Topology optimization of acoustic metamaterials with negative mass density using a level set-based method

Much effort has been made to experimentally fabricate acoustic metamaterials that display novel properties, such as single or double negativity, negative refractive index. The novel properties displayed by acoustic metamaterials and their deep subwavelength nature, whereas the size of phononic cryst...

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Autores principales:	Lirong LU, Masaki OTOMORI, Takayuki YAMADA, Takashi YAMAMOTO, Kazuhiro IZUI, Shinji NISHIWAKI
Formato:	article
Lenguaje:	EN
Publicado:	The Japan Society of Mechanical Engineers 2014
Materias:	topology optimization acoustic metamaterial negative mass density s-parameter retrieval method level set method Mechanical engineering and machinery TJ1-1570
Acceso en línea:	https://doaj.org/article/5e36030bc09a4d94bb1ae082a43e745f
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id	oai:doaj.org-article:5e36030bc09a4d94bb1ae082a43e745f
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spelling	oai:doaj.org-article:5e36030bc09a4d94bb1ae082a43e745f2021-11-26T06:09:52ZTopology optimization of acoustic metamaterials with negative mass density using a level set-based method2187-974510.1299/mej.2014dsm0040https://doaj.org/article/5e36030bc09a4d94bb1ae082a43e745f2014-08-01T00:00:00Zhttps://www.jstage.jst.go.jp/article/mej/1/4/1_2014dsm0040/_pdf/-char/enhttps://doaj.org/toc/2187-9745Much effort has been made to experimentally fabricate acoustic metamaterials that display novel properties, such as single or double negativity, negative refractive index. The novel properties displayed by acoustic metamaterials and their deep subwavelength nature, whereas the size of phononic crystals is in a comparable scale to wavelength, facilitate the development of real-world applications, from sound attenuation to superlenses, and acoustic cloaking. Compared with a conventional trial and error method, a systematic structural design methodology such as topology optimization is useful to achieve optimal designs of acoustic metamaterials. This paper proposes a topology optimization method for the design of acoustic metamaterials with the property of negative mass density. We consider mass-in-mass system that consists of a solid inclusion coated with a soft materials embedded in matrix material to produce a local dipole resonance that demonstrate negative mass density. The optimization is conducted to find optimal configurations of a locally resonant unit cell structure which achieves negative mass density at a certain desired frequency. The S-parameter retrieval method is efficaciously applied to describe the acoustic metamaterial according to its effective mass density. A level set-based method is employed to obtain the optimal configurations that have clear boundaries without gray scales, which would otherwise limit fabricability of the obtained acoustic metamaterial designs. The sensitivity analysis is performed by the adjoint variable method, and a reaction-diffusion equation is used to update the level set function. Several numerical examples are provided to demonstrate how the algorithm works, and the obtained optimal configurations illustrate the achievement of acoustic metamaterials that have negative mass density at certain prescribed frequencies.Lirong LUMasaki OTOMORITakayuki YAMADATakashi YAMAMOTOKazuhiro IZUIShinji NISHIWAKIThe Japan Society of Mechanical Engineersarticletopology optimizationacoustic metamaterialnegative mass densitys-parameter retrieval methodlevel set methodMechanical engineering and machineryTJ1-1570ENMechanical Engineering Journal, Vol 1, Iss 4, Pp DSM0040-DSM0040 (2014)
institution	DOAJ
collection	DOAJ
language	EN
topic	topology optimization acoustic metamaterial negative mass density s-parameter retrieval method level set method Mechanical engineering and machinery TJ1-1570
spellingShingle	topology optimization acoustic metamaterial negative mass density s-parameter retrieval method level set method Mechanical engineering and machinery TJ1-1570 Lirong LU Masaki OTOMORI Takayuki YAMADA Takashi YAMAMOTO Kazuhiro IZUI Shinji NISHIWAKI Topology optimization of acoustic metamaterials with negative mass density using a level set-based method
description	Much effort has been made to experimentally fabricate acoustic metamaterials that display novel properties, such as single or double negativity, negative refractive index. The novel properties displayed by acoustic metamaterials and their deep subwavelength nature, whereas the size of phononic crystals is in a comparable scale to wavelength, facilitate the development of real-world applications, from sound attenuation to superlenses, and acoustic cloaking. Compared with a conventional trial and error method, a systematic structural design methodology such as topology optimization is useful to achieve optimal designs of acoustic metamaterials. This paper proposes a topology optimization method for the design of acoustic metamaterials with the property of negative mass density. We consider mass-in-mass system that consists of a solid inclusion coated with a soft materials embedded in matrix material to produce a local dipole resonance that demonstrate negative mass density. The optimization is conducted to find optimal configurations of a locally resonant unit cell structure which achieves negative mass density at a certain desired frequency. The S-parameter retrieval method is efficaciously applied to describe the acoustic metamaterial according to its effective mass density. A level set-based method is employed to obtain the optimal configurations that have clear boundaries without gray scales, which would otherwise limit fabricability of the obtained acoustic metamaterial designs. The sensitivity analysis is performed by the adjoint variable method, and a reaction-diffusion equation is used to update the level set function. Several numerical examples are provided to demonstrate how the algorithm works, and the obtained optimal configurations illustrate the achievement of acoustic metamaterials that have negative mass density at certain prescribed frequencies.
format	article
author	Lirong LU Masaki OTOMORI Takayuki YAMADA Takashi YAMAMOTO Kazuhiro IZUI Shinji NISHIWAKI
author_facet	Lirong LU Masaki OTOMORI Takayuki YAMADA Takashi YAMAMOTO Kazuhiro IZUI Shinji NISHIWAKI
author_sort	Lirong LU
title	Topology optimization of acoustic metamaterials with negative mass density using a level set-based method
title_short	Topology optimization of acoustic metamaterials with negative mass density using a level set-based method
title_full	Topology optimization of acoustic metamaterials with negative mass density using a level set-based method
title_fullStr	Topology optimization of acoustic metamaterials with negative mass density using a level set-based method
title_full_unstemmed	Topology optimization of acoustic metamaterials with negative mass density using a level set-based method
title_sort	topology optimization of acoustic metamaterials with negative mass density using a level set-based method
publisher	The Japan Society of Mechanical Engineers
publishDate	2014
url	https://doaj.org/article/5e36030bc09a4d94bb1ae082a43e745f
work_keys_str_mv	AT lironglu topologyoptimizationofacousticmetamaterialswithnegativemassdensityusingalevelsetbasedmethod AT masakiotomori topologyoptimizationofacousticmetamaterialswithnegativemassdensityusingalevelsetbasedmethod AT takayukiyamada topologyoptimizationofacousticmetamaterialswithnegativemassdensityusingalevelsetbasedmethod AT takashiyamamoto topologyoptimizationofacousticmetamaterialswithnegativemassdensityusingalevelsetbasedmethod AT kazuhiroizui topologyoptimizationofacousticmetamaterialswithnegativemassdensityusingalevelsetbasedmethod AT shinjinishiwaki topologyoptimizationofacousticmetamaterialswithnegativemassdensityusingalevelsetbasedmethod
_version_	1718409778869305344

Topology optimization of acoustic metamaterials with negative mass density using a level set-based method

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