声场与结构耦合系统的模态分析与灵敏度计算
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摘要
随着对车、船、飞机乘坐舒适性要求的不断提高，其乘坐室(舱)内的噪声问题越来越引起人们的高度重视。乘坐室(舱)是一个相当复杂的声学系统，不仅结构复杂而且形状不规则，加之结构壁面都不同程度地贴有吸声材料而产生对声波的吸收，使得用传统理论方法对室(舱)内噪声声压级进行预估非常困难。有限元等数值方法是分析几何形状和边界条件复杂的振动问题和声学问题的得力工具之一，将其用于声固耦合分析，可实现设计阶段乘坐室(舱)内噪声响应进行理论分析与预测。而乘坐室(舱)为典型的弹性薄壁腔体结构，其内部噪声与壁结构振动之间存在着强烈的耦合关系。因而，对乘坐室(舱)声振耦合特性的分析研究即成为噪声控制与低噪声设计的前提和关键。
声振耦合系统的灵敏度分析可以方便、快速地对乘坐室(舱)结构进行动态修改而达到降低噪声的目的。而在结构的内壁面敷贴吸声材料是车辆等普遍采用的噪声控制方法之一，因此分析吸声材料对室内噪声响应的灵敏度更具有实用价值。
本文的工作是结合大型结构分析和优化软件JIFEX的方法和功能，发展声场—结构耦合系统的有限元分析及优化设计方法。本文的研究涉及到空腔声学分析理论、声振耦合有限元模型的模态频率响应分析方法以及优化设计中的灵敏度分析、阻尼减振等。主要工作如下：
1．空腔声学的有限元分析及优化设计。用有限元法求解波动方程。利用8节点块体单元，在刚性壁条件下，对声场的基本方程进行数值求解，在JIFEX系统中发展了这种新的有限元模型，计算了封闭空腔的声学模态(固有频率和振型)。本文采用基于局部差分的半解析算法，进行特征值的灵敏度分析，并将计算结果提供给结构力学分析模块，实现了空腔声学的有限元分析和灵敏度计算。最后，建立了优化设计模型，进行声场动力优化设计。
2．声振耦合系统的有限元分析方法。由声空间波动方程和薄板理论出发，对声场—结构耦合系统的模态分析提出了有限元数值方法，采用共扼子空间迭代法对非对称特征方程进行处理，采用静凝聚法消除质量矩阵的奇异性。然后，将结构力学分析模块与共扼子空间迭代法模块相结合，求解经过降阶后的模态方程，并为灵敏度分析提供了必要的基础。
3．有阻尼声振耦合系统的有限元分析及灵敏度计算。讨论了阻尼降噪问题，建立了有阻尼声振耦合系统的有限元模型，采用振型叠加法，将系统位移转换到以固有振型为基向量，进行结构壁面有吸声材料的声振耦合系统响应的有限元分析与灵敏度分析，推导了比例阻尼条件的灵敏度计算公式。
本文的研究工作是国家自然科学基金资助项目(10032030)和国家重点基础专项经费(G1999032805)资助计划的一部分
The acoustic design for a passenger compartment of the vehicle, ship, and plane is very important to improve the carborne acoustic comfort and to enhance the competitiveness for the products in market.
The research work in this dissertation involves the theories of interior noise analysis for the cavity, the sensitivity analysis of dynamic optimization, and the modal analysis of acoustic-structural coupled system with proportional damping. Main contents of dissertation are as follows:
(1) The finite element method is demonstrated to apply for the solution of the wave equation. If rigid walls are assumed in the finite element model for the boundary panels, an eight node, isoparametric acoustic finite element model is developed for calculating the acoustic modes of cavities. Initially a rectangular enclosure is analyzed in order to study the convergence of the results. The element is then used to analyse an irregular shaped cavity. A semi-analytic method, in which the derivatives of stiffness matrix and mass matrix are obtained by the difference technique, for sensitivity analysis in dynamic shape optimization is presented in this dissertation.
(2) Based on the wave equation in the acoustic fluid space and the theory of thin-wall structure, the non-symmetrical coupled structure-acoustic dynamic equation without damping is studied. The non-symmetric system of the finite element model for coupled structure-acoustic response is solved by the conjugate subspace iteration method. The numerical methods have been implemented in a finite element software system - JIFEX.
(3) Introducing the proportional damping, the finite element formula of structural-acoustic coupled system lined with sound absorbing materials is obtained. Mode-superposition technique for modal frequency response analysis of coupled structure-acoustic systems is also used to deal with the sensitivities of the eigenvalues and eigenvectors of coupled systems for the purpose of reducing cavity interior noise in theory.
