内腔声—结构耦合系统的数值模拟与优化设计
|
摘要
噪声控制技术是工程界普遍关心的问题。目前,对于空腔内噪声的研究越来越受到重视,例如汽车、轮船、飞机等乘坐室,由于空腔形状的复杂性,用传统的理论方法很难取得满意的结果,目前主要通过实验技术和各种数值方法的研究来控制噪声。本文通过数值模拟技术,对空腔噪声进行优化设计研究,可实现在设计阶段对乘坐室等腔内噪声响应的理论分析、预测及优化设计。
本文在论述了内腔声-结构系统数值方法的历史及其现状的基础上,给出了内腔声-结构耦合系统的有限元方程和合理高效的求解算法,进一步提出了尺寸、形状、拓扑三个层次的优化设计模型,详细推导了灵敏度分析公式,给出了优化求解方法。特别是在随机激励下内腔声-结构耦合系统的求解方法、灵敏度分析及优化设计方面做了深入研究和有益的探讨。
本文的工作是结合大型结构分析和优化软件JIFEX的现有方法和功能,进一步发展了内腔声-结构耦合系统的动力分析和优化设计的功能模块。本文的主要工作包括以下几部分:
第一章综述了噪声控制技术的研究现状以及目前主要遇到的问题,论述了目前应用于声学领域的各种研究方法,包括有限元法、边界元法、统计能量法等,同时介绍了本文的软件开发平台JIFEX,给出了本论文的主要研究内容。
第二章由声学波动方程及各类边界条件的等效积分弱形式推导出小阻尼声场的有限元方程。在此基础上,假设声压向量的非负性,求解小阻尼声场有限元方程。利用半解析方法计算了声学刚度阵、质量阵和阻尼阵的导数,并且用全局差分方法进行了校核,最后分别以特征频率和声压级响应为目标函数,对三维汽车模型的声场特性进行了边界形状优化,得到了满意的优化结果。
第三章推导了内腔声-结构耦合系统方程,采用静凝聚法消除了质量矩阵的奇异性,采用了求解耦合系统非对称系数矩阵特征对的共轭子空间迭代算法,并证明了耦合系统左右特征向量的关系以及正交归一化条件。采用模态法、直接法和迭代法求解耦合系统响应,并通过数值算例证明了方法和程序的正确性和可行性。
第四章研究了稳态激励下内腔声-结构耦合系统的特征频率和声压响应的灵敏度分析和优化设计方法。首先建立了尺寸、形状优化设计模型,给出了灵敏度分析算法。然后结合结构拓扑优化设计理论,建立了声场-结构耦合系统的拓扑优化模型,推导了拓扑设计变量的灵敏度公式。并利用材料分布拓扑优化方法,对内腔声-结构耦合系统的刚度层分布进行了拓扑优化设计。
第五章研究了随机激励下内腔声-结构耦合系统的分析求解方法。考虑到随机激励下耦合问题算法求解的精度和效率,提出了一种求解耦合系统随机响应的迭代算法,并在每个迭代步过程中采用了虚拟激励法求解。通过求解过程的推导可以发现,虚拟激励法除了保持结构动力随机分析中高效的特点外,对于声固耦合系统的迭代求解,在计算效率上还具有常规算法无法比拟的优势。
第六章推导了随机声学响应功率谱的灵敏度分析公式,并与差分法比较。以空腔内某点的随机声压级响应功率谱和内腔平均声压级响应功率谱为目标函数,以结构重量作为约束函数,以结构的厚度作为设计变量,建立了随机激励作用下的内空腔声-结构耦合系统的声学优化设计模型。通过修改SIMP模型和RAMP模型,建立了随机激励下耦合系统的拓扑优化模型,给出了优化求解算法。数值算例验证了本章提出的灵敏度分析方法的正确性,以及各种随机响应优化模型的可行性,为工程设计提供了有效的参考依据。
最后对全文进行了总结和展望。
Nowadays, the techniques of noise control are paid more and more attention in engineering design. For interior noise problems, more research papers can be found in many fields, such as the cabins of automobiles, ships and airplanes. Because of the complex shape, it can not be solved by traditional theory methods. Experiment techniques and numerical methods are more suitable for these problems. In this dissertation, the numerical simulations are used to study the interior noise for analysis and optimizing the acoustic problems of the cabins at design stages.
