Group delay in resonant scattering

Abstract

For a slightly damped structural system with low modal overlap, roughly half the zeros of the mobility transfer function (MTF) remain on the pole line, and the group delay of the MTF is π/2 times the structural modal density. But in the case of sound scattering, 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 the resonant scattering function (RSF) is determined by the number of poles alone, and thus the group delay of the RSF is roughly a factor of 2 times of that of the MTF. To verify this conjecture, an in-air plate scattering experiment was carried out and the results show a factor of 1.67. Furthermore, the zero density distribution patterns versus modal overlap for both the MTF and RSF were obtained through numerical simulation of a 20-degree-of-freedom system. The simulation shows that in the smaller modal overlap case, the RSF group delay is nearly twice that of the MTF. When modal overlap increases, however, this factor decreases and approaches unity. Physically this means in a high modal overlap system, as in room acoustics, the group delay of the RSF is determined by the energy decay rate.