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PubMed2003

The radiation Q factors obtained from the partial derivatives of the phase of the reflection coefficient of an elastic plate.

The phase gradient method is applied to study the partial derivatives of the phase of the reflection coefficient of a fluid-loaded elastic plate. We consider the derivatives with respect to the frequency f, the incidence angle theta, the phase velocities of the longitudinal and transverse waves propagating in the plate, cL and cT, respectively, and the phase velocity in the fluid cF. The partial derivatives with respect to f, cL, cT, cF are linked by a relation involving products of one of these variables with the corresponding partial derivative. At a resonance frequency, the product of frequency with the frequency phase derivative can be identified as a radiation quality factor. By analogy, the other products correspond to quality factors. It can be shown that the product assigned to the fluid phase velocity corresponds to an angular radiation quality factor. The products assigned to the longitudinal and transverse phase velocities are identified as longitudinal and transverse radiation quality factors. These quality factors are shown to be related to stored energies associated with either standing waves across the plate, guided waves, longitudinal waves or transverse waves. A reactive power balance between the plate and the fluid is also established.

Journal Article↗

PubMed2002

The complex phase gradient method applied to leaky Lamb waves.

The classical phase gradient method applied to the characterization of the angular resonances of an immersed elastic plate, i.e., the angular poles of its reflection coefficient R, was proved to be efficient when their real parts are close to the real zeros of R and their imaginary parts are not too large compared to their real parts. This method consists of plotting the partial reflection coefficient phase derivative with respect to the sine of the incidence angle, considered as real, versus incidence angle. In the vicinity of a resonance, this curve exhibits a Breit-Wigner shape, whose minimum is located at the pole real part and whose amplitude is the inverse of its imaginary part. However, when the imaginary part is large, this method is not sufficiently accurate compared to the exact calculation of the complex angular root. An improvement of this method consists of plotting, in 3D, in the complex angle plane and at a given frequency, the angular phase derivative with respect to the real part of the sine of the incidence angle, considered as complex. When the angular pole is reached, the 3D curve shows a clear-cut transition whose position is easily obtained.

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