Acoustic radiation from membranes at high frequencies: The quantum chaos regime

An efficient and reliable numerical scheme is developed to compute the radiation directivity and total power radiated by isolated eigenmodes and by finite bandwidth excitations of a membrane of arbitrary shape over the whole frequency domain. Results are presented for the case of a membrane having the shape of a stadium, this shape having been studied intensively in the literature concerned with the correspondence between classical geometrical ray trajectories and high-frequency vibrations, the so-called ''quantum chaos'' problem, Localization of the radiation directivity is shown to be due to ''scars'' of eigenmodes made by resonance on periodic ray orbits. The dependence of the radiation efficiency as a function of the ratio c(M)/C of the membrane wave velocity c(M) over the air sound speed c and its important fluctuations from mode-to-mode is explained by the theory of random matrices. (C) 1997 Acoustical Society of America.