Y.S. Cheng

Vibration of railway bridges under a moving train by using bridge-track-vehicle element

During the last two decades, much attention has been paid to various vibration problems associated with railways. They include the dynamic response of railway bridges and railway tracks at grade under the action of moving trains. However, studies on the role of track structures on the vibration of railway bridges are rather limited. In this paper, a new element called bridge-track-vehicle element is proposed for investigating the interactions among a moving train, and its supporting railway track structure and bridge structure. The moving train is modelled as a series of two-degree-of-freedom mass-spring-damper systems at the axle locations. A bridge-track-vehicle element consists of vehicles modelled as mass-spring-damper systems, an upper beam element to model the rails and a lower beam element to model the bridge deck. The two beam elements are interconnected by a series of springs and dampers to model the rail bed. The investigation shows that the effect of track structure on the dynamic response of bridge structure is insignificant. However, the effect of the bridge structure on the dynamic response of the track structure is considerable.

On the determination of natural frequencies and mode shapes of cable-stayed bridges

Abstract An accurate analysis of the natural frequencies and mode shapes of a cable-stayed bridge is fundamental to the solution of its dynamic responses due to seismic, wind and traffic loads. In most previous studies, the stay cables have been modelled as single truss elements in conventional finite element analysis. This method is simple but it is inadequate for the accurate dynamic analysis of a cable-stayed bridge because it essentially precludes the transverse cable vibrations. This paper presents a comprehensive study of various modelling schemes for the dynamic analysis of cable-stayed bridges. The modelling schemes studied include the finite element method and the dynamic stiffness method. Both the mesh options of modelling each stay cable as a single truss element with an equivalent modulus and modelling each stay cable by a number of cable elements with the original modulus are studied. Their capability to account for transverse cable vibrations in the overall dynamic analysis as well as their accuracy and efficiency are investigated.

Effects of random road surface roughness and long-term deflection of prestressed concrete girder and cable-stayed bridges on impact due to moving vehicles

The effects of random road surface roughness and long-term deflection of prestressed concrete bridges on the impact effects due to moving vehicles are investigated. The concrete bridges studied include multi-span girder bridges and cable-stayed bridges. The random road surface roughness is described by a zero-mean stationary Gaussian random process, while the long-term deflection of the concrete deck is represented as a kind of global roadway surface roughness in the study. The bridge is modelled by finite element method. Each moving vehicle is idealised as a one-foot dynamic system, in which a mass is supported by a spring and a dashpot. Numerical results show that the effect of random road surface roughness on the impact induced by moving vehicles is significant in the girder bridges, while that of the long-term deflection of concrete deck is small to moderate. The impact effects of the random road surface roughness and the long-term deflection of concrete deck on a cable-stayed bridge vary a lot depending on the location. In general, such effects on the bridge deck are more significant at sections closed to the bridge towers. Such effects on the bending moment at the tower base are also significant. The effects on the stay cables vary much, with significant effects on the short cables and negligible effects on the longest cables.

Vibration Analysis of Bridges Under Moving Vehicles and Trains

Publisher Summary This chapter discusses the vibration of bridges under moving vehicles and trains, which is of great theoretical and practical significance in civil engineering. The chapter describes some recent developments in the vibration analysis of girder and slab bridges under the action of moving vehicles or trains. A bridge-track-vehicle element is developed for investigating the dynamic interactions among a moving train, its supporting railway track structure, and the bridge structure. The effect of track structure on the dynamic response of the bridge structure and the effect of bridge structure on that of the track structure are identified. The proposed bridge-track-vehicle element can be easily degenerated to a vehicle-beam element, which is employed to study the effects of the random road surface roughness and the long-term deflection of concrete deck on the dynamic response of a girder bridge. The chapter also describes the plate-vehicle strip for simulating the interaction between a rectangular slab bridge and moving vehicles. It also explains two kinds of plate finite strips—namely, the plate-vehicle strip and the conventional plate strip, which are employed to model a slab bridge. In the analysis, each moving vehicle is idealized as a one-foot dynamic system with the unsprung mass and sprung mass interconnected by a spring and a dashpot. A train is modeled as a series of moving vehicles at the axle locations. The efficiency and accuracy of the proposed methods are demonstrated in the chapter by numerical examples.