Spectral statistics in damped systems. Part I. Modal decay rate statistics

A revised model for the statistical distribution of eigenmode decay rates in complex acoustic systems is presented. Analytical predictions based on a real-valued diffuse field description of modal amplitudes indicate that modal decay rates should be distributed according to a modified chi-square distribution. Numerical experiments performed on damped, irregularly shaped membranes indicate that the chi-square distribution is accurate, provided the membrane is sufficiently lightly damped. For high dissipation levels, as measured by the mean modal overlap, the observed decay rates increasingly disagree with the prediction.