Articles 2026

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: 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.

Résumé: We study the scattering of elastic waves by a periodic array of cavities buried in an elastic half-space. This configuration is relevant in seismology, where shallow voids can locally amplify ground motion. Building on homogenized interface models developed for infinite media, we extend the approach to account for the presence of a stress-free surface. The resulting model yields an analytical solution to the 2D elastodynamic problem for incident longitudinal L and transverse T waves. A semi-analytical multimodal solution is used for validation. The analysis reveals the conditions under which resonances occur in the soil layer between the cavity tops and the surface, with particular emphasis on the low-frequency resonance that dominates in seismic contexts. The model identifies the key parameters governing resonance and provides insights into the transition from infinite to finite cavity arrays. It offers a simplified yet accurate framework for assessing site-specific seismic amplification.