Vibration response of beams supported by finite-thickness elastic foundation under a moving concentrated force

This paper derives the motion equation for a Winkler foundation beam considering the movement of a finite-thickness soil mass under a moving concentrated force. The decay function of foundation displacement is introduced to facilitate this analysis. Using the modal superposition method, displacement formulas for both the forced and free vibration stages of the finite beam are obtained, considering a moving concentrated force. Through numerical calculations and parametric analysis, this study assesses the impact of soil mass, soil damping, and subgrade reaction coefficient on the vibration response of an Euler-Bernoulli beam. The results demonstrate that an increase in soil mass significantly reduces the critical velocity. The effect of soil mass motion on the beam's vibration response is closely tied to the moving speed of the load. Additionally, as soil damping increases, both the vibration cancellation phenomenon and resonance are suppressed. The subgrade reaction coefficient prevents the occurrence of a complete vibration cancellation point in the elastic foundation beam system.