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| SYMPLECTIC ANALYSIS FOR BAND GAPS IN ONE DIMENSIONAL PHONON CRYSTAL BASED ON NONLOCAL ELASTIC THEORY |
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Abstract The elastic wave propagation in periodic composite structure (Phonon crystal) appears especial dispersion relations: the wave can only propagate in some frequency ranges (called pass-band) without dissipation. The dispersion relations of one dimensional phonon crystal can be analysed as the eigen-value problems of elastic wave propagation in layered media. In this paper, we investigate the nonlocal effect on the band gaps in phonon crystal. The two dimensional nonlocal linear elastic theory presented by Eringen is derived to the Hamilton system. The precise integration method and external Wittrick-Williams algorithm are used to calculate the eigen-solutions in arbitrary frequency ranges. The numerical results of typical problems and the comparison between nonlocal theory and classical local theory are given out and discussed. The advantages and applicability of the approach are also presented.
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Received: 19 November 2010
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2012, Vol. 33 