ON THE SPECTRAL ASYMPTOTICS OF WAVES IN PERIODIC MEDIA WITH DIRICHLET OR NEUMANN EXCLUSIONS

doi:10.1093/qjmam/hbab003

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	ON THE SPECTRAL ASYMPTOTICS OF WAVES IN PERIODIC MEDIA WITH DIRICHLET OR NEUMANN EXCLUSIONS
	Oudghiri-Idrissi, Othman 1; Guzina, Bojan B.1; Meng, Shixu2
	2021-05-01
发表期刊	QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS
ISSN	0033-5614
卷号	74 期号:2 页码:173-221
摘要	We consider homogenization of the scalar wave equation in periodic media at finite wavenumbers and frequencies, with the focus on continua characterized by: (a) arbitrary Bravais lattice in R-d, d >= 2, and (b) exclusions, that is, `voids' that are subject to homogeneous (Neumann or Dirichlet) boundary conditions. Making use of the Bloch-wave expansion, we pursue this goal via asymptotic ansatz featuring the `spectral distance' from a given wavenumber-eigenfrequency pair (situated anywhere within the first Brillouin zone) as the perturbation parameter. We then introduce the effective wave motion via projection(s) of the scalar wavefield onto the Bloch eigenfunction(s) for the unit cell of periodicity, evaluated at the origin of a spectral neighborhood. For generality, we account for the presence of the source term in the wave equation and we consider-at a given wavenumber-generic cases of isolated, repeated, and nearby eigenvalues. In this way, we obtain a palette of effective models, featuring both wave- and Dirac-type behaviors, whose applicability is controlled by the local band structure and eigenfunction basis. In all spectral regimes, we pursue the homogenized description up to at least first order of expansion, featuring asymptotic corrections of the homogenized Bloch-wave operator and the homogenized source term. Inherently, such framework provides a convenient platform for the synthesis of a wide range of intriguing wave phenomena, including negative refraction and topologically protected states in metamaterials and phononic crystals. The proposed homogenization framework is illustrated by approximating asymptotically the dispersion relationships for (i) Kagome lattice featuring hexagonal Neumann exclusions and (ii) square lattice of circular Dirichlet exclusions. We complete the numerical portrayal of analytical developments by studying the response of a Kagome lattice due to a dipole-like source term acting near the edge of a band gap.
DOI	10.1093/qjmam/hbab003
收录类别	SCI
语种	英语
WOS研究方向	Mathematics ; Mechanics
WOS类目	Mathematics, Applied ; Mechanics
WOS记录号	WOS:000705428900003
出版者	OXFORD UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59375
专题	应用数学研究所
通讯作者	Guzina, Bojan B.
作者单位	1.Univ Minnesota, Dept Civil Environm & Geoen Qineering, Minneapolis, MN 55405 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Oudghiri-Idrissi, Othman,Guzina, Bojan B.,Meng, Shixu. ON THE SPECTRAL ASYMPTOTICS OF WAVES IN PERIODIC MEDIA WITH DIRICHLET OR NEUMANN EXCLUSIONS[J]. QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS,2021,74(2):173-221.
APA	Oudghiri-Idrissi, Othman,Guzina, Bojan B.,&Meng, Shixu.(2021).ON THE SPECTRAL ASYMPTOTICS OF WAVES IN PERIODIC MEDIA WITH DIRICHLET OR NEUMANN EXCLUSIONS.QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS,74(2),173-221.
MLA	Oudghiri-Idrissi, Othman,et al."ON THE SPECTRAL ASYMPTOTICS OF WAVES IN PERIODIC MEDIA WITH DIRICHLET OR NEUMANN EXCLUSIONS".QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS 74.2(2021):173-221.