The research of this dissertation is part of the projects supported by the National Natural Science Foundation of China (No. 10032030) and the Special Funds for National Key Basic Research of China (No.G1999032805).
声振耦合系统的灵敏度分析可以方便、快速地对乘坐室(舱)结构进行动态修改而达到降低噪声的目的。而在结构的内壁面敷贴吸声材料是车辆等普遍采用的噪声控制方法之一，因此分析吸声材料对室内噪声响应的灵敏度更具有实用价值。
本文的工作是结合大型结构分析和优化软件JIFEX的方法和功能，发展声场—结构耦合系统的有限元分析及优化设计方法。本文的研究涉及到空腔声学分析理论、声振耦合有限元模型的模态频率响应分析方法以及优化设计中的灵敏度分析、阻尼减振等。主要工作如下：
1．空腔声学的有限元分析及优化设计。用有限元法求解波动方程。利用8节点块体单元，在刚性壁条件下，对声场的基本方程进行数值求解，在JIFEX系统中发展了这种新的有限元模型，计算了封闭空腔的声学模态(固有频率和振型)。本文采用基于局部差分的半解析算法，进行特征值的灵敏度分析，并将计算结果提供给结构力学分析模块，实现了空腔声学的有限元分析和灵敏度计算。最后，建立了优化设计模型，进行声场动力优化设计。
2．声振耦合系统的有限元分析方法。由声空间波动方程和薄板理论出发，对声场—结构耦合系统的模态分析提出了有限元数值方法，采用共扼子空间迭代法对非对称特征方程进行处理，采用静凝聚法消除质量矩阵的奇异性。然后，将结构力学分析模块与共扼子空间迭代法模块相结合，求解经过降阶后的模态方程，并为灵敏度分析提供了必要的基础。
3．有阻尼声振耦合系统的有限元分析及灵敏度计算。讨论了阻尼降噪问题，建立了有阻尼声振耦合系统的有限元模型，采用振型叠加法，将系统位移转换到以固有振型为基向量，进行结构壁面有吸声材料的声振耦合系统响应的有限元分析与灵敏度分析，推导了比例阻尼条件的灵敏度计算公式。
本文的研究工作是国家自然科学基金资助项目(10032030)和国家重点基础专项经费(G1999032805)资助计划的一部分
The acoustic design for a passenger compartment of the vehicle, ship, and plane is very important to improve the carborne acoustic comfort and to enhance the competitiveness for the products in market.
The research work in this dissertation involves the theories of interior noise analysis for the cavity, the sensitivity analysis of dynamic optimization, and the modal analysis of acoustic-structural coupled system with proportional damping. Main contents of dissertation are as follows:
(1) The finite element method is demonstrated to apply for the solution of the wave equation. If rigid walls are assumed in the finite element model for the boundary panels, an eight node, isoparametric acoustic finite element model is developed for calculating the acoustic modes of cavities. Initially a rectangular enclosure is analyzed in order to study the convergence of the results. The element is then used to analyse an irregular shaped cavity. A semi-analytic method, in which the derivatives of stiffness matrix and mass matrix are obtained by the difference technique, for sensitivity analysis in dynamic shape optimization is presented in this dissertation.
(2) Based on the wave equation in the acoustic fluid space and the theory of thin-wall structure, the non-symmetrical coupled structure-acoustic dynamic equation without damping is studied. The non-symmetric system of the finite element model for coupled structure-acoustic response is solved by the conjugate subspace iteration method. The numerical methods have been implemented in a finite element software system - JIFEX.
(3) Introducing the proportional damping, the finite element formula of structural-acoustic coupled system lined with sound absorbing materials is obtained. Mode-superposition technique for modal frequency response analysis of coupled structure-acoustic systems is also used to deal with the sensitivities of the eigenvalues and eigenvectors of coupled systems for the purpose of reducing cavity interior noise in theory.
The research of this dissertation is part of the projects supported by the National Natural Science Foundation of China (No. 10032030) and the Special Funds for National Key Basic Research of China (No.G1999032805).
