| 一维声子晶体带隙的非局部辛分析 |
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| 引用本文： | 姚征, 郑长良. 一维声子晶体带隙的非局部辛分析[J]. 固体力学学报, 2012, 33(1): 91-97. doi: 10.3969/j.issn.0254-7805.2012.01.014 |
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| 作者姓名： | 姚征 郑长良 |
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| 作者单位： | 1.大连海事大学交通装备与海洋工程学院,大连,116026;2.大连海事大学交通装备与海洋工程学院,大连,116026 |
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| 基金项目： | 国家自然科学基金项目(11072042);中央高校基本科研业务专项资金项目(2011QN045)资助 |
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| 摘 要： | 周期性弹性复合结构(声子晶体)中传播的弹性波存在特殊的色散关系:弹性波只能在某段频率范围内无损耗的传播,该频率范围称为通带.一维声子晶体的色散问题可以看作分层介质中弹性波的传播问题,利用二维弹性理论予以分析.为了研究非局部效应对声子晶体带隙特性的影响,将Eringen的二维非局部弹性理论引入到Hamilton体系下,利用精细积分与扩展的Wittrick Williams算法可获取任意频率范围内的本征解.通过对不同算例的数值计算,分析和对比了非局部理论方法与传统局部理论方法的差别.并进一步指出了该套算法的适用性和优势所在.
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| 关 键 词： | 声子晶体 能带理论 非局部 Hamilton原理 辛几何算法 |
SYMPLECTIC ANALYSIS FOR BAND GAPS IN ONE DIMENSIONAL PHONON CRYSTAL BASED ON NONLOCAL ELASTIC THEORY |
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| Zheng Yao, Changliang Zheng. SYMPLECTIC ANALYSIS FOR BAND GAPS IN ONE DIMENSIONAL PHONON CRYSTAL BASED ON NONLOCAL ELASTIC THEORY[J]. Chinese Journal of Solid Mechanics, 2012, 33(1): 91-97. doi: 10.3969/j.issn.0254-7805.2012.01.014 |
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| Authors: | Zheng Yao Changliang Zheng |
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| Affiliation: | Zheng Yao Changliang Zheng (Transportation Equipment and Ocean Engineering College,Dalian Maritime University,Dalian,116026) |
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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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| Keywords: | phonon crystal energy band theory nonlocal Hamilton theory symplectic algorithm |
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