频变阻抗边界声空间特征频率灵敏度分析的有限元法

PDF(1003 KB)

振动与冲击 ›› 2022, Vol. 41 ›› Issue (16) : 19-25.

论文

刘强，梁梦辉，郑昌军，毕传兴

作者信息 +

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

LIU Qiang，LIANG Menghui，ZHENG Changjun，BI Chuanxing

Author information +

文章历史 +

摘要

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。本文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，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。
关键词：吸声材料；频变阻抗；声模态；灵敏度分析；非线性特征值问题

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

导出引用

刘强，梁梦辉，郑昌军，毕传兴. 频变阻抗边界声空间特征频率灵敏度分析的有限元法[J]. 振动与冲击, 2022, 41(16): 19-25

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

参考文献

[1] 商林源, 赵国忠, 陈刚. 声结构耦合系统双材料模型的拓扑优化设计[J]. 振动与冲击, 2016, 35(16): 192-198.
SHANG Linyuan, ZHAO Guozhong, CHEN Gang. Topology optimization of a bi-material model for acoustic-structural coupled systems [J]. Journal of Vibration and Shock, 2016, 35(16):192-198.
[2] Zhang Y, Wu H, Jiang W, Kessissoglou N. Acoustic topology optimization of sound power using mapped acoustic radiation modes [J]. Wave Motion, 2017, 70:90-100.
[3] Zhao W, Zheng C, Liu C, Chen H. Minimization of sound radiation in fully coupled structural-acoustic systems using FEM-BEM based topology optimization [J]. Structural and Multidisciplinary Optimization, 2018, 58:115-128.
[4] 陈刚, 赵国忠, 顾元宪. 小阻尼空间声学特征频率灵敏度分析与优化设计[J]. 大连理工大学学报, 2007, 47(4):483-487.
CHEN Gang, ZHAO Guozhong, GU Yuanxian. Sensitivity analysis and design optimization of acoustic eigenfrequencies for lightly damped cavities [J]. Journal of Dalian University of Technology, 2007, 47(4): 483-487.
[5] 郑昌军. 三维声学敏感度分析的宽频快速多极边界元法研究[D]. 合肥:中国科学技术大学, 2011.
ZHEN Changjun. Wideband FMBEM for 3D acoustic sensitivity analysis [D]. Hefei: University of Science and Technology of China, 2011.
[6] Delany ME, Bazley EN. Acoustical properties of fibrous absorbent materials [J]. Applied Acoustics, 1970, 3: 105-116.
[7] Miki Y. Acoustical properties of porous materials-Modifications of Delany-Bazley models [J]. Journal of the Acoustical Society of America, 1990, 11(1):19-24.
[8] Zhang Y-B, Yao Q, Xiao L, Zhang X-Z, Zheng C-J, Bi C-X. On the resonance of a lined tire cavity [J]. Acta Acustica United with Acustica, 2019, 105:1237-1242.
[9] Luo Z-W, Zheng C-J, Zhang Y-B, Bi C-X. Estimating the acoustical properties of locally reactive finite materials using the boundary element method [J]. Journal of the Acoustical Society of America, 2020, 147(6): 3917-3931.
[10] 李颖洁, 王焘, 校金友, 文立华. 复杂阻抗吸声结构的大规模有限元声模态分析方法[J]. 噪声与振动控制, 2016, 33(3): 9-15.
LI Yingjie, WANG Tao, XIAO Jinyou, WEN Lihua. Finite element method for large-scale acoustic modal analysis of complex impedance absorption structures[J]. Noise and Vibration Control, 2018, 38(1):9-15.
[11] Guttel S, Tisseur F. The nonlinear eigenvalue problem[J]. Acta Numerica, 2017, 1-94.
[12] Asakura J, Sakurai T, Tadano H, Ikegami T, Kimura K. A numerical method for nonlinear eigenvalue problems using contour integrals[J]. JSIAM Letters, 2009, 1:52-55.
[13] Xiao J, Meng S, Zhang C, Zheng C. Resolvent sampling based Rayleigh-Ritz method for large-scale nonlinear eigenvalue problems[J]. Computer Methods in Applied Mechanics and Engineering, 2016, 310: 33-57.
[14] Zheng C-J, Gao H-F, Du L, Chen H-B, Zhang C. An accurate and efficient acoustic eigensolver based on a fast multipole BEM and a contour integral method[J]. Journal of Computational Physics, 2016,305:677-699.
[15] Zheng C-J, Bi C-X, Zhang C, Gao H-F, Chen H-B. Free vibration analysis of elastic structures submerged in an infinite or semi-infinite fluid domain by means of a coupled FE-BE solver[J], Journal of Computational Physics, 2018, 359:183-198.
[16] 周航, 校金友, 徐超. 考虑频变阻尼的黏弹性阻尼层板结构模态分析方法[J]. 振动与冲击, 2018, 37(14): 208-213,253.
ZHOU Hang, XIAO Jinyou, XU Chao. Modal analysis method for viscoelastically damped laminated structures with frequency-dependent damping [J]. Journal of Vibration and Shock, 2018, 37(14):208-213, 253.
[17] Li L, Hu Y, Wang X. Design sensitivity and Hessian matrix of generalized eigenproblems[J]. Mechanical Systems and Signal Processing, 2014, 43: 272-294.
[18] Wang S-Y, Sun Y, Gallagher RH. Sensitivity analysis in shape optimization of continuum structures [J]. Computers & Structures, 1985, 20(5):855-867.
[19] Sakata T, Morimura H, Ide H. Effects of tire cavity resonance on vehicle road noise. Tire Science and Technology, 1990, 18(2):68-79.
[20] 邓佑鲜, 庄志鹏, 金先柱, 杨晓光. 轮胎气压对车内噪声影响的研究[J]. 振动与冲击, 2018, 37(20): 135-140.
DENG Youxian, ZHUANG Zhipeng, KIM Songjoo, YANG Xiaoguang. A study on the influence of tire air pressure on its interior noise[J]. Journal of Vibration and Shock, 2018, 37(20):135-140.
[21] Zheng C-J, Zhang C, Bi C-X, Gao H-F, Chen H-B. Coupled FE-BE method for eigenvalue analysis of elastic structures submerged in an infinite fluid domain[J]. International Journal for Numerical Methods in Engineering, 2017, 110:163-185.
[22] Wu H, Yu L, Jiang W. A coupling FEM/BEM method with linear continuous elements for acoustic-structural interaction problems[J]. Applied Acoustics, 2019, 150:44-54.