Abstract:
The transient response of a single degree of freedom master oscillator attached to a simple undamped N degree of freedom ``fuzzy substructure'' is studied numerically and theoretically. Results at early times are found to be in accord with the predictions of the Pierce--Sparrow--Russell theory; in particular, the master oscillation manifests an apparent damping. At later times, however, the energy is returned from fuzzy to master. The precise manner in which the energy is returned and the time taken to do this depend on the details of the mass and frequency distribution within the fuzzy and, in particular, on the distribution of spacings between the fuzzy resonances. For the case of irregularly positioned fuzzy resonances the energy returns immediately and the master then oscillates randomly. For the case of regularly spaced fuzzy resonances the energy returns after a longer time, and does so coherently. Theory is presented which supports the accuracy of the Pierce--Sparrow--Russell result at short times. Other arguments (for the case of random fuzzy resonances) predict the root-mean-square level of the subsequent random oscillations. Still others (for the case of regularly spaced fuzzy resonances) predict the return time. [Work supported by ONR.]