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基于SiPESC平台的声子晶体能带结构分析算法研究及软件实现

姜殿恒 陈飙松 张盛 李云鹏

姜殿恒, 陈飙松, 张盛, 李云鹏. 基于SiPESC平台的声子晶体能带结构分析算法研究及软件实现[J]. 工程力学, 2022, 39(12): 1-12. doi: 10.6052/j.issn.1000-4750.2021.07.0563
引用本文: 姜殿恒, 陈飙松, 张盛, 李云鹏. 基于SiPESC平台的声子晶体能带结构分析算法研究及软件实现[J]. 工程力学, 2022, 39(12): 1-12. doi: 10.6052/j.issn.1000-4750.2021.07.0563
JIANG Dian-heng, CHEN Biao-song, ZHANG Sheng, LI Yun-peng. RESEARCH AND SOFTWARE IMPLEMENTATION OF ENERGY BAND STRUCTURE ANALYSIS ALGORITHM OF PHONONIC CRYSTALS BASED ON SiPESC PLATFORM[J]. Engineering Mechanics, 2022, 39(12): 1-12. doi: 10.6052/j.issn.1000-4750.2021.07.0563
Citation: JIANG Dian-heng, CHEN Biao-song, ZHANG Sheng, LI Yun-peng. RESEARCH AND SOFTWARE IMPLEMENTATION OF ENERGY BAND STRUCTURE ANALYSIS ALGORITHM OF PHONONIC CRYSTALS BASED ON SiPESC PLATFORM[J]. Engineering Mechanics, 2022, 39(12): 1-12. doi: 10.6052/j.issn.1000-4750.2021.07.0563

基于SiPESC平台的声子晶体能带结构分析算法研究及软件实现

doi: 10.6052/j.issn.1000-4750.2021.07.0563
基金项目: 国家重点研发计划项目(2020YFB1709403);国家自然科学基金项目(12072059)
详细信息
    作者简介:

    姜殿恒(1991−),男,辽宁人,博士生,主要从事声光晶体仿真优化研究(E-mail:dh_jiang@hotmail.com)

    张 盛(1976−),男,长春人,副教授,博士,主要从事CAE软件研发研究(E-mail: zhangs@dlut.edu.cn)

    李云鹏(1970−),男(满族),辽宁人,副教授,硕士,主要从事CAE软件研发研究(E-mail: lyp@dlut.edu.cn)

    通讯作者:

    陈飙松(1973−),男,广东人,教授,博士,博导,主要从事国产自主CAE软件研发研究(E-mail: chenbs@dlut.edu.cn)

  • 中图分类号: TB123

RESEARCH AND SOFTWARE IMPLEMENTATION OF ENERGY BAND STRUCTURE ANALYSIS ALGORITHM OF PHONONIC CRYSTALS BASED ON SiPESC PLATFORM

  • 摘要: 为了快速准确得分析声子晶体的能带结构,该文基于工程与科学计算仿真平台SiPESC,开发了一类高效三维声子晶体能带结构分析软件。软件针对能带结构分析过程中计算量庞大的Hermitian矩阵的广义特征值求解问题和边界约束节点匹配问题,提出了相关软件设计方案。针对Hermitian矩阵的广义特征值求解,在实对称矩阵子空间迭代法的基础上,发展了Hermitian矩阵子空间迭代法。针对边界约束节点匹配问题,该文将三维周期性条件划分为点、边、面约束分别处理。针对面约束,该文使用定位格匹配策略将单层的点-点匹配更改为2层的点-定位格-点加速匹配。开展了与多物理场分析软件COMSOL进行数值算例对比。使用三维局域共振声子晶体算例验证了软件在满足数值精度的前提下计算效率高于对比软件。通过大规模模型算例验证了软件具有高效的大规模计算能力。
  • 图  1  Hermitian子空间迭代法算法流程

    Figure  1.  Hermitian subspace iterative algorithm

    图  2  定位格节点关系

    Figure  2.  sub-patches-node relationship

    图  3  主节点和定位格的关联信息数组

    Figure  3.  Association information array of master node and sub-patches

    图  4  SiPESC平台能带结构分析流程

    Figure  4.  band structure analysis process of SiPESC platform

    图  5  SiPESC科学计算平台声子晶体软件模块的UML类图

    Figure  5.  UML class diagram of phononic crystal plugin in SiPESC platform

    图  6  三类约束几何关系及其关系树

    Figure  6.  Three kinds of constrained geometric relations and their relation trees

    图  7  能带结构分析算法流程

    Figure  7.  Band structure analysis algorithm

    图  8  局域共振声子晶体模型

    Figure  8.  Locally resonant sonic materials

    图  9  局域共振声子晶体能带结构及振型

    Figure  9.  Band structure and mode shapes of local resonant sonic crystals

    图  10  气/固声子晶体

    Figure  10.  Gas / solid phononic crystal

    图  11  气/固声子晶体能带结构及振型

    Figure  11.  Band structure and mode shapes of gas/solid phononic crystal

    图  12  折叠结构声子晶体模型

    Figure  12.  Folded structure phononic crystal model

    图  13  折叠结构声子晶体能带结构

    Figure  13.  Band structure of folded phononic crystals

    表  1  材料数据

    Table  1.   Material data

    设备SiPESC平台
    部署环境
    COMSOL Multiphysics
    5.5部署环境
    处理器Intel(R) Xeon(R) E5-2600
    CPU @ 28核2.00 GHz
    Intel(R) Core(TM) i7-8700
    CPU @ 6核3.20 GHz
    内存128 GB
    三星DDR3 1600 MHz
    24 GB
    三星DDR4 2666 MHz
    系统Linux Kubuntu
    2106Lts
    Win10
    下载: 导出CSV

    表  2  材料数据

    Table  2.   Material data

    材料弹性模量
    E/Pa
    泊松比
    ν
    密度
    ρ/(kg/m3)
    环氧树脂4.348×1063.674×10−11180
    1.176×1024.687×10−11300
    5.630×1073.698×10−111 600
    下载: 导出CSV

    表  3  几何尺寸

    Table  3.   Geometric dimension

    晶格常数a/mm散射体半径r1/mm包覆层半径r2/mm
    15.557.5
    下载: 导出CSV

    表  4  材料数据

    Table  4.   Material data

    材料弹性模量
    E/GPa
    泊松比
    ν
    密度
    ρ/(kg/m3)
    树脂10.41097
    下载: 导出CSV

    表  5  几何尺寸

    Table  5.   Geometric dimension

    晶格常数a/m空心球直径r1/m实心球直径r2/m圆柱直径r3/m
    11.320.90.06
    下载: 导出CSV

    表  6  材料数据

    Table  6.   Material data

    材料弹性模量
    E/GPa
    泊松比
    ν
    密度
    ρ/(kg/m3)
    700.3462697
    下载: 导出CSV

    表  7  几何尺寸

    Table  7.   Geometric dimension

    短边长度L/m长边长度A/m$ \beta $/(°)$\theta $/(°)
    0.020.044520
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-07-21
  • 录用日期:  2021-12-17
  • 修回日期:  2021-12-09
  • 网络出版日期:  2021-12-17
  • 刊出日期:  2022-12-01

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