Torsional Oscillations in Moving Bands

The torsional vibration of moving bands subject to harmonic tension fluctuation is investigated. A thin rectangular strip translating longitudinally with a constant speed and simply supported at its end is considered. The linearized equation of motion, when suitably discretized, represents a linear gyroscopic system with periodically varying stiffness. The stability of the trivial solution of this system of equations, for tension fluctuations of small amplitude, is examined using the method of averaging. Analytic conditions for stability of torsional motion are obtained explicitly and shown graphically in the frequency vs excitation parameter space.