声场结构耦合系统的有限元分析及灵敏度计算
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摘要
声场及其与结构耦合系统的数值分析在汽车、航空、航天等工业领域有着广泛的应用。噪声问题越来越引起人们的高度重视，在汽车等结构设计中减少噪声和振动已经成为一个重要的问题，噪声水平是评价工程结构设计质量优劣的重要指标之一。传统理论方法对复杂结构的内场噪声声压级进行预估非常困难，而有限元等方法则可以对几何形状和边界条件复杂的振动问题和声学问题进行数值分析，将其用于声场-结构耦合系统分析，可在设计阶段实现噪声响应的理论分析与预测，为声振耦合特性的分析研究提供声学设计的基础。因此，应用计算机辅助设计技术，特别是结构和多学科系统的优化设计方法，来降低结构噪声是有实际意义的。
本文应用有限元方法对声场-结构耦合系统进行数值模拟和灵敏度分析。内场噪声分析与优化设计，不仅要计算声场-结构耦合系统的本征值和本征向量，还要计算它们对设计变量的敏度。本文计算采用了声场-结构耦合系统本征值所对应的左、右本征向量，对其四个基本假设给予了证明。在耦合系统的正交归一化条件下，实现了特征值和特征向量及其灵敏度计算、声压响应水平及其灵敏度计算。研究工作结合大型有限元分析与结构优化设计软件JIFEX展开，为声场-结构耦合系统优化设计建立了基础。
本文主要研究内容如下：
(1)在声场和结构分别进行有限元分析的基础上，建立了声场-结构耦合系统分析的有限元模型，应用新的正交归一化条件实现了声场-结构耦合系统的频率和模态计算。
(2)声场-结构耦合系统的灵敏度分析，实现了耦合系统特征值灵敏度和特征向量灵敏度的计算，并对本文方法可能产生的误差进行了分析。
(3)分别采用直接法和模态叠加法，计算声场-结构耦合系统的声压响应水平及其敏度。
本文研究工作是国家重点基础研究发展规划项目“大规模科学计算研究”课题(G1999032805)和国家自然科学基金重点项目“耦合系统的多学科优化设计理论与数值方法”(10032030)的部分内容。
The numerical analysis for acoustic and the acoustic-structural coupling system has broad application in the industrial fields, such as the automobile, the aviation and the aerospace. Nowadays, people pay more and more serious attention to the noise problems. To reduce the noise and the vibration in the structure design, such as the automobile, has become a serous problem. The noise level is one of the key indexes to the evaluation for the design quality of the engineering structure. The conventional method for the analysis of the interior field noise sound level of the complicated structure is very difficulty, but the finite element method provides a very powerful methodology for analyzing vibration and acoustic problems with complicated geometry and boundary conditions. Therefore, this method can be used to acoustic-structural coupled system and to accomplish the theoretical analysis and prediction of noise response during design stages and provide the sound design basis for the analysis of the acoustic-structural coupling system. Therefore, it is helpful to reduce the noise with computer-aided design technique, in particular, the design optimization method of structural and multidisciplinary systems.
This paper studies the numerical simulation and sensitivity analysis of coupled acoustic-structure systems with finite element method. For the analyzing and the optimization design of the interior noise, it is necessary not only to calculate the eigenvalue and the eigenvector, but also to calculate their sensitivities to the design variables. The concept of the left and right eigenvectors with regard to the eigenvalue problems of coupled systems is used in the paper and four propositions concerning this concept are then proved. In the new orthogonality and M-normalization condition of the coupled system, this paper accomplished the calculation of the eigenvalue, the eigenvector and their sensitivities, the sound pressure level and its sensitivity. The aim of this thesis is to provide the basis analysis of the acoustic-structural systems based on JIFEX, the large-scale engineering structural analysis and optimization software.
The author's work includes:
(1) Development of the finite element model for the acoustic-structural system based on the sound and the structure finite element analysis. Accomplishment the calculation of frequencies and modes with the new orthogonality and the M-normalization condition.
(2) Dynamic sensitivity analyses of natural frequencies and the eigenvectors for the coupled system. Accomplishment of the calculation of the sensitivities of eigenvalue and the eigenvector. The accuracy analysis of this method is performed.
(3) The modal frequency response and its sensitivity analysis for the coupled system using the direct method and the eigenmodes.
This thesis is one of the part of the national key basis research development plan project (G1999032805) and the key project of the National Natural Science Foundation of China (No. 10032030).
