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广义有限差分法在含阻抗边界空腔声学分析中的应用

陈增涛 王发杰 王超

陈增涛, 王发杰, 王超. 广义有限差分法在含阻抗边界空腔声学分析中的应用[J]. 力学学报, 2021, 53(4): 1183-1195. doi: 10.6052/0459-1879-20-311
引用本文: 陈增涛, 王发杰, 王超. 广义有限差分法在含阻抗边界空腔声学分析中的应用[J]. 力学学报, 2021, 53(4): 1183-1195. doi: 10.6052/0459-1879-20-311
Chen Zengtao, Wang Fajie, Wang Chao. APPLICATION OF GENERALIZED FINITE DIFFERENCE METHOD IN ACOUSTIC ANALYSIS OF CAVITY WITH IMPEDANCE BOUNDARY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(4): 1183-1195. doi: 10.6052/0459-1879-20-311
Citation: Chen Zengtao, Wang Fajie, Wang Chao. APPLICATION OF GENERALIZED FINITE DIFFERENCE METHOD IN ACOUSTIC ANALYSIS OF CAVITY WITH IMPEDANCE BOUNDARY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(4): 1183-1195. doi: 10.6052/0459-1879-20-311

广义有限差分法在含阻抗边界空腔声学分析中的应用

doi: 10.6052/0459-1879-20-311
基金项目: 1)国家自然科学基金(11802151);山东省自然科学基金(ZR2019BA008);中国博士后科学基金(2019M652315);青岛市民生科技计划(19-6-1-88-nsh);青岛市民生科技计划(19-6-1-92-nsh)
详细信息
    作者简介:

    2)王发杰, 副教授, 主要研究方向: 力学建模、计算力学、数值仿真. E-mail: wfj1218@126.com

    通讯作者:

    王发杰

  • 中图分类号: O302,O422.2

APPLICATION OF GENERALIZED FINITE DIFFERENCE METHOD IN ACOUSTIC ANALYSIS OF CAVITY WITH IMPEDANCE BOUNDARY

  • 摘要: 声学分析在噪声控制、室内隔音等工程计算中有着重要的作用. 由于现实生活中的声学模型往往伴随着吸声材料, 因此分析含阻抗边界条件的声学问题显得十分必要. 广义有限差分法是一种新型区域型无网格数值离散方法, 该方法基于多元函数泰勒级数展开式和加权最小二乘拟合, 将控制方程中未知参量的各阶偏导数表示为相邻节点函数值的线性组合. 本文首次将广义有限差分法应用于含阻抗边界条件空腔声学问题的分析中, 建立了空腔声场问题的广义有限差分法数值离散格式. 与传统算法相比, 所建立的数值模型具有无需网格剖分和数值积分、计算精度高、适用于大规模声学分析等优点. 通过具有解析解的经典算例, 研究了总节点数目和局部支撑点数目对数值结果的影响, 得到了最大计算频率与节点间距之间关系的经验公式. 此外, 将广义有限差分法应用于无解析解的二维和三维复杂声学模型, 并与COMSOL Multiphysics软件所得的有限元结果进行了比较分析. 数值实验表明, 该算法是一种高效、精确、稳定、收敛的数值模拟方法, 在含阻抗边界空腔声学分析中具有广阔的应用前景.

     

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出版历程
  • 收稿日期:  2020-09-07
  • 刊出日期:  2021-04-10

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