Application for a Novel Perturbation Expansion Method

We formulate a coupled vibration problem between a structure and an acoustic field by FEM (finite element methods). The problem leads to a nonstandard eigenvalue problem. Furthermore, we introduce a coupling strength parameter ε as a multiplier applied to the non-diagonal coupling terms. A natural i...
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Autor*in:	Li Deng [verfasserIn] Craig C. Douglas [verfasserIn] Gundolf Haase [verfasserIn] Takashi Kako [verfasserIn] Ichiro Hagiwara [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2009

Übergeordnetes Werk:	In: Journal of Algorithms & Computational Technology - SAGE Publishing, 2017, 3(2009)
Übergeordnetes Werk:	volume:3 ; year:2009

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc Journal toc

DOI / URN:	10.1260/174830109787186532

Katalog-ID:	DOAJ036595381

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520			\|a We formulate a coupled vibration problem between a structure and an acoustic field by FEM (finite element methods). The problem leads to a nonstandard eigenvalue problem. Furthermore, we introduce a coupling strength parameter ε as a multiplier applied to the non-diagonal coupling terms. A natural interpretation of this parameter is given. We represent an eigenpair for the coupled system by a perturbation series with respect to ε which enables us to express the eigenpair for the coupled case by those for the decoupled case. In some practical applications, by using this perturbation series, it would become unnecessary to perform time consuming computations to get coupled eigenvalues, and hence the present results obtained by the perturbation analysis might have considerable engineering importance. We confirm the adequacy of this perturbation analysis by investigating numerical examples. The results are given for a two dimensional coupled problem which given exact solution so that we can compare the results.
653		0	\|a Applied mathematics. Quantitative methods
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700	0		\|a Ichiro Hagiwara \|e verfasserin \|4 aut
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allfields	10.1260/174830109787186532 doi (DE-627)DOAJ036595381 (DE-599)DOAJ69e8f667ddc146d5bb508727fe1cbecb DE-627 ger DE-627 rakwb eng T57-57.97 QA1-939 Li Deng verfasserin aut Application for a Novel Perturbation Expansion Method 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We formulate a coupled vibration problem between a structure and an acoustic field by FEM (finite element methods). The problem leads to a nonstandard eigenvalue problem. Furthermore, we introduce a coupling strength parameter ε as a multiplier applied to the non-diagonal coupling terms. A natural interpretation of this parameter is given. We represent an eigenpair for the coupled system by a perturbation series with respect to ε which enables us to express the eigenpair for the coupled case by those for the decoupled case. In some practical applications, by using this perturbation series, it would become unnecessary to perform time consuming computations to get coupled eigenvalues, and hence the present results obtained by the perturbation analysis might have considerable engineering importance. We confirm the adequacy of this perturbation analysis by investigating numerical examples. The results are given for a two dimensional coupled problem which given exact solution so that we can compare the results. Applied mathematics. Quantitative methods Mathematics Craig C. Douglas verfasserin aut Gundolf Haase verfasserin aut Takashi Kako verfasserin aut Ichiro Hagiwara verfasserin aut In Journal of Algorithms & Computational Technology SAGE Publishing, 2017 3(2009) (DE-627)591513978 (DE-600)2478205-1 17483026 nnns volume:3 year:2009 https://doi.org/10.1260/174830109787186532 kostenfrei https://doaj.org/article/69e8f667ddc146d5bb508727fe1cbecb kostenfrei https://doi.org/10.1260/174830109787186532 kostenfrei https://doaj.org/toc/1748-3018 Journal toc kostenfrei https://doaj.org/toc/1748-3026 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2034 GBV_ILN_2057 GBV_ILN_2068 GBV_ILN_2098 GBV_ILN_2706 GBV_ILN_2707 GBV_ILN_2890 GBV_ILN_2954 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 3 2009
spelling	10.1260/174830109787186532 doi (DE-627)DOAJ036595381 (DE-599)DOAJ69e8f667ddc146d5bb508727fe1cbecb DE-627 ger DE-627 rakwb eng T57-57.97 QA1-939 Li Deng verfasserin aut Application for a Novel Perturbation Expansion Method 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We formulate a coupled vibration problem between a structure and an acoustic field by FEM (finite element methods). The problem leads to a nonstandard eigenvalue problem. Furthermore, we introduce a coupling strength parameter ε as a multiplier applied to the non-diagonal coupling terms. A natural interpretation of this parameter is given. We represent an eigenpair for the coupled system by a perturbation series with respect to ε which enables us to express the eigenpair for the coupled case by those for the decoupled case. In some practical applications, by using this perturbation series, it would become unnecessary to perform time consuming computations to get coupled eigenvalues, and hence the present results obtained by the perturbation analysis might have considerable engineering importance. We confirm the adequacy of this perturbation analysis by investigating numerical examples. The results are given for a two dimensional coupled problem which given exact solution so that we can compare the results. Applied mathematics. Quantitative methods Mathematics Craig C. Douglas verfasserin aut Gundolf Haase verfasserin aut Takashi Kako verfasserin aut Ichiro Hagiwara verfasserin aut In Journal of Algorithms & Computational Technology SAGE Publishing, 2017 3(2009) (DE-627)591513978 (DE-600)2478205-1 17483026 nnns volume:3 year:2009 https://doi.org/10.1260/174830109787186532 kostenfrei https://doaj.org/article/69e8f667ddc146d5bb508727fe1cbecb kostenfrei https://doi.org/10.1260/174830109787186532 kostenfrei https://doaj.org/toc/1748-3018 Journal toc kostenfrei https://doaj.org/toc/1748-3026 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2034 GBV_ILN_2057 GBV_ILN_2068 GBV_ILN_2098 GBV_ILN_2706 GBV_ILN_2707 GBV_ILN_2890 GBV_ILN_2954 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 3 2009
