Vibration of a winkler beam due to moving loads on soft foundation

In high-speed conditions,when moving loads reached certain speed,the structure would vibrate heavily.Here,according to the vibration differential equation of a Winkler beam under moving loads,a critical speed expression was obtained.Then,the influences of foundation supporting stiffness and moving loads speed on the Winkler foundation beam vibration were studied in detail.The conclusions were as follows:(1) critical speed and dynamic deflection of the Winkler foundation beam grew with increase in the number of moving loads,superposition of moving loads led to critical speed increasing and vibration intensified;(2) when foundation supporting stiffness decreased,the strong vibration of the Winkler foundation beam moved to the lower speed regions and vibration strength increased rapidly;(3) it was also proved that the increase in the Winkler foundation supporting stiffness could effectively raise the critical speed of the Winkler foundation beam.