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.

Effects of periodicity perturbations on the transmission by underwater phononic crystals.

The effects of periodicity perturbations in underwater phononic crystal layers composed of noninterpenetrating rows of identical shells are investigated. The results for one row are obtained by using a multiple scattering method between shells. Then, taking into account the multiple reflections and transmissions between two adjacent rows, a Debye series method is used to calculate the reflection and transmission coefficients by a finite number of rows. The paper focuses on three kinds of perturbations: (i) variation of the inner radius of shells from row to row, (ii) increase in the spacing from row to row and of the number of rows, and (iii) substitution of simple steel rows by steel-polyethylene bilayers. It is shown by studying the transmission coefficient that the case (i) permits the insertion of narrow pass bands in the stop band while the two other cases (ii) and (iii) widen the stop band. The study intends to model simple underwater acoustic filters.

Guided waves in elastic plates with Gaussian section variation: experimental and numerical results.

Experimental and numerical results are presented on the behavior of guided waves in elastic plates in plane strain that include a Gaussian variation of their section, located between two areas of constant thickness. The area of varying section is wide compared to the used wavelengths, which allows wave propagation inside this area. The experimental results show that an incident Lamb wave is indeed converted into an adiabatic wave inside the varying section domain. A trapped wave in the Gaussian domain is also observed, depending on the incident mode and on the Gaussian maximum height. Outside the varying section domain, conversion into different Lamb waves is observed. This conversion phenomenon is experimentally quantified by the measurement of the Lamb wave normal displacement and of its carried energy. A numerical study, based on the Finite Elements Method is performed, and successfully compared to the experimental results.