allfields_unstemmed	10.1260/174830109787186532 doi (DE-627)DOAJ036595381 (DE-599)DOAJ69e8f667ddc146d5bb508727fe1cbecb DE-627 ger DE-627 rakwb eng T57-57.97 QA1-939 Li Deng verfasserin aut Application for a Novel Perturbation Expansion Method 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We formulate a coupled vibration problem between a structure and an acoustic field by FEM (finite element methods). The problem leads to a nonstandard eigenvalue problem. Furthermore, we introduce a coupling strength parameter ε as a multiplier applied to the non-diagonal coupling terms. A natural interpretation of this parameter is given. We represent an eigenpair for the coupled system by a perturbation series with respect to ε which enables us to express the eigenpair for the coupled case by those for the decoupled case. In some practical applications, by using this perturbation series, it would become unnecessary to perform time consuming computations to get coupled eigenvalues, and hence the present results obtained by the perturbation analysis might have considerable engineering importance. We confirm the adequacy of this perturbation analysis by investigating numerical examples. The results are given for a two dimensional coupled problem which given exact solution so that we can compare the results. Applied mathematics. Quantitative methods Mathematics Craig C. Douglas verfasserin aut Gundolf Haase verfasserin aut Takashi Kako verfasserin aut Ichiro Hagiwara verfasserin aut In Journal of Algorithms & Computational Technology SAGE Publishing, 2017 3(2009) (DE-627)591513978 (DE-600)2478205-1 17483026 nnns volume:3 year:2009 https://doi.org/10.1260/174830109787186532 kostenfrei https://doaj.org/article/69e8f667ddc146d5bb508727fe1cbecb kostenfrei https://doi.org/10.1260/174830109787186532 kostenfrei https://doaj.org/toc/1748-3018 Journal toc kostenfrei https://doaj.org/toc/1748-3026 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2034 GBV_ILN_2057 GBV_ILN_2068 GBV_ILN_2098 GBV_ILN_2706 GBV_ILN_2707 GBV_ILN_2890 GBV_ILN_2954 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 3 2009
allfieldsGer	10.1260/174830109787186532 doi (DE-627)DOAJ036595381 (DE-599)DOAJ69e8f667ddc146d5bb508727fe1cbecb DE-627 ger DE-627 rakwb eng T57-57.97 QA1-939 Li Deng verfasserin aut Application for a Novel Perturbation Expansion Method 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We formulate a coupled vibration problem between a structure and an acoustic field by FEM (finite element methods). The problem leads to a nonstandard eigenvalue problem. Furthermore, we introduce a coupling strength parameter ε as a multiplier applied to the non-diagonal coupling terms. A natural interpretation of this parameter is given. We represent an eigenpair for the coupled system by a perturbation series with respect to ε which enables us to express the eigenpair for the coupled case by those for the decoupled case. In some practical applications, by using this perturbation series, it would become unnecessary to perform time consuming computations to get coupled eigenvalues, and hence the present results obtained by the perturbation analysis might have considerable engineering importance. We confirm the adequacy of this perturbation analysis by investigating numerical examples. The results are given for a two dimensional coupled problem which given exact solution so that we can compare the results. Applied mathematics. Quantitative methods Mathematics Craig C. Douglas verfasserin aut Gundolf Haase verfasserin aut Takashi Kako verfasserin aut Ichiro Hagiwara verfasserin aut In Journal of Algorithms & Computational Technology SAGE Publishing, 2017 3(2009) (DE-627)591513978 (DE-600)2478205-1 17483026 nnns volume:3 year:2009 https://doi.org/10.1260/174830109787186532 kostenfrei https://doaj.org/article/69e8f667ddc146d5bb508727fe1cbecb kostenfrei https://doi.org/10.1260/174830109787186532 kostenfrei https://doaj.org/toc/1748-3018 Journal toc kostenfrei https://doaj.org/toc/1748-3026 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2034 GBV_ILN_2057 GBV_ILN_2068 GBV_ILN_2098 GBV_ILN_2706 GBV_ILN_2707 GBV_ILN_2890 GBV_ILN_2954 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 3 2009
