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: This work presents experimental and theoretical results concerning the dispersion and attenuation caused by scattering during the propagation of ultrasonic waves on the surface of a polycrystal. Rayleigh and head waves are measured in the case of two Inconel® 600 samples with different average grain sizes. The coherent, i.e., ensemble-averaged, waves are estimated, as well as their frequency-dependent phase velocities and scattering mean-free paths. The results obtained from a contactless laser setup are compared to those obtained from a transducer array placed on the surface of the sample. The influence of contact is highlighted, particularly at low frequency and in the small-grained sample, where the attenuation by scattering is lower. Moreover, the two-point correlation (TPC) functions of both samples are estimated, and it is shown that neither is exponential. Standard theoretical models are adapted to these particular TPCs and yield effective bulk wavenumbers, from which effective surface wavenumbers can be calculated via a simple and approximate method. The theoretical results are then compared to the experimental ones.

Résumé: A time-domain effective model for acoustic wave propagation through a two-dimensional periodic array of gas bubbles embedded in a liquid is presented. The model is expressed as transmission conditions: pressure remains continuous, whereas the normal velocity exhibits a jump induced by the internal pressure of the bubbles. This internal pressure follows a damped mass–spring equation, with damping arising solely from radiative coupling to the surrounding liquid, which makes the resonance frequency and quality factor of the array emerge unambiguously. Aside from the bubble density in the lattice, these quantities are fully governed by two independent geometric parameters: a dimensionless capacitance, depending solely on bubble shape, and a lattice coefficient, depending solely on lattice geometry. For plane wave scattering, comparisons with direct numerical simulations demonstrate that the model accurately reproduces the resonant behavior of bubble screens across a range of configurations, including spherical, spheroidal, and cylindrical bubbles, as well as square and rectangular lattices. This generalizes the classical model of Leroy et al. [Eur. Phys. J. E 29(1), 123–130 (2009)] for spherical bubbles in square lattices. Notably, the model reveals—and simulations confirm—that the resonance frequency shift relative to an isolated bubble, usually positive (blue shift), can become negative (red shift) in rectangular lattices with aspect ratios exceeding seven.