This dissertation presents the finite element equation and proposes reasonable and high efficient solution algorithms for interior acoustic-structural coupled systems based on the research history and actuality of numerical methods. Then the optimization models are presented for size, shape and topology design variables. Furthermore, the sensitivity analysis equations and optimization argorithms are derived. Specially, the random response analysis, its sensitiviy and design optimization methods are studied in this dissertation.
New functional models of dynamic analysis and optimization design for interior acoustic-structural coupled systems are implemented in JIFEX, which is a large-scale engineering structural analysis and optimization software. The main content of this dissertation includes the following chapters:
In chapter 1, the research motivation and the main problems of noise control techniques are investigated. Several numerical methods used in acoustic fields, such as FEM, BEM, SEA (Statistical Energy Analysis), are discussed. Then the software-JIFEX is introduced. Finally, the brief description of the research work in the dissertation is presented.
In the second chapter, based on the wave equation for linear acoustics and various boundary conditions, the finite element equations for lightly damped acoustic cavity are given. The equations are solved based on the assumption that the acoustic pressure vector, which indicates the magnitude and relative phases at all locations in the system, is entirely real. The semi-analytical method is used to calculate the sensitivity of stiffness, mass and damping matrices comparing with finite difference method. In the last section, the eigenfrequency and sound pressure level response of a 3D-car model are optimized to show the validity and efficiency of the sensitivity analysis and design optimization methods.
In chapter 3, the finite element equations of acoustic-structural coupled systems are given. The static condensation method is used to avoid the singular structural mass matrix. In order to calculate the eigenpairs of non-symmetrical matrix, the adjoint subspace iteration method is given. Also, the relation of the left and right eigenvectors and the normalized orthogonality conditions are confirmed. The responses of coupled systems are calculated using the modal method, direct method and iteration method. Numerical examples are given to illustrate the validity of these methods
In chapter 4, the sensitivity of the eigenfrequency and sound pressure with respect to size and shape design parameters for those coupled systems are derived. Then the design optimization models are also presented. The topology optimization method for the coupled acoustic-structural systems is studied with the topology optimization theory. The sensitivity of acoustic pressure with respect to topology design variables and topology optimization method of stiffener distribution for the acoustic-structural coupled systems are proposed to study the stiffener material distribution of structure for interior sound pressure level (SPL) reduction of the coupled system. Numerical examples are given to show the validity and the efficiency of the sensitivity analysis and design optimization methods.
In the fifth chapter, the interior acoustic-structural coupled systems subjected to random excitations are studied. An iteration method is proposed to improve the efficient and accuracy of the computation. The pseudo-excitation method is used to calculate the random response in iterations. It was found that the pseudo excitation method is more efficiency than traditional random analysis methods for iteration calculation of interior acoustic-structural coupled systems beside its high efficiency.
In chapter 6, the sensitivity analysis formulas for the random responses of coupled acoustic-structural systems are derived and compared with finite difference method. The node sound pressure level (SPL) or average SPL of acoustic pressure power spectral density (PSD) is selected as the objective function with the structural weight constraint. The thickness of the structural plate is chosen as design variables. The design optimization model of the coupled systems subjected to random excitations is proposed. Furthermore, the topology optimization models of the coupled systems subjected to random excitations are presented through improving the SIMP and RAMP topology optimization models. Numerical examples are given to show the validity and efficiency of the sensitivity analysis and design optimization methods.
In the conclusion, the main contributions of the dissertation are summarized and the further work is suggested.
