Analysis of dynamic response of infinite beam on a periodical viscoelastic foundation subjected to moving loads and calculation of the critical train speed

The dynamic behaviour of infinite beams resting on a homogeneous foundation subjected to moving loads has been extensively analysed through analytical methods. However, these approaches are not directly applicable to non-homogeneous foundations. This study presents an analytical framework for modelling infinite beams supported by a periodically varying viscoelastic foundation, wherein the foundation’s constitutive properties exhibit periodic variations along the beam’s longitudinal axis. In the steady-state regime, the reaction forces exerted by the foundation on the beam are assumed to exhibit periodicity, repeating as the moving loads traverse one complete period of the foundation. This periodicity condition is analogous to that observed in beams supported by discrete periodic supports. By employing the Fourier transform, the governing dynamic equation of the beam, combined with the imposed periodicity condition, leads to a linear differential equation with a periodic coefficient. To determine the system’s response, Floquet’s theorem is utilized, providing a rigorous mathematical framework for analysing the stability and dynamics of the beam. Furthermore, numerical investigations are conducted to examine the effects of foundation periodicity on the beam’s dynamic response. The results highlight the significant influence of periodic foundation properties on the vibration characteristics of the system. Finally, the critical train speed is derived based on the stability conditions of the problem, offering key insights into the structural performance of the beam under moving loads.