On The Lateral Stability of a Flexible Truck

Analytic formulae for the critical speed and frequency of an interconnected pair of wheelsets based on an asymptotic expansion in a truck geometric parameter are derived. No restriction is placed on the values of either the shear or bending stiffness; consequently, the entire structure of the stability surface is obtained. The surface is a symmetric function of the two dimensionless stiffnesses and it depends predominantly on their series combination. Expressions are obtained for the local and global extrema and their locations. The frequency varies monotonically from the wheelset kinematic frequency to the rigid truck frequency as a function of stiffness. The results are compared with numerical solutions and found to be accurate in the region of physically obtainable values of the expansion parameter.