This study investigates the dynamic responses of cracked beams placed on a visco-elastic foundation and subjected to moving loads. Utilizing the Euler–Bernoulli beam model, the behavior of the beams is characterized, accounting for multiple open cracks on one side with varying depths. Through the application of Fourier transform techniques and Green's function, the dynamic response of the beam is analytically determined in the frequency domain. Furthermore, an analytical model for railway sleepers is developed by integrating them with a periodically supported beam model. This integrated model enables efficient computation of the dynamic behavior of damaged sleepers, where cracks are present at specific locations. Additionally, a calculation model utilizing the finite element method is established and compared with the analytical model. The parametric study shows the influence of crack properties on the dynamic beam responses
