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A boundary element method for the eigenfrequency sensitivity analysis of three dimensional acoustic problems

DOI：

 作者 单位 邮编 余志强 合肥工业大学 230009 刘强 合肥工业大学 郑昌军 合肥工业大学 230009

声系统特征频率的灵敏度分析为其优化设计提供了基础，具有重要意义。边界元法在声学问题的求解中具有独特优势，但因其系统方程系数矩阵的频率相关性导致的非线性特征值问题给声学特征频率的灵敏度分析带来了很大困难。为此，本文首先对非线性特征值问题进行了线性化处理，利用围道积分投影方法将非线性特征方程转换为小规模广义特征方程，然后对其关于设计变量直接求导，并引入左特征向量和转换矩阵构造了一种适用于内外声场的三维声学单/重特征频率灵敏度分析的边界元法。数值算例验证了该方法的适用性，以及对单/重特征频率灵敏度的计算精度。

The eigenfrequency sensitivity analysis is of significance as it provides the basis for the eigenfrequency design of acoustic systems. Boundary element method (BEM) has unique advantages in solving acoustic problems. However, it is complicated to use BEM to compute the eigenfrequency sensitivities since the coefficient matrix of the BEM system is implicitly frequency dependent which leads to a nonlinear eigenvalue problem (NEP). In this paper, the NEP is first converted into a small generalized eigenvalue problem (GEP) through a contour integral method. After taking the derivatives of the GEP with respect to design variables, a BEM approach which can compute the sensitivities of distinct/repeated eigenfrequencies of both the interior and exterior three-dimensional acoustic fields is achieved by introducing the left eigenvectors and a transform matrix. Numerical examples are used to verify the applicability of the method and also the accuracy for calculating the sensitivities of both distinct and repeated eigenfrequencies.
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