Group delay in resonant scattering

Abstract

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 π/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.