Scattering of acoustic waves by a nonlinear resonant bubbly screen

Abstract

Abstract

Time-delayed interactions on acoustically driven bubbly screens

“…As shown by Pham et al (2021), this expression is similar to the extension of the asymptotic analyses proposed by Caflisch et al (1985) and later extended by Miksis and Ting (1989) to the second order, where the correction due to the collective effects of the bubbly screen is (Pham et al, 2021) f EMT (kD) = −3.9 − ı 2π kD .…”

“…In this section, we compare the results obtained from the model presented for infinite bubbly screens imposing synchronous motion (R i = R j = R) with the results obtained from the EMT in non-linear regimes (Pham et al, 2021) where…”

“…In non-linear regime, the asymptotic analysis based on effective medium theory (Miksis and Ting, 1989;Pham et al, 2021) have shed light into the role of compressibility on the mechanisms of multiple interactions among bubbles. However, these models still face some challenges.…”

Time domain modelling of a Helmholtz resonator analogue for water waves

“…Other extensions consist in including the effect of the losses due to the viscosity that we expect to be significant in the neck or due to nonlinearities within the cavity as the velocity reaches large values. Although this can be done by adding heuristically a damping term in the equation of the resonator (2.11), as in Monsalve et al (2019), these ingredients can by explicitly accounted for in the analysis, see Caflisch et al (1985) for viscous effects and Pham et al (2020) for nonlinear effects. We have in mind the perfect absorption obtained with acoustic HRs (Romero-García et al 2020) and for water waves in reflection (Monsalve et al 2019).…”

Acoustic and elastic wave propagation in microstructured media with interfaces: homogenization, simulation and optimization

“…For wave propagation in elasticity, studies focused on rows of non-resonant inclusions (Marigo, Maurel, Pham, & Sbitti, 2017a; and then on resonant inclusions (Pham, Maurel, & Marigo, 2017). One also notes that similar methods can also be used to get effective jump conditions for stratified media (Marigo & Maurel, 2017c), metallic structures (Marigo & Maurel, 2016b;Maurel, Marigo, & Ourir, 2016), Helmholtz resonators (Mercier, Marigo, & Maurel, 2017;Maurel, Marigo, Mercier, & Pham, 2018), bubble screens (Pham, Mercier, Fuster, Marigo, & Maurel, 2020), adhesive layers (Abdelmoula, Coutris, & Marigo, 1998;Burel, 2014;Rizzoni, Dumont, Lebon, & Sacco, 2014;Rizzoni, Dumont, & Lebon, 2017) and for the latter the results are equivalent to those obtained with energy-based methods (Lebon & Rizzoni, 2011;Dumont, Rizzoni, Lebon, & Sacco, 2018;. The case of non-periodic layers has also been studied for seismic waves (Capdeville & Marigo, 2012).…”