The Coupled Response of a Dynamic Element Riding on a Continuously Supported Beam

The dynamic interaction between a Linear Induction Motor primary, modeled as a spring-mass-damper element, and its secondary-rail, modeled as a prestressed, continuously supported, infinitely long beam, is studied theoretically. The existence of two transition speeds is established. At the lower transition speed, the frequency and damping ratio of the coupled system response attain their minimum and maximum values, respectively. The system is unstable at speeds higher than the second transition speed. Using a rotating annular disk to simulate the secondary rail, measured values of the frequency and damping ratio confirm the validity of the mathematical model for speeds up to nearly the lower transition speed.