allfieldsSound	10.1260/174830109787186532 doi (DE-627)DOAJ036595381 (DE-599)DOAJ69e8f667ddc146d5bb508727fe1cbecb DE-627 ger DE-627 rakwb eng T57-57.97 QA1-939 Li Deng verfasserin aut Application for a Novel Perturbation Expansion Method 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We formulate a coupled vibration problem between a structure and an acoustic field by FEM (finite element methods). The problem leads to a nonstandard eigenvalue problem. Furthermore, we introduce a coupling strength parameter ε as a multiplier applied to the non-diagonal coupling terms. A natural interpretation of this parameter is given. We represent an eigenpair for the coupled system by a perturbation series with respect to ε which enables us to express the eigenpair for the coupled case by those for the decoupled case. In some practical applications, by using this perturbation series, it would become unnecessary to perform time consuming computations to get coupled eigenvalues, and hence the present results obtained by the perturbation analysis might have considerable engineering importance. We confirm the adequacy of this perturbation analysis by investigating numerical examples. The results are given for a two dimensional coupled problem which given exact solution so that we can compare the results. Applied mathematics. Quantitative methods Mathematics Craig C. Douglas verfasserin aut Gundolf Haase verfasserin aut Takashi Kako verfasserin aut Ichiro Hagiwara verfasserin aut In Journal of Algorithms & Computational Technology SAGE Publishing, 2017 3(2009) (DE-627)591513978 (DE-600)2478205-1 17483026 nnns volume:3 year:2009 https://doi.org/10.1260/174830109787186532 kostenfrei https://doaj.org/article/69e8f667ddc146d5bb508727fe1cbecb kostenfrei https://doi.org/10.1260/174830109787186532 kostenfrei https://doaj.org/toc/1748-3018 Journal toc kostenfrei https://doaj.org/toc/1748-3026 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2034 GBV_ILN_2057 GBV_ILN_2068 GBV_ILN_2098 GBV_ILN_2706 GBV_ILN_2707 GBV_ILN_2890 GBV_ILN_2954 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 3 2009
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callnumber-first	T - Technology
author	Li Deng
spellingShingle	Li Deng misc T57-57.97 misc QA1-939 misc Applied mathematics. Quantitative methods misc Mathematics Application for a Novel Perturbation Expansion Method
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topic_title	T57-57.97 QA1-939 Application for a Novel Perturbation Expansion Method
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title	Application for a Novel Perturbation Expansion Method
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title_sort	application for a novel perturbation expansion method
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title_auth	Application for a Novel Perturbation Expansion Method
abstract	We formulate a coupled vibration problem between a structure and an acoustic field by FEM (finite element methods). The problem leads to a nonstandard eigenvalue problem. Furthermore, we introduce a coupling strength parameter ε as a multiplier applied to the non-diagonal coupling terms. A natural interpretation of this parameter is given. We represent an eigenpair for the coupled system by a perturbation series with respect to ε which enables us to express the eigenpair for the coupled case by those for the decoupled case. In some practical applications, by using this perturbation series, it would become unnecessary to perform time consuming computations to get coupled eigenvalues, and hence the present results obtained by the perturbation analysis might have considerable engineering importance. We confirm the adequacy of this perturbation analysis by investigating numerical examples. The results are given for a two dimensional coupled problem which given exact solution so that we can compare the results.
abstractGer	We formulate a coupled vibration problem between a structure and an acoustic field by FEM (finite element methods). The problem leads to a nonstandard eigenvalue problem. Furthermore, we introduce a coupling strength parameter ε as a multiplier applied to the non-diagonal coupling terms. A natural interpretation of this parameter is given. We represent an eigenpair for the coupled system by a perturbation series with respect to ε which enables us to express the eigenpair for the coupled case by those for the decoupled case. In some practical applications, by using this perturbation series, it would become unnecessary to perform time consuming computations to get coupled eigenvalues, and hence the present results obtained by the perturbation analysis might have considerable engineering importance. We confirm the adequacy of this perturbation analysis by investigating numerical examples. The results are given for a two dimensional coupled problem which given exact solution so that we can compare the results.
abstract_unstemmed	We formulate a coupled vibration problem between a structure and an acoustic field by FEM (finite element methods). The problem leads to a nonstandard eigenvalue problem. Furthermore, we introduce a coupling strength parameter ε as a multiplier applied to the non-diagonal coupling terms. A natural interpretation of this parameter is given. We represent an eigenpair for the coupled system by a perturbation series with respect to ε which enables us to express the eigenpair for the coupled case by those for the decoupled case. In some practical applications, by using this perturbation series, it would become unnecessary to perform time consuming computations to get coupled eigenvalues, and hence the present results obtained by the perturbation analysis might have considerable engineering importance. We confirm the adequacy of this perturbation analysis by investigating numerical examples. The results are given for a two dimensional coupled problem which given exact solution so that we can compare the results.
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title_short	Application for a Novel Perturbation Expansion Method
url	https://doi.org/10.1260/174830109787186532 https://doaj.org/article/69e8f667ddc146d5bb508727fe1cbecb https://doaj.org/toc/1748-3018 https://doaj.org/toc/1748-3026
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up_date	2024-07-03T21:28:21.098Z
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