## 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**

**Abstract:**

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