Vibration of simple beams due to trains moving at high speeds

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 bridge with track irregularities by beam elements. Two sets of equations of motion that are coupled can be written, one for the bridge and the other for each of the sprung masses. To resolve the problem of coupling, the sprung mass equation is first discretized using Newmark's finite difference formulas and then condensed to that of the bridge element in contact. The element derived is referred to as the vehicle-bridge interaction element, which has the same number of degrees of freedom (DOF) as the parent element, while possessing the properties of symmetry and bandedness in element matrices. For this reason, conventional assembly procedures can be employed to ...

Vehicle-Bridge Interaction Element for Dynamic Analysis

Use of a passing vehicle to scan the fundamental bridge frequencies: An experimental verification

Vehicle–bridge interaction dynamics and potential applications

This paper is aimed at the development of a computationally efficient procedure for simulating the dynamic response of general vehicle-bridge systems. With the finite-element method, a vehicle is modeled as lumped masses supported by springs and dashpots, and a bridge with rough pavement by beam elements. An interaction element is defined to consist of a bridge element and the suspension units of the vehicle resting on the element. The composition of an interaction element and the parts of car bodies in contact is regarded as a substructure. By the dynamic condensation method, all the degrees of freedom associated with the car bodies existing within each substructure are eliminated. As the condensation has been performed on the element level, a conventional assembly process can be applied to form the structural equations. Compared with most existing procedures, the present technique appears to be computationally more efficient. It is particularly suitable for the simulation of bridges with a series of veh...

Vehicle-Bridge Interaction Analysis by Dynamic Condensation Method

In this paper, a new set of impact formulas are developed for simple and continuous beams subjected to moving vehicle loads. By modeling a vehicle as sprung masses and a bridge structure by beam elements, a parametric study is performed for various simple and continuous beams traversed by five-axle trucks. Central to this study is the adoption of a nondimensional speed parameter s , which is defined as the ratio of the driving frequency of the vehicle, as represented by πv/L, with v denoting the velocity of the vehicle and L the characteristic length of the beam, to the fundamental frequency ω of the beam. From the numerical study, it is concluded that the impact factors for the deflections, bending moments, and shear forces at the midpoints of simple beams are linearly proportional to the speed parameter, and that these formulas can be multiplied by certain modification factors to yield results for continuous beams and support shears. Other parameters studied herein include the vehicle/bridge frequency r...

B-H Lin

Papers

Vehicle-Bridge Interaction Analysis by Dynamic Condensation Method

Impact Formulas for Vehicles Moving over Simple and Continuous Beams