D. Delande et D. Sornette, ACOUSTIC RADIATION FROM MEMBRANES AT HIGH-FREQUENCIES - THE QUANTUM CHAOS REGIME, The Journal of the Acoustical Society of America, 101(4), 1997, pp. 1793-1807
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 stud
ied intensively in the literature concerned with the correspondence be
tween classical geometrical ray trajectories and high-frequency vibrat
ions, the so-called ''quantum chaos'' problem, Localization of the rad
iation directivity is shown to be due to ''scars'' of eigenmodes made
by resonance on periodic ray orbits. The dependence of the radiation e
fficiency as a function of the ratio c(M)/C of the membrane wave veloc
ity c(M) over the air sound speed c and its important fluctuations fro
m mode-to-mode is explained by the theory of random matrices. (C) 1997
Acoustical Society of America.