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

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Journal of Vibration and Shock ›› 2022, Vol. 41 ›› Issue (16) : 19-25.

LIU Qiang，LIANG Menghui，ZHENG Changjun，BI Chuanxing

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Abstract

Sensitivity analysis of acoustic eigenfrequencies provides a basis for the acoustic design optimization. For the acoustic cavities lined with sound absorbing materials, a nonlinear eigenvalue problem (NEP) has to be solved in the acoustic modal analysis because the equivalent impedance is frequency dependent. The sensitivity analysis of the NEP is 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 is developed to compute the sensitivities of acoustic eigenfrequencies. Numerical examples are used to show the accuracy, applicability and potential of the proposed method.
Key words: sound absorbing material; frequency-dependent impedance; acoustic modal; sensitivity analysis; nonlinear eigenvalue problem

Key words

sound absorbing material / frequency-dependent impedance / acoustic modal / sensitivity analysis / nonlinear eigenvalue problem

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LIU Qiang，LIANG Menghui，ZHENG Changjun，BI Chuanxing. A finite element method for the sensitivity analysis of acoustic eigenfrequencies of cavities with frequency-dependent impedance boundary conditions[J]. Journal of Vibration and Shock, 2022, 41(16): 19-25

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