuracy in performing time history analysis. To improve...

As a maglev transport route has to cross a region with occasional earthquakes, the train/guideway interaction is an issue of great concern in dominating safety of the maglev system. This paper intends to present a computational framework of interaction analysis for a maglev train traveling over a suspension bridge shaken by horizontal earthquakes....

For dynamic analysis of a suspended beam subject to the simultaneous action of moving oscillators and multiple support motions, we need to deal with nonlinear interaction problems in conjunction with time-dependent boundary conditions. In this study, the total response of the suspended beam is decomposed into two parts: the pseudo-static response a...

This paper presents an incremental-iterative procedure to investigate the influence of ground settlement on dynamic interactions of train–bridge system. The train is simulated as a sequence of identical sprung mass units with equal intervals and the bridge system as a series of simple beams with identical properties. To resolve the train-induced vi...

The objective of this study is to investigate the dynamic response of a maglev (magnetically levitated) vehicle traveling over a series of guideway girders undergoing ground support settlement. The maglev vehicle is simulated as a rigid car body supported by a rigid levitation frame using a uniformly distributed spring–dashpot system, and the guide...

This paper is intended to present a neuro-PD (Proportional-Derivative) controller for tuning the dynamic response of a maglev vehicle running at high speeds around speficic accelration amplitude. The maglev vehicle is simulated as a rigid car body supported by a rigid magnetic bogie-set with a uniformly distributed spring-dashpot system, in which t...

As a series of maglev (magnetically levitated) vehicles travel over a flexible guideway with constant speeds, their acceleration amplitudes will be amplified significantly at resonant or higher speeds. This paper intends to develop a neuro-PI (proportional-integral) controller to control the dynamic response of the maglev vehicles around an allowab...

With the inclusion of warping deformations, lateral buckling behavior for angled frames with I-beams under the action of in-plan bending moments will be conducted in this paper. By adopting the joint equilibrium for the angled frame and the force-displacement relations for the members defined at the buckled position (rather than the initial positio...

The paper deals with the vibration of suspended bridges subjected to the simultaneous action of moving loads and vertical support motions due to earthquake. The basic partial integro-differential equation is applied to the vertical vibration of a suspended beam. The dynamic actions of traffic loads are modelled as a row of equidistant moving forces...

In this paper, an incremental iterative procedure was carried out to study aerodynamic response of an EMS-type maglev vehicle moving over a series of guideway girders at constant speeds. The maglev vehicle is simulated as a rigid car body supported by a rigid levitation frame using a uniformly distributed spring-dashpot system, in which the electro...

This paper presents a computational framework of incremental-iterative procedure for solving the dynamic response of suspended bridges under the simultaneous action of wind loads and moving train loads. For this coupled nonlinear problem due to the motion-dependent nature of the aerodynamic forces, the suspension bridge is modeled as a thin-walled...

Uniform I-beam elements are not suitable for simulating the torsional behavior of web-tapered I-beams since they fail to account for the torsional effect associated with web-tapering. To resolve this problem, an iterative approach is presented for computing the linear torsional response of web-tapered I-beams using an existing uniform I-beam elemen...

To overcome the difficulty involved in selecting proper shape functions for simulating the bending-tension coupling of a curved beam, a non-conventional “structural” approach is presented in this paper. For curved-beam elements with small subtended angles, the elastic stiffness matrix is derived as the composition of two chordwise straight beam ele...

This paper presents a first study on the vibration of a suspension bridge installed with a water pipeline and subjected to moving trains. The suspension bridge is modeled as a single-span beam suspended by the hangers and hinged at the two ends. The train is simulated as a sequence of equidistant moving loads with identical weights. The liquid flow...

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 a...

In this paper, the vibration of a suspension bridge due to moving loads of equidistant, identical forces and shaken by vertical support motions caused by earthquake is studied. The suspension bridge is modelled as a single-span suspended beam. To conduct the beam vibration with time-dependent boundary conditions, the total response of the suspended...

Since a long-term oscillation of a tuned mass damper (or TMD) in vibration control may impair the spring stiffness of the TMD, this phenomenon will directly down-tune the target frequency of the TMD. For this reason, this study intends to present a string-type tuned mass damper (or STMD) with an adjustable tuning frequency to mitigate the resonant...

This paper intends to offer an alternative approach for deriving the buckling differential equations and boundary conditions of a straight I-column subjected to various loads. Regarding a uniformly thin-walled I-column as an assembly of three flat plates (two flanges and one web) and modeling each of the plates as a Bernoulli-Euler beam with narrow...

This paper is focused on the vibration in a two-hinged arch bridge subjected to the combined action of moving loads and vertical ground excitations. The arch bridge is modeled as a flat-rise parabolic arch with constant sectional properties along the horizontal axis of span, and the train loadings over it as a sequence of identical lumped loads wit...

Previous investigations on the buckling of torsionally loaded bars indicate that the critical loads depend upon the mechanical device that generates the end torque. By representing the torsional moment on an I-section as the combination of St. Venant and warping torsions, this study presents a finite element model for buckling analysis of tapered I...

In this paper, the vertical acceleration response of a simple beam traveled by a series of equally spaced moving loads at constant speeds is studied by the superposition method. From the closed-form solution derived, the key parameters dominating the resonant response of the beam are identified, along with the effect of higher modes of vibration on...

