Energy bands of a periodic viaduct in out-of-plane vibration: Coupling with a half-space

Jian-Fei Lu, Dong-Sheng Jeng

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    In this study, the periodic viaduct is used as an example to introduce a new type of phononic crystal structure: the “open”-type phononic crystal structure. A numerical model for analysis of the energy band of a periodic viaduct undergoing out-of-plane vibration is developed in this study. The most remarkable characteristic of the proposed model for the energy band of the periodic viaduct is that it can take into account the coupling between the periodic viaduct and the half-space soil. The viaduct considered in this study is assumed to be a regularly periodic arrangement of unit cells along its longitudinal direction. For simplicity, each unit cell is assumed to be consisted of a pile foundation, a pier and a horizontal beam. To obtain the compliances for the pile foundations, the pile-soil interaction problem is solved by the fictitious pile method first. Using the transfer matrix method and the obtained compliances for the pile foundations, the impedances for the piers are obtained. Based on the Bloch theorem and the transfer matrix method, the nonlinear polynomial eigenvalue equation for the periodic viaduct is derived using the impedance of the piers. Utilizing the obtained nonlinear eigenvalue equation, the approximate linear eigenvalue equation for the periodic viaduct is obtained and numerical results for the energy bands of the periodic viaduct are presented. Numerical results of this paper show that for the out-of-plane vibration of the periodic viaduct, there are three kinds of lattice waves propagating in the periodic viaduct. Moreover, in a low frequency range, all three lattice waves are evanescent, which will lead to the localization of lattice waves in the periodic viaduct.
    Original languageEnglish
    Pages (from-to)21-36
    Number of pages16
    JournalEuropean Journal of Mechanics A. Solids
    Volume31
    DOIs
    Publication statusPublished - Jul 2011

    Fingerprint

    pile foundations
    wharves
    Pile foundations
    Piers
    half spaces
    Band structure
    energy bands
    Transfer matrix method
    eigenvalues
    piles
    matrix methods
    vibration
    Piles
    soils
    Crystal structure
    impedance
    Soils
    crystal structure
    evanescent waves
    cells

    Keywords

    • Out-of-plane vibration
    • Phononic crystal structure
    • Energy band
    • Periodic viaduct
    • Pile-soil interaction

    Cite this

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    title = "Energy bands of a periodic viaduct in out-of-plane vibration: Coupling with a half-space",
    abstract = "In this study, the periodic viaduct is used as an example to introduce a new type of phononic crystal structure: the “open”-type phononic crystal structure. A numerical model for analysis of the energy band of a periodic viaduct undergoing out-of-plane vibration is developed in this study. The most remarkable characteristic of the proposed model for the energy band of the periodic viaduct is that it can take into account the coupling between the periodic viaduct and the half-space soil. The viaduct considered in this study is assumed to be a regularly periodic arrangement of unit cells along its longitudinal direction. For simplicity, each unit cell is assumed to be consisted of a pile foundation, a pier and a horizontal beam. To obtain the compliances for the pile foundations, the pile-soil interaction problem is solved by the fictitious pile method first. Using the transfer matrix method and the obtained compliances for the pile foundations, the impedances for the piers are obtained. Based on the Bloch theorem and the transfer matrix method, the nonlinear polynomial eigenvalue equation for the periodic viaduct is derived using the impedance of the piers. Utilizing the obtained nonlinear eigenvalue equation, the approximate linear eigenvalue equation for the periodic viaduct is obtained and numerical results for the energy bands of the periodic viaduct are presented. Numerical results of this paper show that for the out-of-plane vibration of the periodic viaduct, there are three kinds of lattice waves propagating in the periodic viaduct. Moreover, in a low frequency range, all three lattice waves are evanescent, which will lead to the localization of lattice waves in the periodic viaduct.",
    keywords = "Out-of-plane vibration, Phononic crystal structure, Energy band, Periodic viaduct, Pile-soil interaction",
    author = "Jian-Fei Lu and Dong-Sheng Jeng",
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    language = "English",
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    journal = "European Journal of Mechanics A. Solids",
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    Energy bands of a periodic viaduct in out-of-plane vibration: Coupling with a half-space. / Lu, Jian-Fei; Jeng, Dong-Sheng.