引文
1．黎志勤，黎苏．汽车排气系统噪声与消声器设计．北京：中国环境科学出版社，1991
2．马大猷．噪声控制学．北京：科学出版社，1987
3. G M L Gladwell and G Zimmermann. On energy and complementary energy formulations of acoustic and structural viberation problem. Journal of sound and viberatin, 1966, 3:233-241
4. A Craggs. The use of simple three-dimensional acoustic finite element for ddetermining the natural modes and frequencies of complex shaped enclosure. Journal of sound and viberation, 1972, 23:331-339
5. T shuku and K Ishihara. The analysis of the acoustic field in irregular shaped rooms by the finite element methods. Journal of sound and viberation, 1973, 29:67-76
6. A Craggs. An acoustic finite element approach for studying boundary flexibility and sound transmission between irregular enclosure. Journal of sound and viberation, 1973,30:343-357
7. M Petyt, J Lea and G H Koopmann. A Finite element method for determining the acoustic modes of irregular Shaped Cavities. Journal of sound and viberation, 1976, 45(4): 495-502
8. Wang Yanping, Zheng Muqiao. Prediction and Reduction of Structure Borne Noise in Vehicle. Journal of Institute of Technology, 1995, 4(2): 160-167
9. Yong J and Croker M J. Prediction of Transmission Loss in Muffers by the Finite Element Method. J. A. S. A, 1956, 57:144
10. D J Nefske and L J Howell. Automible interior noise reduction using finite element methods. Transations of the society of Automotive Engineering, 1978, 87:1726-1737
11. D J Nefske, J A Wolf and L J Howell, Structural-acoustic finite element analysis of the automible passenger compartment: a review of current practice. Journal of sound and viberation, 1982, 80(2): 247-266
12．沈壕，孙洪生．工程声学的有限元法．声学学报，1981，7：249-259
13．高虎，冉一元，杨涛．二维声场的边界元分析．振动与冲击，1991，3：
14．王维琮，吴卫彬，孙洪生．轴对称性消声器的有限元分析．应用声学，1985，1：
15. R J Bernhard. A Finite element method for synthesis of acoustical shapes. Journal of sound and viberation, 1985, 9(1): 55-65
16. Macneal R H, Citepley R and chargin M, A symmetric modal formulation of Fluid-structure Iteration. ASME paper, 1980, 90-117.
17. Zheng-Dong Ma and Ichiro Hagiwara. Sensitivity Analysis Methods for Coupled Acoustic-Structural Systems Part Ⅰ: Modal Sensitivities. AIAA Journal, 1991, 29(11):1787-1795.
18. Zheng-Dong Ma and Ichiro Hagiwara. Sensitivity Analysis Methods for Coupled Acoustic-Structural Systems Part Ⅱ: Direct Frequency Response and Its Sensitivities. AIAA Journal, 1991, 29(11): 1796-1801.
19. Zheng-Dong Ma and Ichiro Hagiwara. A sensitivities calculation methods for conducting modal frequency response analysis of coupled acoustic-structural systems. JSME series3,1992, 35(1).
20．吴小清，王登峰，徐诚，程悦荪．壁面有吸声材料时驾驶室内噪声响应的灵敏度分析．农业工程学报，1999，15(3)：151-155
21．杨满宏，李国香，机动车噪声与其结构振动耦合研究的现状及发展趋势，公路交通科技，1996，13(4)：67-71
22．王登峰．拖拉机驾驶室的声固耦合动态择优声学设计．农业机械学报，1994，25(3)：23-26
23. Kozukue Wakae And Hagiwara Ichiro. Topology optimization analysis for reduction of interior noise using homogenization method for mean eigenvalue. JSME, 1995: 2746-2752
24. Christensen T, Sorokin S V and Olhoff N. On analysis and optimization in structural acoustics-Part Ⅰ: Problem formulation and solution techniques. Structural Optimization, 1998, 16:83-95
25. Christensen T, Sorokin S V and Olhoff N. On analysis and optimization in structural acoustics-Part Ⅱ: Exemplifications for axisymmetric structures. Structural Optimization,1998, 16:96-107
26. Gu Y X, Zhang H W, etc. New generation software of structural analysis and design optimization—JIFEX. Structural Engineering and Mechanics, 1999, 7(6): 589-599.
