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基于人工弹簧模型的周期结构带隙计算方法研究

冯青松 杨舟 郭文杰 陆建飞 梁玉雄

冯青松, 杨舟, 郭文杰, 陆建飞, 梁玉雄. 基于人工弹簧模型的周期结构带隙计算方法研究[J]. 力学学报, 2021, 53(6): 1684-1697. doi: 10.6052/0459-1879-21-007
引用本文: 冯青松, 杨舟, 郭文杰, 陆建飞, 梁玉雄. 基于人工弹簧模型的周期结构带隙计算方法研究[J]. 力学学报, 2021, 53(6): 1684-1697. doi: 10.6052/0459-1879-21-007
Feng Qingsong, Yang Zhou, Guo Wenjie, Lu Jianfei, Liang Yuxiong. RESEARCH ON BAND GAP CALCULATION METHOD OF PERIODIC STRUCTURE BASED ON ARTIFICIAL SPRING MODEL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(6): 1684-1697. doi: 10.6052/0459-1879-21-007
Citation: Feng Qingsong, Yang Zhou, Guo Wenjie, Lu Jianfei, Liang Yuxiong. RESEARCH ON BAND GAP CALCULATION METHOD OF PERIODIC STRUCTURE BASED ON ARTIFICIAL SPRING MODEL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(6): 1684-1697. doi: 10.6052/0459-1879-21-007

基于人工弹簧模型的周期结构带隙计算方法研究

doi: 10.6052/0459-1879-21-007
基金项目: 1)国家自然科学基金(51878277);国家自然科学基金(52068029);江西省主要学科学术和技术带头人培养计划(20194BCJ22008);江西省重点研发计划(20192BBE50008);江西省青年科学基金(20202BABL214049)
详细信息
    作者简介:

    2)郭文杰, 博士, 主要研究方向: 结构振动与噪声控制. E-mail: guowenjie@ecjtu.edu.cn.

    通讯作者:

    郭文杰

  • 中图分类号: O327,O328

RESEARCH ON BAND GAP CALCULATION METHOD OF PERIODIC STRUCTURE BASED ON ARTIFICIAL SPRING MODEL

  • 摘要: 能量法具有将求解微分方程边值问题转化为泛函极值问题的优点,故而在结构动力学分析中被广泛使用, 近年来也被引入到周期结构带隙计算中. 然而,由于周期结构边界条件相对复杂,采用传统能量法(如Rayleigh-Ritz法)分析时位移函数构造难度大;且由于位移函数中包含波数项,扫描波数计算带隙的过程中质量、刚度矩阵需不断重算, 导致计算量较大. 鉴于此,本文对传统能量法进行改进,通过引入人工弹簧来模拟包含周期边界在内的各类边界条件,可将边界约束转化为人工弹簧的弹性势能,故而各能量分部中仅有周期边界弹性势能包含波数项,扫描波数时仅需重新计算与其对应的刚度矩阵,其余的质量、刚度矩阵只需要计算一次, 继而显著降低了计算量. 研究结果表明,本文方法准确、可靠, 且相较于传统能量法, 本文方法的计算效率更高,随着结构质量、刚度矩阵的维度增大, 或者扫描波数点数的增多,本文方法计算效率优势更加明显. 此外, 人工弹簧模型使用灵活、便捷,可进一步地拓展到更为复杂的周期性组合结构带隙分析中.

     

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  • 收稿日期:  2020-01-06
  • 刊出日期:  2021-06-01

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