    In: European Journal of Mechanics A. Solids, Vol. 31, 07.2011, p. 21-36.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Energy bands of a periodic viaduct in out-of-plane vibration: Coupling with a half-space

    AU - Lu, Jian-Fei

    AU - Jeng, Dong-Sheng

    N1 - dc.publisher: Elsevier

    PY - 2011/7

    Y1 - 2011/7

    N2 - In this study, the periodic viaduct is used as an example to introduce a new type of phononic crystal structure: the “open”-type phononic crystal structure. A numerical model for analysis of the energy band of a periodic viaduct undergoing out-of-plane vibration is developed in this study. The most remarkable characteristic of the proposed model for the energy band of the periodic viaduct is that it can take into account the coupling between the periodic viaduct and the half-space soil. The viaduct considered in this study is assumed to be a regularly periodic arrangement of unit cells along its longitudinal direction. For simplicity, each unit cell is assumed to be consisted of a pile foundation, a pier and a horizontal beam. To obtain the compliances for the pile foundations, the pile-soil interaction problem is solved by the fictitious pile method first. Using the transfer matrix method and the obtained compliances for the pile foundations, the impedances for the piers are obtained. Based on the Bloch theorem and the transfer matrix method, the nonlinear polynomial eigenvalue equation for the periodic viaduct is derived using the impedance of the piers. Utilizing the obtained nonlinear eigenvalue equation, the approximate linear eigenvalue equation for the periodic viaduct is obtained and numerical results for the energy bands of the periodic viaduct are presented. Numerical results of this paper show that for the out-of-plane vibration of the periodic viaduct, there are three kinds of lattice waves propagating in the periodic viaduct. Moreover, in a low frequency range, all three lattice waves are evanescent, which will lead to the localization of lattice waves in the periodic viaduct.

    AB - In this study, the periodic viaduct is used as an example to introduce a new type of phononic crystal structure: the “open”-type phononic crystal structure. A numerical model for analysis of the energy band of a periodic viaduct undergoing out-of-plane vibration is developed in this study. The most remarkable characteristic of the proposed model for the energy band of the periodic viaduct is that it can take into account the coupling between the periodic viaduct and the half-space soil. The viaduct considered in this study is assumed to be a regularly periodic arrangement of unit cells along its longitudinal direction. For simplicity, each unit cell is assumed to be consisted of a pile foundation, a pier and a horizontal beam. To obtain the compliances for the pile foundations, the pile-soil interaction problem is solved by the fictitious pile method first. Using the transfer matrix method and the obtained compliances for the pile foundations, the impedances for the piers are obtained. Based on the Bloch theorem and the transfer matrix method, the nonlinear polynomial eigenvalue equation for the periodic viaduct is derived using the impedance of the piers. Utilizing the obtained nonlinear eigenvalue equation, the approximate linear eigenvalue equation for the periodic viaduct is obtained and numerical results for the energy bands of the periodic viaduct are presented. Numerical results of this paper show that for the out-of-plane vibration of the periodic viaduct, there are three kinds of lattice waves propagating in the periodic viaduct. Moreover, in a low frequency range, all three lattice waves are evanescent, which will lead to the localization of lattice waves in the periodic viaduct.

    KW - Out-of-plane vibration

    KW - Phononic crystal structure

    KW - Energy band

    KW - Periodic viaduct

    KW - Pile-soil interaction

    U2 - 10.1016/j.euromechsol.2011.07.001

    DO - 10.1016/j.euromechsol.2011.07.001

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    VL - 31

    SP - 21

    EP - 36

    JO - European Journal of Mechanics A. Solids

    JF - European Journal of Mechanics A. Solids

    SN - 0997-7538

    ER -