A wideband multiple tuned mass dampers (MTMD) system has been developed for reducing the multiple resonant responses of continuous truss bridges to moving train loads. This system is composed of several MTMD subsystems, each of which consists of one set of TMD units covering a specific frequency bandwidth, but with its medium tuned to one of the fi...

This paper is aimed at investigating the dynamic response of a compound beam subjected to moving loads at high speeds. The compound beam structure is composed of a simple beam and a two- member truss connected by a set of rigid bars at the midpoint of the beam. Based on the nonlinear elastic theory of a symmetric two- member truss under the action...

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...

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 Ernst's equivalent modulus. In particular, the previously derived vehicle–bridge interac...

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 t...

Geometric nonlinear analysis of structures is not a simple extension from its counterpart of linear analysis. In this article, some research works conducted primarily in the past two decades on the geometric nonlinear analysis of framed structures that are readily available to the authors, including, in particular, those conducted by the senior aut...

Conventionally, seismic design of building structures is based on the concept of increasing the resistance capacity of the structures against earthquakes by employing, for example, the use of shear walls, braced frames, or moment-resistant frames. However, these traditional methods often result in high floor accelerations for stiff buildings, or la...

In this paper, the dynamic response of bridge girders with elastic bearings to moving train loads is studied using an analytical approach. Such a problem hàs not been very well investigated in the literature. The present results indicate that the dynamic response of the beam at resonance remains generally constant, if the effect of damping is taken...

In this paper, the dynamic response of beams with simple supports to moving train loads is studied using an analytical approach. The present results indicate that the dynamic response of the beam at resonance remains rather bounded, if the effect of damping is taken into account. An envelope impact formula is proposed for the deflection of the beam...

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 com...

In this paper, the vibration of continuous bridges subjected to the passage of high-speed trains is studied. Only the bridges with uniform spans are considered and the train moving over a bridge is modeled as a series of moving loads. According to the resonant formula of simple beams to moving loads, the effect of multiple resonant peaks for contin...

Analytic solutions are derived for a horizontal curved beam subjected to vertical and horizontal moving loads. The horizontal moving loads may be regarded as the centrifugal forces generated by vehicles moving along a curved path, which were rarely studied by previous researchers. Both a single moving load and a series of equidistant moving loads a...

Vehicle–bridge interaction (VBI) elements that were derived by treating a vehicle as discrete sprung masses lack the capability to simulate the pitching effect of the car body on the vehicle and bridge responses. To overcome this drawback, a vehicle is modelled instead as a rigid beam supported by two spring-dashpot units in this paper. The equatio...

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...

According to the rigid body rule, for a solid member subjected to rigid body rotations, the initial forces acting on the member that form an equilibrating set must rotate following the rigid body rotations, while remaining unchanged in magnitude. Such a rule is physically intuitive and is employed in this paper to derive an approximate geometric st...

The impact response of moving vehicles on bridges is an important factor that must be considered in the design of bridges. Research on this problem dates from the mid-nineteenth century. Early studies of vehicle-bridge interaction problems concentrated primarily on the impact response of simply supported bridges traversed by simple vehicle models a...

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 respo...

The objective of this study is to develop an element that is both accurate and efficient for modeling the vehicle-bridge interaction (VBI) in analysis of railway bridges carrying high-speed trains, which may consist of a number of cars in connection. In this study, a train is modeled as a series of sprung masses lumped at the bogie positions and a...

In computing the critical load for a linear nonconservative system, one needs to construct the load-frequency curve from the characteristic equation that contains asymmetric matrices, based on the finite element formulation. Traditionally, this requires repeated solution of complex eigenvalues from the characteristic equation at many load levels, w...

This chapter focuses on some fundamental points regarding the formulation of buckling equations for tapered beams. Unlike conventional studies that consider only three components of stress, this study considers all the six components of stress in the derivation of the buckling equations for tapered beams. By invoking the conditions of equilibrium f...

A torque may be classified as semi- or quasi-tangential, depending on whether it is generated by two couples or one couple of direct forces. Both types of torque may cause a torsionally loaded bar to buckle at certain critical values. This paper presents an analytical approach for investigating the instability of tapered bars of circular cross-sect...

That straight-beam elements cannot be used to study the buckling of curved beams is an incorrect argument made by previous researchers. The inconsistency originates largely from their overlooking the moment terms induced by initial bending moments undergoing three-dimensional rotations, which, in principle, is a violation to the rule that all physi...

A torque may be classified as semitangential or quasitangential, according to the way in which it is generated. Both types of torques may cause a torsionally loaded bar to buckle at certain critical values. This paper investigates the instability of an initially straight but pretwisted bar subjected to a semi- or quasi-tangential torque. The govern...

The purposes of the paper are: (1) To derive differential equations of equilibrium for a tapered I-beam; and (2) to formulate a finite element for the beam that takes into account the effect of nonuniform torsion. In the virtual work formulation, the updated Lagrangian approach is adopted, in which the effect of geometric nonlinearity is considered...

This paper deals with the vibration suppression of railway bridges subjected to the passage of high-speed trains. In a practical design, the impact factor is used to evaluate the dynamic amplification effect of a bridge due to the action of vehicles moving over it. In this study, the impact factor I is defined as the ratio of the maximum dynamic to...