### ASA 127th Meeting M.I.T. 1994 June 6-10

## 1aSA7. Group delay in resonant scattering.

**Hua He
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*Dept. of Ocean Eng., MIT, Cambridge, MA 02139
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**Richard H. Lyon
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*MIT, Cambridge, MA 02139
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For a slightly damped structural system with low modal overlap, roughly
half the zeros of the transfer function (TF) remain on the pole line and the
group delay of the TF is (pi)/2 times the structural modal density. But in the
sound scattering case, the zeros are translated and rotated randomly and far
fewer zeros will remain on the pole line. It is then reasonable to conjecture
that the phase of resonance scattering function (RSF) be determined by the
number of poles alone and thus the group delay of RSF is roughly a factor of 2
times that of the TF. To verify this conjecture, an in-air plate scattering
experiment was carried out and the results show the factor of 1.67.
Furthermore, the zero density distribution patterns versus modal overlap for
both TF and RSF were obtained through numerical simulation of a 20-DOF system.
The simulation shows that in the smaller modal overlap case, the RSF group
delay is nearly twice that of TF. When modal overlap increases, however, this
factor decreases and approaches 1. Physically this means in a high modal
overlap system, like room acoustics, the group delay of RSF approaches the
energy decay rate.