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    Combining Plane Wave Expansion and Variational Techniques for Fast Phononic Computations

    Source: Journal of Engineering Mechanics:;2017:;Volume ( 143 ):;issue: 012
    Author:
    Yan Lu
    ,
    Ankit Srivastava
    DOI: 10.1061/(ASCE)EM.1943-7889.0001362
    Publisher: American Society of Civil Engineers
    Abstract: In this paper, the salient features of the plane wave expansion (PWE) method and the mixed variational technique are combined for the fast eigenvalue computations of arbitrarily complex phononic unit cells. This is done by expanding the material properties in a Fourier expansion, as is the case with PWE. The required matrix elements in the variational scheme are identified as the discrete Fourier transform coefficients of material properties, thus obviating the need for any explicit integration. The process provides succinct, closed-form expressions for all the matrices involved in the mixed variational method. The scheme proposed preserves both the simplicity of expression that is inherent in the PWE method and the superior convergence properties of the mixed variational scheme. This paper presents numerical results and comments upon the convergence and stability of the current method. The current representation renders the results of the method stable over the entire range of the expansion terms as allowed by the spatial discretization. When compared with a zero-order numerical integration scheme, the present method results in greater computational accuracy of all eigenvalues. A higher-order numerical integration scheme comes close to the accuracy of the present method but only with significantly more computational expense.
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      Combining Plane Wave Expansion and Variational Techniques for Fast Phononic Computations

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    contributor authorYan Lu
    contributor authorAnkit Srivastava
    date accessioned2017-12-30T12:54:14Z
    date available2017-12-30T12:54:14Z
    date issued2017
    identifier other%28ASCE%29EM.1943-7889.0001362.pdf
    identifier urihttp://138.201.223.254:8080/yetl1/handle/yetl/4243177
    description abstractIn this paper, the salient features of the plane wave expansion (PWE) method and the mixed variational technique are combined for the fast eigenvalue computations of arbitrarily complex phononic unit cells. This is done by expanding the material properties in a Fourier expansion, as is the case with PWE. The required matrix elements in the variational scheme are identified as the discrete Fourier transform coefficients of material properties, thus obviating the need for any explicit integration. The process provides succinct, closed-form expressions for all the matrices involved in the mixed variational method. The scheme proposed preserves both the simplicity of expression that is inherent in the PWE method and the superior convergence properties of the mixed variational scheme. This paper presents numerical results and comments upon the convergence and stability of the current method. The current representation renders the results of the method stable over the entire range of the expansion terms as allowed by the spatial discretization. When compared with a zero-order numerical integration scheme, the present method results in greater computational accuracy of all eigenvalues. A higher-order numerical integration scheme comes close to the accuracy of the present method but only with significantly more computational expense.
    publisherAmerican Society of Civil Engineers
    titleCombining Plane Wave Expansion and Variational Techniques for Fast Phononic Computations
    typeJournal Paper
    journal volume143
    journal issue12
    journal titleJournal of Engineering Mechanics
    identifier doi10.1061/(ASCE)EM.1943-7889.0001362
    page04017141
    treeJournal of Engineering Mechanics:;2017:;Volume ( 143 ):;issue: 012
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
    نرم افزار کتابخانه دیجیتال "دی اسپیس" فارسی شده توسط یابش برای کتابخانه های ایرانی | تماس با یابش
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