## 3pSA1. Numerical solutions of a prototypical master structure/fuzzy substructure system.

### Session: Wednesday Afternoon, May 15

### Time: 12:30

**Author: Richard L. Weaver**

**Location: Dept. of Theoretical and Appl. Mechanics, 216 Talbot Lab., Univ. of Illinois, 104 S. Wright St., Urbana, IL 61801**

**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.]

from ASA 131st Meeting, Indianapolis, May 1996