27．钟万勰．一个多用途的结构分析程序JIGFEX．大连理工大学学报，1977，16(3)：19-42，16(4)：14-35．
28．钟万勰．计算结构力学微机程序设计．北京：水利水电出版社，1986．
29．顾元宪．计算机辅助结构优化设计的研究与MCADS系统的开发．[博士学位论文]．大连：大连理工大学，1988
30．杜功焕，朱哲民，龚秀芬．声学基础(下册)．上海：上海科学技术出版社，1981
31．丁渭平．车身结构低频声学分析理论及设计方法研究．[博士学位论文]．西安：西安交通大学
32．丁渭平，陈花玲，胡选利．腔体声振耦合方程低频解耦误差的研究．噪声与振动控制，2000，8：6-10
33．胡选利，陈花玲，赵建平．声振耦合数值模型合理性分析和实验验证．西安交通大学学报，1997，31(7)：1-6
34．张维峰，翟红生，冯华．汽车乘坐室内声学特性的有限元分析．西安公路交通大学学报，1995，15(2)：50-55
35．林家浩．结构动力优化中的灵敏度分析．振动与冲击，1985，1：1-7
36．林树枝，程耿东．动力响应灵敏度分析的振型空间法．地震工程与工程振动，1990，3：85-91
37．顾元宪，程耿东．结构形状优化设计数值方法的研究与应用．计算结构力学及其应用，1993，3：321-335
38．张传立，张系斌，宋天霞．结构动力形状优化中灵敏度分析的两种算法。江汉石油学院学报，1994，16(4)：83-89
39．刘鸿文．板壳理论．杭州：浙江大学出版社，1987
40．王勖成，邵敏．有限单元法基本原理和数值方法．第二版．北京：清华大学出版社，1997
41．林家浩，曲乃泗，孙焕纯．计算结构动力学．高等教育出版社，1989
42．钟万勰．计算结构力学与最优控制．大连：大连理工大学出版社，1993
43. G H Golub, C F Van Loan. Matrix Computation，The John Hopkins Univ. Press, 1983.廉庆荣，邓健新，刘秀兰译．熊西文校．矩阵计算．大连：大连理工大学出版社，1988
44．丁渭平，陈花玲．腔体声振耦合的对称化有限元模型及其特性研究．西安交通大学学报，2000，34(7)：58-62
45．戴德沛．阻尼减振降噪技术．西安：西安交通大学出版社，1986
46．徐稼轩，郑铁生．结构动力分析的数值方法．西安：西安交通大学出版社，1993
47．傅志方．振动模态分析与参数辨识．机械工业出版社，1990
48．朱伯方．有限单元法的原理与应用．水利出版社
49．刘延柱，陈文良，陈立群．振动力学．高等教育出版社，1998
50．王彦平，郑慕侨，杨景义．用动力吸振器降低车辆内部的振动噪声．北京理工大学学报，1995，15(3)：278-282
2．马大猷．噪声控制学．北京：科学出版社，1987
3. G M L Gladwell and G Zimmermann. On energy and complementary energy formulations of acoustic and structural viberation problem. Journal of sound and viberatin, 1966, 3:233-241
4. A Craggs. The use of simple three-dimensional acoustic finite element for ddetermining the natural modes and frequencies of complex shaped enclosure. Journal of sound and viberation, 1972, 23:331-339
5. T shuku and K Ishihara. The analysis of the acoustic field in irregular shaped rooms by the finite element methods. Journal of sound and viberation, 1973, 29:67-76
6. A Craggs. An acoustic finite element approach for studying boundary flexibility and sound transmission between irregular enclosure. Journal of sound and viberation, 1973,30:343-357
7. M Petyt, J Lea and G H Koopmann. A Finite element method for determining the acoustic modes of irregular Shaped Cavities. Journal of sound and viberation, 1976, 45(4): 495-502
8. Wang Yanping, Zheng Muqiao. Prediction and Reduction of Structure Borne Noise in Vehicle. Journal of Institute of Technology, 1995, 4(2): 160-167
9. Yong J and Croker M J. Prediction of Transmission Loss in Muffers by the Finite Element Method. J. A. S. A, 1956, 57:144
10. D J Nefske and L J Howell. Automible interior noise reduction using finite element methods. Transations of the society of Automotive Engineering, 1978, 87:1726-1737
11. D J Nefske, J A Wolf and L J Howell, Structural-acoustic finite element analysis of the automible passenger compartment: a review of current practice. Journal of sound and viberation, 1982, 80(2): 247-266
12．沈壕，孙洪生．工程声学的有限元法．声学学报，1981，7：249-259
13．高虎，冉一元，杨涛．二维声场的边界元分析．振动与冲击，1991，3：
14．王维琮，吴卫彬，孙洪生．轴对称性消声器的有限元分析．应用声学，1985，1：
15. R J Bernhard. A Finite element method for synthesis of acoustical shapes. Journal of sound and viberation, 1985, 9(1): 55-65
16. Macneal R H, Citepley R and chargin M, A symmetric modal formulation of Fluid-structure Iteration. ASME paper, 1980, 90-117.
17. Zheng-Dong Ma and Ichiro Hagiwara. Sensitivity Analysis Methods for Coupled Acoustic-Structural Systems Part Ⅰ: Modal Sensitivities. AIAA Journal, 1991, 29(11):1787-1795.
