Flexural instabilities in moving bands under harmonic tension fluctuation are investigated. The discretized equations of flexural motion represent a periodically perturbed linear gyroscopic system. Explicit conditions for the onset of instability are established employing the method of averaging. The effects due to damping, mean band speed, and the band compliance on the band stability are discussed. The present analysis is adequate in the design of moving bands where it is necessary to avoid critical speed ranges.

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