An efficient algorithm for dynamic analysis of bridges under moving vehicles using a coupled modal and physical components approach

A general and efficient method is proposed for the resolution of the dynamic interaction problem between a bridge, discretized by a three-dimensional finite element model, and a dynamic system of vehicles running at a prescribed speed. The resolution is easily performed with a step-by-step solution technique using the central difference scheme to solve the coupled equation system. This leads to a modified mass matrix called a pseudo-static matrix, for which its inverse is known at each time step without any numerical effort. The method uses a modal superposition technique for the bridge components. The coupled system vectors contain both physical and modal components. The physical components are the degrees of freedom of a vehicle modelled as linear discrete mass-spring-damper systems. The modal components are the degrees of freedom of a linear finite element model of the bridge. In this context, the resolution of the eigenvalue problem for the bridge is indispensable. The elimination of the interaction forces between the two systems (bridge and vehicles) gives a unique coupled system (supersystem) containing the modal and physical components. In this study, we duly consider the bridge pavement as a random irregularity surface. The comparison between this study and the uncoupled iterative method is performed. (C) 1998 Academic Press Limited.