Application of magnetic field to reduce the forced response of steel bridges to high speed train

•Train-track-bridge interaction of a steel bridge is modeled to reduce bridge vibrations using a magnetic field.•The motion equations have been derived with the Lagrange method.•The motion equations obtained have been solved with the fourth-degree Runge-Kutta method.•Intensities of the magnetic field and train velocity on the interaction of the train-track-bridge system are analyzed.•It has been observed that bridge vibrations are reduced by applying a magnetic field. This paper uses a train-track-bridge interaction system to assess the dynamic performance of railway bridges exposed to a high-speed train and magnetic field. A 24° of freedom 3D train model and thin steel bridge beam are considered. In the interaction of train and bridge, a new six-parameter track system consisting of rail, sleeper, and ballast is modeled. The governing equations of the bridge, track and train motions are derived based on the Lagrange method. The Lorentz force induced by the directed magnetic field in the axial direction is obtained by Maxwell's equation. Using state-space forms, the second-order equations of motion are transformed into first-order differential equations, which are then solved using the Runge-Kutta method. Studies using parametric data are done to show how the suggested approach may be used to investigate the dynamic interaction of the entire system. The magnetic field intensities and moving train speed on the interaction of the railway bridge system were investigated and analyzed for the first time in the literature. Depending on the speed of the vehicle, when the dimensionless magnetic field is Hxm=30, it can be seen that the train body's vertical displacement falls by around 50%. The obtained results are helpful for the design of railway bridges and the safe and comfortable ride of high-speed trains over flexible structures. [Display omitted]