A rational framework for dynamic homogenization at finite wavelengths and frequencies

B. B. Guzina, S. Meng, O. Oudghiri-Idrissi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this work, we establish an inclusive paradigm for the homogenization of scalar wave motion in periodic media at finite frequencies and wavenumbers spanning the first Brillouin zone. We take the eigenvalue problem for the unit cell of periodicity as a point of departure, and we consider the projection of germane Bloch wave function onto a suitable eigenfunction as descriptor of effective wave motion. For generality the finite wavenumber, finite frequency (FW-FF) homogenization is pursued Rd via second-order asymptotic expansion about the apexes of “wavenumber quadrants” comprising the first Brillouin zone, at frequencies near given dispersion branch. We also consider the junctures of dispersion branches and “dense” clusters thereof, where the asymptotic analysis reveals several distinct regimes driven by the parity and symmetries of the germane eigenfunction basis. In the case of junctures, one of these asymptotic regimes is shown to describe the so-called Dirac points, that are relevant to the phenomenon of topological insulation. On the other hand, the effective model for nearby solution branches is found to invariably entail a Dirac-like system of equations that describes the interacting dispersion surfaces as “blunted cones”. We illustrate the analysis by considering wave dispersion through a chessboard-like medium featuring junctures and clusters of nearby dispersion surfaces.

Original languageEnglish (US)
Title of host publicationAdvances in Engineering Materials, Structures and Systems
Subtitle of host publicationInnovations, Mechanics and Applications - Proceedings of the 7th International Conference on Structural Engineering, Mechanics and Computation, 2019
EditorsAlphose Zingoni
PublisherCRC Press/Balkema
Pages362-367
Number of pages6
ISBN (Print)9781138386969
DOIs
StatePublished - 2019
Event7th International Conference on Structural Engineering, Mechanics and Computation, 2019 - Cape Town, South Africa
Duration: Sep 2 2019Sep 4 2019

Publication series

NameAdvances in Engineering Materials, Structures and Systems: Innovations, Mechanics and Applications - Proceedings of the 7th International Conference on Structural Engineering, Mechanics and Computation, 2019

Conference

Conference7th International Conference on Structural Engineering, Mechanics and Computation, 2019
Country/TerritorySouth Africa
CityCape Town
Period9/2/199/4/19

Bibliographical note

Publisher Copyright:
© 2019 Taylor & Francis Group, London, UK.

Fingerprint

Dive into the research topics of 'A rational framework for dynamic homogenization at finite wavelengths and frequencies'. Together they form a unique fingerprint.

Cite this