Non-stationary random vibration analysis of three-dimensional train–bridge systems

Sensitivity analysis and optimization of vehicle–bridge systems based on combined PEM–PIM strategy

“…Lu and Zhang [25,26] applied three kinds of precise integration techniques to the coupled dynamic analysis for bridges subjected to moving harmonic loads, and the efficiency and computational accuracy were also numerically justified. As a vehicle crosses a bridge, the interaction forces at the contact points are related to the vertical displacements, velocities and accelerations of the bridge at these points.…”

“…In FEM, external loads must be replaced by equivalent nodal forces and so the vehicle load is decomposed, at time t = t k + s, into the equivalent nodal forces f i (t). The direct decomposition scheme [26], the development of which is based on the equilibrium principle of parallel force systems, can be applied when it is necessary to decompose a force at any arbitrary internal point of an element into an equivalent force system applied at the nodes. This method not only reduces the computational cost considerably, but is also very easy to understand and convenient to program.…”

Dynamic Characteristics of Coupled Vehicle–Track–Tunnel Interaction System

“…Therefore, the geometric size of the 3D finite element model can be thrice the hole height over the tunnel arc along the horizontal direction, and the tunnel bottom was larger than the hole height. According to existing experimental data and computing parameters, the longitudinal length of the model should be at least 24 sleeper bays to ensure computing accuracy [3][4][5][6]. In the established model, the longitudinal length of the tunnel was 50 m. The constraints of the artificial boundary in the model include horizontal constraint at the side surface and fixed constraint at the bottom surface.…”

“…Then, coupling vehicle and track-tunnel vibration equations were converted into independent modal equations. The low-orders of vibration modes were selected in the computation because the vibration of structures is mainly controlled by several low-order vibration modes [4,5]. Therefore, only orders of vibration mode at contact point between wheelset and rail or rail nodes were analysed.…”

“…Currently, studies on vehicle-tunnel coupled dynamics mainly focus on solving the dynamic equation of vehicle running on an irregular track [1][2][3][4][5], which were summarized into "vehicle dynamics," "track dynamics," and "wheel-track interaction" [5][6][7][8][9]. Established coupling models can be divided into two types, namely vehicle-track system [6] and vehicletrack-roadbed system [7].…”