3aSAa2. The phase gradient method applied to the plate: Analysis of the partial derivatives with respect to the phase velocities.

Session: Wednesday Morning, May 15

Time: 8:15

Author: O. Lenoir
Author: J. M. Conoir
Author: J. L. Izbicki
Location: Lab. d'Acoust. Ultrason. et d'Electron. LAUE, URA CNRS 1373, Univ. du Havre, Pl. Robert Schuman, 76610 Le Havre, France


The phase gradient method is a convenient tool in order to analyze the frequential and angular resonances of an immersed elastic plate [J. Acoust. Soc. Am. 94, 330--343 (1993)]. It consists in the study of the derivative of the phase of the reflection coefficient with respect to the frequency x---the obtaining of the resonance frequency x[sup *] and the resonance width (Gamma)[sup *] is then straightforward---or with respect to the angular parameter y (which is the sine of the incidence angle). It is shown that the derivatives with respect to the different phase velocities involved in the scattering problem also permit the isolation of the resonances. The derivatives with respect to the longitudinal (c[inf L]) and shear (c[inf T]) velocities of the plate and to the longitudinal velocity of the fluid (c[inf F]) are studied. The plot of the previous derivatives, versus the frequency, exhibits Breit--Wigner peaks. Their half-widths are equal to (Gamma)[sup *] and the coefficients (Gamma)[inf L], (Gamma)[inf T], (Gamma)[inf F] related to their amplitude are introduced. The physical meaning of the previous amplitude coefficient is given. Then a resonant energy conservation law is shown: (Gamma)[sup *]+(Gamma)[inf F]=(Gamma)[inf L]+(Gamma)[inf T].

from ASA 131st Meeting, Indianapolis, May 1996