18. Zheng-Dong Ma and Ichiro Hagiwara. Sensitivity Analysis Methods for Coupled Acoustic-Structural Systems Part Ⅱ: Direct Frequency Response and Its Sensitivities. AIAA Journal, 1991, 29(11): 1796-1801.
19. Zheng-Dong Ma and Ichiro Hagiwara. A sensitivities calculation methods for conducting modal frequency response analysis of coupled acoustic-structural systems. JSME series3,1992, 35(1).
20．吴小清，王登峰，徐诚，程悦荪．壁面有吸声材料时驾驶室内噪声响应的灵敏度分析．农业工程学报，1999，15(3)：151-155
21．杨满宏，李国香，机动车噪声与其结构振动耦合研究的现状及发展趋势，公路交通科技，1996，13(4)：67-71
22．王登峰．拖拉机驾驶室的声固耦合动态择优声学设计．农业机械学报，1994，25(3)：23-26
23. Kozukue Wakae And Hagiwara Ichiro. Topology optimization analysis for reduction of interior noise using homogenization method for mean eigenvalue. JSME, 1995: 2746-2752
24. Christensen T, Sorokin S V and Olhoff N. On analysis and optimization in structural acoustics-Part Ⅰ: Problem formulation and solution techniques. Structural Optimization, 1998, 16:83-95
25. Christensen T, Sorokin S V and Olhoff N. On analysis and optimization in structural acoustics-Part Ⅱ: Exemplifications for axisymmetric structures. Structural Optimization,1998, 16:96-107
26. Gu Y X, Zhang H W, etc. New generation software of structural analysis and design optimization—JIFEX. Structural Engineering and Mechanics, 1999, 7(6): 589-599.
27．钟万勰．一个多用途的结构分析程序JIGFEX．大连理工大学学报，1977，16(3)：19-42，16(4)：14-35．
28．钟万勰．计算结构力学微机程序设计．北京：水利水电出版社，1986．
29．顾元宪．计算机辅助结构优化设计的研究与MCADS系统的开发．[博士学位论文]．大连：大连理工大学，1988
30．杜功焕，朱哲民，龚秀芬．声学基础(下册)．上海：上海科学技术出版社，1981
31．丁渭平．车身结构低频声学分析理论及设计方法研究．[博士学位论文]．西安：西安交通大学
32．丁渭平，陈花玲，胡选利．腔体声振耦合方程低频解耦误差的研究．噪声与振动控制，2000，8：6-10
33．胡选利，陈花玲，赵建平．声振耦合数值模型合理性分析和实验验证．西安交通大学学报，1997，31(7)：1-6
34．张维峰，翟红生，冯华．汽车乘坐室内声学特性的有限元分析．西安公路交通大学学报，1995，15(2)：50-55
35．林家浩．结构动力优化中的灵敏度分析．振动与冲击，1985，1：1-7
36．林树枝，程耿东．动力响应灵敏度分析的振型空间法．地震工程与工程振动，1990，3：85-91
37．顾元宪，程耿东．结构形状优化设计数值方法的研究与应用．计算结构力学及其应用，1993，3：321-335
38．张传立，张系斌，宋天霞．结构动力形状优化中灵敏度分析的两种算法。江汉石油学院学报，1994，16(4)：83-89
39．刘鸿文．板壳理论．杭州：浙江大学出版社，1987
40．王勖成，邵敏．有限单元法基本原理和数值方法．第二版．北京：清华大学出版社，1997
41．林家浩，曲乃泗，孙焕纯．计算结构动力学．高等教育出版社，1989
42．钟万勰．计算结构力学与最优控制．大连：大连理工大学出版社，1993
43. G H Golub, C F Van Loan. Matrix Computation，The John Hopkins Univ. Press, 1983.廉庆荣，邓健新，刘秀兰译．熊西文校．矩阵计算．大连：大连理工大学出版社，1988
44．丁渭平，陈花玲．腔体声振耦合的对称化有限元模型及其特性研究．西安交通大学学报，2000，34(7)：58-62
45．戴德沛．阻尼减振降噪技术．西安：西安交通大学出版社，1986
46．徐稼轩，郑铁生．结构动力分析的数值方法．西安：西安交通大学出版社，1993
47．傅志方．振动模态分析与参数辨识．机械工业出版社，1990
48．朱伯方．有限单元法的原理与应用．水利出版社
49．刘延柱，陈文良，陈立群．振动力学．高等教育出版社，1998
50．王彦平，郑慕侨，杨景义．用动力吸振器降低车辆内部的振动噪声．北京理工大学学报，1995，15(3)：278-282
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