频变阻抗边界声空间特征频率灵敏度分析的有限元法

A finite element method for the sensitivity analysis of acoustic eigenfrequencies of cavities with frequency-dependent impedance boundary conditions

声学特征频率的灵敏度分析为声学优化设计提供了基础。对于铺设吸声材料的声腔,由于等效声阻抗的频率相关性,声模态分析面临着非线性特征值问题。通过围道积分法将复杂的非线性特征值灵敏度问题转化为规模很小的广义特征值灵敏度问题(nonlinear eigenvalue problem,NEP),并采用直接微分方式构造了一种声学特征频率灵敏度分析的有限元法。数值算例表明,该方法的求解精度高、适用性好,为求解复杂阻抗边界下的声场特征频率灵敏度提供了一种通用方法。

Sensitivity analysis of acoustic eigenfrequencies provides a basis for acoustic design optimization.For the acoustic cavities lined with sound absorbing materials,a nonlinear eigenvalue problem(NEP)has to be solved in acoustic modal analysis because equivalent impedance is frequency dependent.The sensitivity analysis of the NEP was first converted into the sensitivity analysis of a generalized eigenvalue problem with the aid of a contour integral method.Then,a finite element scheme based on the direct differentiation method was developed to compute the sensitivities of acoustic eigenfrequencies.Numerical examples were used to show the accuracy,applicability,and potential of the proposed method.