A numerical method for elastic wave scattering in multi-layered periodic media based on the scattering matrix and BEM

This paper presents a numerical method for analyzing elastic wave scattering by multi-layered periodic structures in two dimensions. The proposed method is based on the boundary element method (BEM) and scattering matrix representing a relationship between incoming and outgoing waves in the vicinity...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Kei MATSUSHIMA, Hiroshi ISAKARI, Toru TAKAHASHI, Toshiro MATSUMOTO
Formato:	article
Lenguaje:	EN
Publicado:	The Japan Society of Mechanical Engineers 2020
Materias:	layer-doubling method scattering matrix elastic wave boundary element method phononic crystal elastic metamaterial Mechanical engineering and machinery TJ1-1570
Acceso en línea:	https://doaj.org/article/9fd817b21d774bd9a66e1c2dfa77aae5
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:9fd817b21d774bd9a66e1c2dfa77aae5
record_format	dspace
spelling	oai:doaj.org-article:9fd817b21d774bd9a66e1c2dfa77aae52021-11-29T06:04:29ZA numerical method for elastic wave scattering in multi-layered periodic media based on the scattering matrix and BEM2187-974510.1299/mej.20-00364https://doaj.org/article/9fd817b21d774bd9a66e1c2dfa77aae52020-12-01T00:00:00Zhttps://www.jstage.jst.go.jp/article/mej/8/1/8_20-00364/_pdf/-char/enhttps://doaj.org/toc/2187-9745This paper presents a numerical method for analyzing elastic wave scattering by multi-layered periodic structures in two dimensions. The proposed method is based on the boundary element method (BEM) and scattering matrix representing a relationship between incoming and outgoing waves in the vicinity of a periodic structure. First, we define the scattering matrix using a plane-wave expansion of the solution of the elastic problem. Then, we show the integral formulae that convert the solution of a system of boundary integral equations into elements of the scattering matrix. The proposed scattering matrix method with the BEM enables us to reduce the scattering problem in a multi-layered structure to a purely algebraic one in terms of the scattering matrix of each layer, resulting into less requirement in computational resources than in the methods which are based on the meshing of an entire boundary and solution of the corresponding boundary integral equations. Such a procedure called layer-doubling method is implemented in a numerically stable manner based on the eigendecomposition of a relevant matrix. Moreover, some scattering properties and phononic band structures of semi-infinite phononic crystals are yielded through an asymptotic analysis on the scattering matrix. Some numerical examples are presented to demonstrate that the proposed method can solve accurately scattering problems and also can calculate some related eigenmodes including the Bloch modes and guided waves within stacked structures.Kei MATSUSHIMAHiroshi ISAKARIToru TAKAHASHIToshiro MATSUMOTOThe Japan Society of Mechanical Engineersarticlelayer-doubling methodscattering matrixelastic waveboundary element methodphononic crystalelastic metamaterialMechanical engineering and machineryTJ1-1570ENMechanical Engineering Journal, Vol 8, Iss 1, Pp 20-00364-20-00364 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	layer-doubling method scattering matrix elastic wave boundary element method phononic crystal elastic metamaterial Mechanical engineering and machinery TJ1-1570
spellingShingle	layer-doubling method scattering matrix elastic wave boundary element method phononic crystal elastic metamaterial Mechanical engineering and machinery TJ1-1570 Kei MATSUSHIMA Hiroshi ISAKARI Toru TAKAHASHI Toshiro MATSUMOTO A numerical method for elastic wave scattering in multi-layered periodic media based on the scattering matrix and BEM
description	This paper presents a numerical method for analyzing elastic wave scattering by multi-layered periodic structures in two dimensions. The proposed method is based on the boundary element method (BEM) and scattering matrix representing a relationship between incoming and outgoing waves in the vicinity of a periodic structure. First, we define the scattering matrix using a plane-wave expansion of the solution of the elastic problem. Then, we show the integral formulae that convert the solution of a system of boundary integral equations into elements of the scattering matrix. The proposed scattering matrix method with the BEM enables us to reduce the scattering problem in a multi-layered structure to a purely algebraic one in terms of the scattering matrix of each layer, resulting into less requirement in computational resources than in the methods which are based on the meshing of an entire boundary and solution of the corresponding boundary integral equations. Such a procedure called layer-doubling method is implemented in a numerically stable manner based on the eigendecomposition of a relevant matrix. Moreover, some scattering properties and phononic band structures of semi-infinite phononic crystals are yielded through an asymptotic analysis on the scattering matrix. Some numerical examples are presented to demonstrate that the proposed method can solve accurately scattering problems and also can calculate some related eigenmodes including the Bloch modes and guided waves within stacked structures.
format	article
author	Kei MATSUSHIMA Hiroshi ISAKARI Toru TAKAHASHI Toshiro MATSUMOTO
author_facet	Kei MATSUSHIMA Hiroshi ISAKARI Toru TAKAHASHI Toshiro MATSUMOTO
author_sort	Kei MATSUSHIMA
title	A numerical method for elastic wave scattering in multi-layered periodic media based on the scattering matrix and BEM
title_short	A numerical method for elastic wave scattering in multi-layered periodic media based on the scattering matrix and BEM
title_full	A numerical method for elastic wave scattering in multi-layered periodic media based on the scattering matrix and BEM
title_fullStr	A numerical method for elastic wave scattering in multi-layered periodic media based on the scattering matrix and BEM
title_full_unstemmed	A numerical method for elastic wave scattering in multi-layered periodic media based on the scattering matrix and BEM
title_sort	numerical method for elastic wave scattering in multi-layered periodic media based on the scattering matrix and bem
publisher	The Japan Society of Mechanical Engineers
publishDate	2020
url	https://doaj.org/article/9fd817b21d774bd9a66e1c2dfa77aae5
work_keys_str_mv	AT keimatsushima anumericalmethodforelasticwavescatteringinmultilayeredperiodicmediabasedonthescatteringmatrixandbem AT hiroshiisakari anumericalmethodforelasticwavescatteringinmultilayeredperiodicmediabasedonthescatteringmatrixandbem AT torutakahashi anumericalmethodforelasticwavescatteringinmultilayeredperiodicmediabasedonthescatteringmatrixandbem AT toshiromatsumoto anumericalmethodforelasticwavescatteringinmultilayeredperiodicmediabasedonthescatteringmatrixandbem AT keimatsushima numericalmethodforelasticwavescatteringinmultilayeredperiodicmediabasedonthescatteringmatrixandbem AT hiroshiisakari numericalmethodforelasticwavescatteringinmultilayeredperiodicmediabasedonthescatteringmatrixandbem AT torutakahashi numericalmethodforelasticwavescatteringinmultilayeredperiodicmediabasedonthescatteringmatrixandbem AT toshiromatsumoto numericalmethodforelasticwavescatteringinmultilayeredperiodicmediabasedonthescatteringmatrixandbem
_version_	1718407602605391872

A numerical method for elastic wave scattering in multi-layered periodic media based on the scattering matrix and BEM

Ejemplares similares