结构声学耦合随机性分析的等几何有限元-边界元法研究

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摘要采用有限元法（FEM）进行水下壳结构振动响应分析，边界元法（BEM）进行结构振动声学分析；组合有限元法与边界元法构成耦合FEM-BEM方法进行水下薄壳结构声振强耦合分析。为了克服传统拉格朗日函数近似几何模型与物理场插值计算时的不连续与低精度问题，采用Loop细分曲面等几何法构建几何模型，并采用相同的样条函数进行物理场高阶插值计算，实现水下声振强耦合系统的CAD/CAE的集成分析。随机性分析致力于研究系统输入的不确定造成的输出不确定。蒙特卡罗模拟（MCs）以其简单、直接被认为是解决复杂多维不确定性问题的通用工具，然而巨大的计算成本降低了其适用性。采用本征正交分解（POD）和径向基函数（RBF）可降低计算成本，提高计算效率，实现基于MCs的快速随机性分析。考虑结构材料属性参数以及结构形状参数的不确定性对计算结果的影响，采用MCs分析随机变量下的结构声学响应的统计特征。最后通过若干算例验证本文算法的正确性与有效性。

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	胡昊文1
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	王中王1
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	徐延明2
	陈磊磊1
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关键词 ：有限元-边界元法, 细分曲面, 蒙特卡罗模拟, 本征正交分解, 径向基函数

Abstract：The finite element method (FEM) is used to analyze the vibration response of underwater shell structures, and the boundary element method (BEM) is used to analyze structural vibration acoustically. By combining FEM and BEM, the coupled FEM-BEM method is used for the acoustic-vibration strong coupling analysis of underwater thin shell structures. In order to overcome the problems of discontinuity and low precision in the traditional Lagrangian approximate geometric model and physical field interpolation calculation, the Loop subdivision surface isogeometric method is used to construct the geometric model, and the same spline function is used to perform the high-order interpolation calculation of the physical field, so as to realize the integrated CAD/CAE analysis of the underwater acoustic-vibration strong coupling system. Stochastic analysis is devoted to studying the output uncertainty caused by the input uncertainty of the system. Monte Carlo simulation(MCs) is considered to be a universal tool for solving complex and multi-dimensional uncertain problems because of its simplicity and directness. However, the huge computational cost reduces its applicability. Using proper orthogonal decomposition (POD) and radial basis function (RBF) can reduce computational cost, improve computational efficiency, and realize fast stochastic analysis based on Monte Carlo simulation (MCs). Considering the influence of the uncertainty of the structural material property parameters and the structural shape parameters on the calculation results, Monte Carlo simulation is used to analyze the statistical characteristics of the structural acoustic response under random variables. Finally, several practical problems are used to verify the correctness and effectiveness of this algorithm.

Key words： Finite element-Boundary element method Subdivision surface Monte Carlo simulation; Proper orthogonal decomposition Radial basis function

收稿日期: 2021-03-01 出版日期: 2022-06-28

引用本文:

胡昊文1,2，王中王1,2，徐延明2，陈磊磊1,2. 结构声学耦合随机性分析的等几何有限元-边界元法研究[J]. 振动与冲击, 2022, 41(12): 159-167.
HU Haowen1,2,WANG Zhongwang1,2,XU Yanming2,CHEN Leilei1,2. A study on the isogeometric finite element-boundary element method for the stochastic analysis of structural acoustic coupling. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(12): 159-167.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I12/159

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