Yean-Seng Wu

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.

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.

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.

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.

Incrementally small-deformation theory for nonlinear analysis of structural frames

Abstract An incrementally small-deformation theory that is physically self-explainable is presented for the large-displacement nonlinear analysis of structural frames. Strictly based on the assumption of small strains, small rotations, and small displacements within each incremental step, the elastic and geometric stiffness matrices for the beam element are derived from the force–displacement relations. Due consideration is taken of the 3D rotational behavior of nodal moments. The geometric stiffness matrix derived for the element is asymmetric. However, by enforcing all the joints to remain in equilibrium in the deformed configuration, the antisymmetric parts of the geometric stiffness matrices cancel out, resulting in a symmetric stiffness matrix for the structure. Also described is the procedure for updating the element forces and geometry in an incremental-iterative analysis. The present approach in its entire set is demonstrated to be robust and efficient for solving the nonlinear, postbuckling response of structural frames.

Chaotic Behaviors of a Two-Member Truss

In the literature, comparatively few research works have been conducted on the chaotic behaviors of civil engineering structures. By taking a symmetric two-member truss as an example in this paper, one can demonstrate that it is possible for the truss to display certain chaotic phenomena, considering only the effect of geometric nonlinearity. This paper starts with the derivation of the equation of motion for the truss subjected to a vertical harmonic load, which appears to be a general form of the Duffing equation. The fourth-order Runge-Kutta method is then employed to solve for the time-history response. Based on the following two facts, it is confirmed that chaos can occur with the truss under certain loading conditions: (1) the motion of the truss is very sensitive to small changes in initial conditions; (2) strange attracters can be identified using the Poincaré plot. Both the Lyapunov numbers and fractal dimensions calculated for the truss also confirm the occurrence of chaos. From the chaos boundary curves plotted for the truss, one observes that chaos can occur for a wide range of parameter values encountered.