Numerical analysis for dynamic responses of beams subjected to moving loads with non-uniform motion

To analyze the dynamic responses of supporting beams subjected to moving loads with large velocities, large accelerations or large mass, a modeling method combining the finite element method with the modal superposition method is derived. A system of ordinary differential equations about modes coordinates is deducted, which has time-varying coefficients and can be solved by applying Newmark-β algorithm. The method is proved equivalent to the present methods by comparing references and the ABAQUS model. Through analyzing dynamic responses of supporting beams subjected to moving loads with three motion styles (uniform, accelerated and decelerated), this paper concludes that the moving loads' inertia effect is significant when a moving load has large mass, large velocity or large acceleration.