Effect of boundary conditions on the band-gap properties of flexural waves in a periodic compound plate

Zhiwei Guo, Meiping Sheng, Jie Pan

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    This paper examines the effect of boundary conditions on the band-gap properties of flexural waves in a periodic compound plate. The general boundary conditions are modelled by linear and torsional springs, and the traditional free, clamped, and simply supported boundary conditions become their special cases when the spring constants approach extreme values. The forced response of a finite periodic structure and the band-gap frequencies of an infinite periodic structure are solved analytically using the thin plate equations with the boundary conditions and Bloch periodic conditions. The results show that the band-gap and propagating mode properties of the compound plate are highly dependent on the boundary stiffness constants. For a small stiffness, a few branches of dispersion curves tend to be concentrated in the same pass-band. They gradually become separated as the stiffness increases, resulting in band-gaps with broader width. In addition, in the frequency range of interest, the band-gap properties are more sensitive to linear spring stiffness than torsional spring stiffness. The linear spring stiffness has a significant influence on all the dispersion curves, while the effect of the torsional spring stiffness on the band-gap properties varies with the dispersion branches.

    Original languageEnglish
    Pages (from-to)102-126
    Number of pages25
    JournalJournal of Sound and Vibration
    Volume395
    DOIs
    Publication statusPublished - 12 May 2017

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    Elastic waves
    stiffness
    Energy gap
    Stiffness
    Boundary conditions
    boundary conditions
    Periodic structures
    thin plates
    curves
    frequency ranges

    Cite this

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    title = "Effect of boundary conditions on the band-gap properties of flexural waves in a periodic compound plate",
    abstract = "This paper examines the effect of boundary conditions on the band-gap properties of flexural waves in a periodic compound plate. The general boundary conditions are modelled by linear and torsional springs, and the traditional free, clamped, and simply supported boundary conditions become their special cases when the spring constants approach extreme values. The forced response of a finite periodic structure and the band-gap frequencies of an infinite periodic structure are solved analytically using the thin plate equations with the boundary conditions and Bloch periodic conditions. The results show that the band-gap and propagating mode properties of the compound plate are highly dependent on the boundary stiffness constants. For a small stiffness, a few branches of dispersion curves tend to be concentrated in the same pass-band. They gradually become separated as the stiffness increases, resulting in band-gaps with broader width. In addition, in the frequency range of interest, the band-gap properties are more sensitive to linear spring stiffness than torsional spring stiffness. The linear spring stiffness has a significant influence on all the dispersion curves, while the effect of the torsional spring stiffness on the band-gap properties varies with the dispersion branches.",
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    author = "Zhiwei Guo and Meiping Sheng and Jie Pan",
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    Effect of boundary conditions on the band-gap properties of flexural waves in a periodic compound plate. / Guo, Zhiwei; Sheng, Meiping; Pan, Jie.

    In: Journal of Sound and Vibration, Vol. 395, 12.05.2017, p. 102-126.

    Research output: Contribution to journalArticle

    TY - JOUR

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    AU - Guo, Zhiwei

    AU - Sheng, Meiping

    AU - Pan, Jie

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    Y1 - 2017/5/12

    N2 - This paper examines the effect of boundary conditions on the band-gap properties of flexural waves in a periodic compound plate. The general boundary conditions are modelled by linear and torsional springs, and the traditional free, clamped, and simply supported boundary conditions become their special cases when the spring constants approach extreme values. The forced response of a finite periodic structure and the band-gap frequencies of an infinite periodic structure are solved analytically using the thin plate equations with the boundary conditions and Bloch periodic conditions. The results show that the band-gap and propagating mode properties of the compound plate are highly dependent on the boundary stiffness constants. For a small stiffness, a few branches of dispersion curves tend to be concentrated in the same pass-band. They gradually become separated as the stiffness increases, resulting in band-gaps with broader width. In addition, in the frequency range of interest, the band-gap properties are more sensitive to linear spring stiffness than torsional spring stiffness. The linear spring stiffness has a significant influence on all the dispersion curves, while the effect of the torsional spring stiffness on the band-gap properties varies with the dispersion branches.

    AB - This paper examines the effect of boundary conditions on the band-gap properties of flexural waves in a periodic compound plate. The general boundary conditions are modelled by linear and torsional springs, and the traditional free, clamped, and simply supported boundary conditions become their special cases when the spring constants approach extreme values. The forced response of a finite periodic structure and the band-gap frequencies of an infinite periodic structure are solved analytically using the thin plate equations with the boundary conditions and Bloch periodic conditions. The results show that the band-gap and propagating mode properties of the compound plate are highly dependent on the boundary stiffness constants. For a small stiffness, a few branches of dispersion curves tend to be concentrated in the same pass-band. They gradually become separated as the stiffness increases, resulting in band-gaps with broader width. In addition, in the frequency range of interest, the band-gap properties are more sensitive to linear spring stiffness than torsional spring stiffness. The linear spring stiffness has a significant influence on all the dispersion curves, while the effect of the torsional spring stiffness on the band-gap properties varies with the dispersion branches.

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