Formulation of three-dimensional equations of motion for train–slab track–bridge interaction system and its application to random vibration analysis

• A three-dimensional model of train–slab track–bridge coupling system is established.
• The three-dimensional equations of motion for the interaction system consisting of a moving train, slab track, and bridge are derived.
• The excitations between a wheel and rail are formulated by the pseudo-excitation method.
• An approach with greater efficiency and accuracy to evaluating the random vibration characteristics of the system is presented.

This study presents the formulation of three-dimensional equations of motion for a train–slab track–bridge interaction system and its application to random vibration analysis using the finite element and pseudo-excitation methods. In this study, a train, slab track, and bridge are regarded as an integrated system, each vehicle is modeled as a four-wheelset mass-spring-damper system with a two-layer suspension system at 23 degrees of freedom, and the rail, slab, girder, and pier are modeled as elastic Bernoulli–Euler beams connected with each other by discrete or continuous spring and damper elements. Three-dimensional equations of motion for the entire system are derived using the energy principle. Dynamic contact forces between moving vehicles and rails are considered as internal forces, and thus, the excitation vectors of load between a wheel and rail, induced by a vehicle's weight and random track irregularities, are easily formulated using the pseudo-excitation method. These equations can be solved by a step-by-step integration method to simultaneously obtain the random dynamic responses of the system. The three-dimensional random vibration characteristics of the system are investigated using an example of a nine-span simply supported beam bridge on which a train consisting of 8 cars travels.