A Mathematical Treatise On Vibrations In Railway Bridges

Originally published in 1934, this book studies the dynamic effects in railway bridges, produced by the action of locomotives and other moving loads.

The dynamic behaviour of bridges strongly affects the infrastructure system of high-speed railways, and is a crucial factor in safety issues and passenger comfort. Dynamics of High-Speed Railway Bridges covers the latest research in this field, including: Recently developed dynamic analysis techniques; Train excitations; Design issues fo

Bridges’ Dynamics covers the historical review of research and introductory mathematical concepts related to the structural dynamics of bridges. The e-book explains the theory behind engineering aspects such as 1) dynamic loadings, 2) mathematical concepts (calculus elements of variations, the d’ Alembert principle, Lagrange’s equation, the Hamilton principle, the equations of Heilig, and the δ and H functions), 3) moving loads, 4) bridge support mechanics (one, two and three span beams), 5) Static systems under dynamic loading 6) aero-elasticity, 7) space problems (2D and 3D) and 8) absorb systems (equations governing the behavior of the bridge-absorber system). The e-book is a useful introductory textbook for civil engineers interested in the theory of bridge structures.

The Fifth Edition of this classic work retains the most useful portions of Timoshenko's book on vibration theory and introduces powerful, modern computational techniques. The normal mode method is emphasized for linear multi-degree and infinite-degree-of-freedom systems and numerical methods dominate the approach to nonlinear systems. A new chapter on the finite-element method serves to show how any continuous system can be discretized for the purpose of simplifying the analysis. Includes revised problems, examples of applications and computer programs.

' 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 conducted 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 response 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. Contents:Moving Load Problems:Impact Response of Simply-Supported BeamsImpact Response of Railway Bridges with Elastic BearingsMechanism of Resonance and Cancellation for Elastically-Supported BeamsCurved Beams Subjected to Vertical and Horizontal Moving LoadsInteraction Dynamics Problems:Vehicle—Bridge Interaction Element Based on Dynamic CondensationVehicle—Bridge Interaction Element Considering Pitching EffectModeling of Vehicle—Bridge Interactions by the Concept of Contact ForcesVehicle—Rails—Bridge Interaction — Two-Dimensional ModelingVehicle—Rails—Bridge Interaction — Three-Dimensional ModelingStability of Trains Moving over Bridges Shaken by Earthquakes Readership: Graduate students, researchers and engineers in bridge and structural dynamics. Keywords:Bridge;Derailment;Earthquake;High-Speed Railway;Impact;Moving Load;Resonance;Riding Comfort;Vehicle–Bridge Interaction;TrainKey Features:Up-to-date coverage of research on vehicle-bridge interactionsMost problems related to high-speed railway bridges have been investigated; many of them are beyond the scope of traditional books focused only on moving load problemsReviews:“This book is well and understandably written at a high level … In summary, it can be warmly recommended to anybody who is working in structural dynamics, scientists, engineers and students of bridge engineering and generally to anybody who wishes to gain a wealth of knowledge and insight into the problem.”Journal of Sound and Vibration '