### ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

## 4aSA6. Power transmission variance predictions in complex systems with
dissipation.

**John Burkhardt
**

**
Richard Weaver
**

**
**
*Dept. of Theor. and Appl. Mech., Univ. of Illinois, Urbana, IL 61801
*

*
*
The eigenstatistics of damped complex systems are examined for the purpose
of improving statistical response predictions such as those formulated in
statistical energy analysis and statistical room acoustics. Both the
statistical distribution of modal decay rates and the effect of dissipation on
the intermodal correlation of the natural frequencies described by the gaussian
orthogonal ensemble (GOE) of random matrix theory are explored. It is found
that the modal decay rates are distributed according to a chi-square
distribution whose degree depends on the distribution of damping in the system
and the wavelength of the disturbance. The intermodal correlations of the
natural frequencies are found to be unaffected by the presence of moderate
damping. Level repulsion (the absence of near degeneracies) and spectral
rigidity (the near regularity of the spectrum) are found to conform to the
prediction of the GOE provided the system is reverberant. The variance of the
power transmission function for an irregularly shaped membrane is formulated
using a GOE-type natural frequency spectrum and chi-square distributed modal
decay rates. Numerical simulations of membranes are performed which confirm the
calculated effect of a distribution of decay rates on power transmission
characteristics.