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

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. © 2022 Chinese Vibration Engineering Society. All rights reserved.