Vehicle-bridge interaction element for dynamic analysis

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 forming the structure equations. The applicability of the VBI element is demonstrated in the numerical studies.