Stability of accelerating repetitive systems

The spatial stability of a sequence of accelerating repetitive operations is investigated using the output spectral-density in a frequency band enclosing the first resonance peak as a stability indicator. The operations of the sequence are identical in dynamic structure, but subject to a constant rate of acceleration between operations, thus resembling the rolling of metal strip and other repetitive manufacturing processes such as machining. The technique readily yields a value for the critical number of operations within which stability can be expected to be achieved, within the chosen frequency band. Simulation of a variety of systems confirms the physical usefulness of this number which correlates well with the observed number of operations found to be necessary to achieve an output profile that is adequately stable from a practical viewpoint.