Matériaux, résonances et interfaces (MRI)

Résumé: Semi-analytical methods for modeling guided waves in structures of constant cross-section yield frequency-dependent polynomial eigenvalue problems for the wavenumbers and mode shapes. Solving these eigenvalue problems over a range of frequencies results in continuous eigencurves. Recent research has shown that eigencurves of differentiable parameter-dependent eigenvalue problems can alternatively be computed as solutions to a system of ordinary differential equations (ODEs) obtained by postulating an exponentially decaying residual of a modal solution. Starting from an approximate initial guess of the eigenvalue and eigenvector at a given frequency, the complete eigencurve is obtained using standard numerical ODE solvers. We exploit this idea to develop an efficient method for computing the dispersion curves of plate structures coupled to unbounded solid or fluid media. In these scenarios, the approach is particularly useful because the boundary conditions give rise to nonlinear terms that severely hinder the application of traditional solvers. We discuss suitable approximations of the nonlinearity for obtaining initial values, analyze computational costs and robustness of the proposed algorithm, and verify results by comparison against existing methods.

Résumé: We demonstrate the existence of a frequency band exhibiting acoustic transparency in two- and three-dimensional dense granular suspensions, enabling the transmission of a low-frequency ballistic wave excited by a high-frequency broadband ultrasound pulse. This phenomenon is attributed to spatial correlations in the structural disorder of the medium. To support this interpretation, we use an existing model that incorporates such correlations via the structure factor. Its predictions are shown to agree well with those of the generalized coherent potential approximation (GCPA) model, which is known to apply at high volume fractions, including the close packing limit, but does not explicitly account for disorder correlation. Within the transparency band, attenuation is found to be dominated by absorption rather than scattering. Measurements of the frequency dependence of the absorption coefficient reveal significant deviations from conventional models, challenging the current understanding of acoustic absorption in dense granular media.