本文应用有限元方法对声场-结构耦合系统进行数值模拟和灵敏度分析。内场噪声分析与优化设计，不仅要计算声场-结构耦合系统的本征值和本征向量，还要计算它们对设计变量的敏度。本文计算采用了声场-结构耦合系统本征值所对应的左、右本征向量，对其四个基本假设给予了证明。在耦合系统的正交归一化条件下，实现了特征值和特征向量及其灵敏度计算、声压响应水平及其灵敏度计算。研究工作结合大型有限元分析与结构优化设计软件JIFEX展开，为声场-结构耦合系统优化设计建立了基础。
本文主要研究内容如下：
(1)在声场和结构分别进行有限元分析的基础上，建立了声场-结构耦合系统分析的有限元模型，应用新的正交归一化条件实现了声场-结构耦合系统的频率和模态计算。
(2)声场-结构耦合系统的灵敏度分析，实现了耦合系统特征值灵敏度和特征向量灵敏度的计算，并对本文方法可能产生的误差进行了分析。
(3)分别采用直接法和模态叠加法，计算声场-结构耦合系统的声压响应水平及其敏度。
本文研究工作是国家重点基础研究发展规划项目“大规模科学计算研究”课题(G1999032805)和国家自然科学基金重点项目“耦合系统的多学科优化设计理论与数值方法”(10032030)的部分内容。
The numerical analysis for acoustic and the acoustic-structural coupling system has broad application in the industrial fields, such as the automobile, the aviation and the aerospace. Nowadays, people pay more and more serious attention to the noise problems. To reduce the noise and the vibration in the structure design, such as the automobile, has become a serous problem. The noise level is one of the key indexes to the evaluation for the design quality of the engineering structure. The conventional method for the analysis of the interior field noise sound level of the complicated structure is very difficulty, but the finite element method provides a very powerful methodology for analyzing vibration and acoustic problems with complicated geometry and boundary conditions. Therefore, this method can be used to acoustic-structural coupled system and to accomplish the theoretical analysis and prediction of noise response during design stages and provide the sound design basis for the analysis of the acoustic-structural coupling system. Therefore, it is helpful to reduce the noise with computer-aided design technique, in particular, the design optimization method of structural and multidisciplinary systems.
This paper studies the numerical simulation and sensitivity analysis of coupled acoustic-structure systems with finite element method. For the analyzing and the optimization design of the interior noise, it is necessary not only to calculate the eigenvalue and the eigenvector, but also to calculate their sensitivities to the design variables. The concept of the left and right eigenvectors with regard to the eigenvalue problems of coupled systems is used in the paper and four propositions concerning this concept are then proved. In the new orthogonality and M-normalization condition of the coupled system, this paper accomplished the calculation of the eigenvalue, the eigenvector and their sensitivities, the sound pressure level and its sensitivity. The aim of this thesis is to provide the basis analysis of the acoustic-structural systems based on JIFEX, the large-scale engineering structural analysis and optimization software.
The author's work includes:
(1) Development of the finite element model for the acoustic-structural system based on the sound and the structure finite element analysis. Accomplishment the calculation of frequencies and modes with the new orthogonality and the M-normalization condition.
(2) Dynamic sensitivity analyses of natural frequencies and the eigenvectors for the coupled system. Accomplishment of the calculation of the sensitivities of eigenvalue and the eigenvector. The accuracy analysis of this method is performed.
(3) The modal frequency response and its sensitivity analysis for the coupled system using the direct method and the eigenmodes.
This thesis is one of the part of the national key basis research development plan project (G1999032805) and the key project of the National Natural Science Foundation of China (No. 10032030).
引文
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7．李敬东，王炳权，宫瑞婷．建筑设计中声环境的研究．北京建筑工程学院学报，2001，17(4)：104-106．
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2．赵明，田丽江，陈晓东．飞机噪声对机场周围环境污染的调查．中国公共卫生，1999，15(8)：716．
3．陈越澎，潭林森．船舶舱室噪声控制技术综述．武汉造船，1995，No．，34-40．
4．胡正元，史秀凤等．潜艇航行时舱室中噪声水平的探讨．中华航海医学杂志，1997，4(2)：69-71．
5．唐人辉，唐光武．汽车噪声控制技术及低噪声客车产品开发措施．客车技术与研究，2001，23(6)：19-21．
6．金磊．全球减灾与灾害物理学(三)—灾害声学及其噪声控制技术．工程物理，1999，9(1)：29-32．
7．李敬东，王炳权，宫瑞婷．建筑设计中声环境的研究．北京建筑工程学院学报，2001，17(4)：104-106．
8．孙广容．从建筑声学到环境声学．应用声学，2002，21(1)：46-49．
9．田新浩．电力机车司机室的噪声特性研究．环境工程，2000，18(3)：36-39．
10．滕合芹，尹正莲，安月东．舱室噪声对船员听觉及心血管系统的影响．中华劳动卫生职业病杂志，1994，12(5)：286-287．
11．歼-8D飞机噪声对对飞行员工效影响的试验研究．中华航空航天医学杂志，1998，9(3)：172．
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