Application of SQP and dynamic mode tracking to the determination of the critical speed of rail vehicles

Byline: Yuping He, John McPhee A method is presented for determining the critical speed of rail vehicles. Dynamic Mode Tracking (DMT) is used to identify the dynamic modes for a given speed and a Sequential Quadratic Programming (SQP) algorithm determines the critical speed at which the least-damped mode has zero damping. It is shown that the SQP algorithm without DMT often fails to find the critical speed. In comparison, the combined SQP-DMT algorithm provides a reliable identification of the critical speed. This integrated algorithm can be applied to rotor dynamics, wind turbine dynamics, aeronautics, and road vehicle dynamics for automatically identifying the critical speed corresponding to a linear stability analysis.