A rheological model for immersed corrugated elastic plates.

The influence of surface imperfections on the propagation of guided waves in an immersed elastic plate can be interpreted by means of a rheological model. The corrugated surface is modeled by a very thin interface, similar to a Jones spring model, which replaces the continuity boundary conditions at the liquid - corrugated solid-plate interface. As the surrounding liquid is considered to be perfect, only one complex stiffness is used for the model of Jones. The selection of the plate guided mode and the test frequency are motivated by the detectability and non-interference with other modes. The spring stiffness is obtained by a best fit procedure, between the analytical solution and the results obtained by the finite elements method (FEM). One way ensuring the agreement of the two approaches, rheological and FEM, is to consider angular resonances provided by the transmission coefficients. Small changes in the parameters of the roughness keep the positions of the angular resonances of the plate practically unchanged, while at the same time large variations of the half width of the transmission coefficient curve is observed. The effect of corrugation parameters on the guided modes in the plate can be predicted by using the rheological model with the deduced spring complex stiffness.

Lamb wave propagation in a plate with a grooved surface with several spatial periodicities.

In order to investigate non-destructively the bonding between rough plates, the problem of Lamb waves propagating on a rough plate is addressed in this paper. Numerical analysis is performed on periodical gratings made of identical triangular grooves. If the surface profile is made up of grooves with one periodicity, then a mode conversion is observed. In the wave-number/frequency space, a phonon relation is written between phonons related to the grating and to the incident and reflected-converted modes. If the grooved surface is made up of several spatial periodicities, then the phonon relation is still verified. Signal processing allows us to give an interpretation of the results in the dual space (wave-number/frequency). An experimental study is also performed to corroborate the numerical predictions.

Resonant acoustic scattering by a finite linear grating of elastic shells.

Theoretical and experimental studies of the acoustic scattering by a finite linear grating of elastic cylindrical shells are performed. It is observed that a resonant interaction takes place at low frequency when the shells are very close to each other. This phenomenon can be clearly associated to the Scholte-Stoneley wave that propagates around a single shell. It is shown that each resonance of the Scholte-Stoneley wave is split up into N resonances when N shells compose the grating.

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.

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.