Microstructural topological sensitivities of the second-order macroscopic model for waves in periodic media - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Applied Mathematics Année : 2018

Microstructural topological sensitivities of the second-order macroscopic model for waves in periodic media

Résumé

We consider scalar waves in periodic media through the lens of a second-order effective i.e. macroscopic description, and we aim to compute the sensitivities of the germane effective parameters due to topological perturbations of a microscopic unit cell. Specifically, our analysis focuses on the tensorial coefficients in the governing mean-field equation – including both the leading order (i.e. quasi-static) terms, and their second-order companions bearing the effects of incipient wave dispersion. The results demonstrate that the sought sensitivities are computable in terms of (i) three unit-cell solutions used to formulate the unperturbed macroscopic model; (ii) two adoint-field solutions driven by the mass density variation inside the unperturbed unit cell; and (iii) the usual polarization tensor, appearing in the related studies of non-periodic media, that synthesizes the geometric and constitutive features of a point-like perturbation. The proposed developments may be useful toward (a) the design of periodic media to manipulate macroscopic waves via the microstructure-generated effects of dispersion and anisotropy, and (b) sub-wavelength sensing of periodic defects or perturbations.
Fichier principal
Vignette du fichier
siap18.pdf (702.14 Ko) Télécharger le fichier
Origine Fichiers éditeurs autorisés sur une archive ouverte
Loading...

Dates et versions

hal-01742396 , version 1 (24-03-2018)
hal-01742396 , version 2 (28-03-2018)
hal-01742396 , version 3 (09-08-2018)

Identifiants

Citer

Marc Bonnet, Rémi Cornaggia, Bojan B Guzina. Microstructural topological sensitivities of the second-order macroscopic model for waves in periodic media. SIAM Journal on Applied Mathematics, 2018, 78 (4), pp.2057-2082. ⟨10.1137/17M1149018⟩. ⟨hal-01742396v3⟩
420 Consultations
227 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More