Ahmed Mehrem

This work investigates how unit-cell topology controls flexural-wave dispersion and finite-array attenuation in periodic acoustic-black-hole (ABH) plates. Six configurations are compared under identical material constants, lattice parameter, power-law profile, and residual thickness: a uniform reference plate, two isolated ABH inclusions with circular and y-elongated elliptical shapes, a crossed-strip ABH network, and two cross-connected inclusion–strip networks. The plate is modeled using Kirchhoff–Love theory with spatially varying thickness, and dispersion curves are computed with a finite-difference Bloch (FD–Bloch) formulation along the sampled Γ–X–M–Γ path. The numerical dispersion results are checked against a Gaussian-enriched Ritz method and, for the uniform plate, against the analytical folded dispersion relation. To connect the infinite-periodic predictions with practical attenuation, finite arrays are also analyzed through transmission maps and full-aperture transmission curves. The results show that isolated circular and elliptical ABHs mainly distort dispersion branches, produce partial directional stop behavior, and give only moderate forward-transmission reductions in finite arrays. By contrast, connected low-thickness ligaments strengthen modal coupling and generate wider stop intervals along the sampled path. The crossed-strip and cross-connected circular networks reduce the full-aperture transmission at their selected stop-band frequencies. The cross-connected y-elongated elliptical network gives the strongest response. These results show that ABH topology, and especially the connectivity and anisotropy of the thinned regions, is a decisive design parameter for directional attenuation in lightweight periodic plates.

Microbubbles, either in the form of free gas bubbles surrounded by a fluid or encapsulated bubbles used currently as contrast agents for medical echography, exhibit complex dynamics under specific acoustic excitations. Nonetheless, considering their micron size and the complexity of their interaction phenomenon with ultrasound waves, expensive and complex experiments and/or simulations are required for their analysis. The behavior of a microbubble along its equator can be linked to a system of coupled oscillators. In this study, the oscillatory behavior of a microbubble has been investigated through an acousto-mechanical analogy based on a ring-shaped chain of coupled pendula. Observation of parametric vibration modes of the pendula ring excited at frequencies between 1 and 5 Hz is presented. Simulations have been carried out and show mode mixing phenomena. The relevance of the analogy between a microbubble and the macroscopic acousto-mechanical setup is discussed and suggested as an alternative way to investigate the complexity of microbubble dynamics.