Analysis of Track Critical Velocity and Track Vibration under Tram Loading

Track vibration of a tramway in operation was theoretically analyzed. The relationships of critical velocity with elastic modulus of subgrade and thickness of track beds were obtained by solving vibration equation. It was shown that the critical velocity was greater than the design speed of trams. Another vibration differential equation was established to analyze track vibration. Both equations adopted moving impact load and ignored the impact of damping, but irregularities of rails were considered in the second equation. The analytical solutions of vibration deflection and acceleration were deduced. Based on the solutions and superposition principle, the dynamic responses under single axle loading and tram loading were analyzed. The results indicate that: (1) vibration deflection increases exponentially with irregularities amplitude; and (2) vibration acceleration has a negative logarithmic correlation with irregularity amplitude.