基于有限元法的模糊参数二维声场数值分析
NUMERRICAL ANALYSIS OF 2D ACOUSTIC FIELD WITH FUZZY PARAMETERS BASED ON FINITE ELEMENT METHOD
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摘要: 为了分析不确定性二维声场,引入模糊集概念描述声场的物理参数、载荷和边界条件的不确定性,推导了分析模糊参数下二维声场问题的相关计算公式。在不同隶属度的截集下通过对模糊动刚度矩阵和模糊载荷矩阵进行泰勒展开,再用纽曼展开对模糊动刚度矩阵泰勒展开式的逆进行转化,采用摄动有限元法求解,最终得到模糊参数下的声压解集。以二维管道声场模型和某轿车二维声腔模型为研究对象分析了模糊参数下的声压响应,结果表明该文方法能有效分析模糊参数下的二维声场,具有重要的工程应用价值。Abstract: : In order to analyze a two-dimension acoustic field with uncertain parameters, a fuzzy concept was introduced to describe the uncertainties of physical parameters, applied loads as well as boundary conditions, and the correlated formulation about the analysis of the two-dimension acoustic field with fuzzy parameters were presented. The fuzzy dynamic stiffness matrix and fuzzy applied load matrix in different α-level cut were expanded by the first order Taylor series. The fuzzy dynamic stiffness matrix inverse was approximated by the first order Neumann series. Then, the sound pressure solution set can be obtained by using the perturbation finite element method. Numerical examples of the sound pressure response analysis of a 2D acoustic tube model and a 2D car acoustic cavity model with fuzzy parameters were presented, and the results showed that the method proposed can analyze a 2D acoustic field with fuzzy parameters accurately and effectively.