Dynamic response of high speed vehicles and sustaining curved bridges under conditions of resonance

• Analysis of interacting high speed vehicles and horizontally curved bridges under resonance.
• Simulation of the three-dimensional dynamics of vehicles running over horizontally curved paths.
• Consideration of lateral-rolling and yawing deformation modes of the vehicle for the first time.
• The impact factors show the same pattern for the vertical and the radial directions.
• The feedback effect of the bridge’s resonance to the vehicle response is significant.
• The vehicle’s resonance effect on the bridge response is secondary.

This paper examines the dynamic response of vehicle(s) moving at high speeds and the sustaining horizontally curved (simple, continuous or multi-unit) bridges, when each subsystem is set into resonance. The bridge is simulated by finite elements and each vehicle as a multibody system. The coupling contact forces, between the vehicle and the bridge, are derived by adopting a rigid contact assumption. Key feature of the present study is the simulation of the three-dimensional (3D) dynamics of a vehicle running over a horizontally curved path. This simulation allows the examination of deformation modes of the 3D multibody vehicle model (e.g. related to lateral-rolling and yawing degrees of freedom) for the first time. In all cases, the numerical results agree well with pertinent analytical solutions. From the parametric study, the followings are observed: (1) The impact factors show the same pattern for the vertical and the radial directions. (2) The suspension damping can alleviate the resonance response of the car body even when the vehicle’s resonance condition is met. (3) The feedback effect of the bridge’s resonance to the vehicle response is large, but the vehicle’s resonance effect on the bridge response is quite small, especially along the vertical direction. (4) No resonance of the middle span of the continuous bridge occurs for the second mode in the vertical and the radial directions. (5) The increase in the number of spans results in both smaller displacement and lower impact factor.