Firstly, this study proposes an original scheme for the three-dimensional (3D) analysis of the dynamic interaction between trains and horizontally curved railway bridges. Key features are the 3D formulations for both the vehicle system and the bridge system, and the condensed matrix statement of the equations of motion. The scheme is readily applicable for different kinds of bridges (both straight and curved bridges) and vehicle models, or different numbers of vehicles, various types of external loads (e.g. seismic loads or wind loads), by adjusting the pertinent matrices or vectors. Then, the analysis brings forward the interaction along the radial and the torsional sense of curved bridges, which are typically neglected for straight bridges. Specifically, the study presents a ‘competit...[ Read more ]

Firstly, this study proposes an original scheme for the three-dimensional (3D) analysis of the dynamic interaction between trains and horizontally curved railway bridges. Key features are the 3D formulations for both the vehicle system and the bridge system, and the condensed matrix statement of the equations of motion. The scheme is readily applicable for different kinds of bridges (both straight and curved bridges) and vehicle models, or different numbers of vehicles, various types of external loads (e.g. seismic loads or wind loads), by adjusting the pertinent matrices or vectors. Then, the analysis brings forward the interaction along the radial and the torsional sense of curved bridges, which are typically neglected for straight bridges. Specifically, the study presents a ‘competition’ between the excitations generated by the curved path (centrifugal forces and coriolis forces), the external loads (e.g. seismic loads or wind loads) and the self-excitations of the system (rail irregularities and the wheelset hunting motion of the vehicle). Further, the study examines the simultaneous response of the interacting vehicle-bridge system with the proposed 3D VBI analysis approach, when each subsystem is set into resonance. The simulation allows the examination of deformation modes of the fully 3D multibody vehicle model (e.g. related to lateral-rolling and yawing degrees of freedom) for the first time. The study also examines the seismic response of an interacting vehicle-bridge system, under frequent and strong earthquakes.

The study models the vehicles as multibody assemblies, and simulates the straight or horizontally curved bridges with the finite element method (FEM). Specifically, an additional moving trajectory system is employed to describe the 3D dynamics of the vehicles along the curved path. The solution of the global equations of motion provides the response of both the bridge and the vehicle simultaneously. The mass matrix, the stiffness matrix, the damping matrix and the loading vector of the global system all become time-dependent, reflecting the physical reality of the VBI phenomenon. The normal contact forces are derived based on kinematic constraints on the acceleration level. As a first approach a simple tangential contact model is adopted, which is based on a zero tangential contact acceleration kinematic constraint. Later, a more complicated and more realistic tangential contact model considers creep forces and creep moments due to the rolling contact. In order to capture the wheel-rail separation (uplifting) and recontact phenomena under extreme situations (e.g. strong earthquakes), the proposed scheme employs a nonsmooth approach to the model the wheel-rail contact. A most recently proposed algorithm considers the nonlinear wheel and rail profiles and kinematics. The study accounts for the self-excitations, such as the elevation and the alignment irregularities, the wheelset hunting motion and the subsequent rolling rotation due to the conicity of the wheels. The study also considers the track eccentricity (offset) with respect to the bridge deck shear center, the effect of the cant angle and the entry spiral curve (for curved bridges). A numerical simulation computer program is developed using the available commercial programing software MATALB. The multibody vehicle model and the finite element bridge model are modelled with the commercially available software ANSYS. The associated matrices of the vehicle and the bridge subsystems from ANSYS are exported to MATLAB. The post-processing of the response, i.e., the visualization of the deformation of both the vehicle and the bridge, is employed again the software ANSYS.