Vehicle–bridge interaction (VBI) elements that were derived by treating a vehicle as discrete sprung masses lack the capability to simulate the pitching effect of the car body on the vehicle and bridge responses. To overcome this drawback, a vehicle is modelled instead as a rigid beam supported by two spring-dashpot units in this paper. The equations of motion written for the vehicle and the bridge (beam) elements are coupled due to the existence of the interacting forces at contact points. To resolve this problem, the vehicle equations are first reduced to equivalent stiffness equations using Newmark's discretization scheme. Then, the vehicle degrees of freedom (DOFs) are condensed to those of the beam elements in contact. The rigid vehicle–bridge interaction elements derived can be effectively used in computation of not only the bridge response, but also the vehicle response, as required in design of high-speed railroad bridges.
International journal for numerical methods in engineering 46(7), pp.1031-1047