本文在论述了内腔声-结构系统数值方法的历史及其现状的基础上,给出了内腔声-结构耦合系统的有限元方程和合理高效的求解算法,进一步提出了尺寸、形状、拓扑三个层次的优化设计模型,详细推导了灵敏度分析公式,给出了优化求解方法。特别是在随机激励下内腔声-结构耦合系统的求解方法、灵敏度分析及优化设计方面做了深入研究和有益的探讨。
本文的工作是结合大型结构分析和优化软件JIFEX的现有方法和功能,进一步发展了内腔声-结构耦合系统的动力分析和优化设计的功能模块。本文的主要工作包括以下几部分:
第一章综述了噪声控制技术的研究现状以及目前主要遇到的问题,论述了目前应用于声学领域的各种研究方法,包括有限元法、边界元法、统计能量法等,同时介绍了本文的软件开发平台JIFEX,给出了本论文的主要研究内容。
第二章由声学波动方程及各类边界条件的等效积分弱形式推导出小阻尼声场的有限元方程。在此基础上,假设声压向量的非负性,求解小阻尼声场有限元方程。利用半解析方法计算了声学刚度阵、质量阵和阻尼阵的导数,并且用全局差分方法进行了校核,最后分别以特征频率和声压级响应为目标函数,对三维汽车模型的声场特性进行了边界形状优化,得到了满意的优化结果。
第三章推导了内腔声-结构耦合系统方程,采用静凝聚法消除了质量矩阵的奇异性,采用了求解耦合系统非对称系数矩阵特征对的共轭子空间迭代算法,并证明了耦合系统左右特征向量的关系以及正交归一化条件。采用模态法、直接法和迭代法求解耦合系统响应,并通过数值算例证明了方法和程序的正确性和可行性。
第四章研究了稳态激励下内腔声-结构耦合系统的特征频率和声压响应的灵敏度分析和优化设计方法。首先建立了尺寸、形状优化设计模型,给出了灵敏度分析算法。然后结合结构拓扑优化设计理论,建立了声场-结构耦合系统的拓扑优化模型,推导了拓扑设计变量的灵敏度公式。并利用材料分布拓扑优化方法,对内腔声-结构耦合系统的刚度层分布进行了拓扑优化设计。
第五章研究了随机激励下内腔声-结构耦合系统的分析求解方法。考虑到随机激励下耦合问题算法求解的精度和效率,提出了一种求解耦合系统随机响应的迭代算法,并在每个迭代步过程中采用了虚拟激励法求解。通过求解过程的推导可以发现,虚拟激励法除了保持结构动力随机分析中高效的特点外,对于声固耦合系统的迭代求解,在计算效率上还具有常规算法无法比拟的优势。
第六章推导了随机声学响应功率谱的灵敏度分析公式,并与差分法比较。以空腔内某点的随机声压级响应功率谱和内腔平均声压级响应功率谱为目标函数,以结构重量作为约束函数,以结构的厚度作为设计变量,建立了随机激励作用下的内空腔声-结构耦合系统的声学优化设计模型。通过修改SIMP模型和RAMP模型,建立了随机激励下耦合系统的拓扑优化模型,给出了优化求解算法。数值算例验证了本章提出的灵敏度分析方法的正确性,以及各种随机响应优化模型的可行性,为工程设计提供了有效的参考依据。
最后对全文进行了总结和展望。
Nowadays, the techniques of noise control are paid more and more attention in engineering design. For interior noise problems, more research papers can be found in many fields, such as the cabins of automobiles, ships and airplanes. Because of the complex shape, it can not be solved by traditional theory methods. Experiment techniques and numerical methods are more suitable for these problems. In this dissertation, the numerical simulations are used to study the interior noise for analysis and optimizing the acoustic problems of the cabins at design stages.
This dissertation presents the finite element equation and proposes reasonable and high efficient solution algorithms for interior acoustic-structural coupled systems based on the research history and actuality of numerical methods. Then the optimization models are presented for size, shape and topology design variables. Furthermore, the sensitivity analysis equations and optimization argorithms are derived. Specially, the random response analysis, its sensitiviy and design optimization methods are studied in this dissertation.
New functional models of dynamic analysis and optimization design for interior acoustic-structural coupled systems are implemented in JIFEX, which is a large-scale engineering structural analysis and optimization software. The main content of this dissertation includes the following chapters:
In chapter 1, the research motivation and the main problems of noise control techniques are investigated. Several numerical methods used in acoustic fields, such as FEM, BEM, SEA (Statistical Energy Analysis), are discussed. Then the software-JIFEX is introduced. Finally, the brief description of the research work in the dissertation is presented.
In the second chapter, based on the wave equation for linear acoustics and various boundary conditions, the finite element equations for lightly damped acoustic cavity are given. The equations are solved based on the assumption that the acoustic pressure vector, which indicates the magnitude and relative phases at all locations in the system, is entirely real. The semi-analytical method is used to calculate the sensitivity of stiffness, mass and damping matrices comparing with finite difference method. In the last section, the eigenfrequency and sound pressure level response of a 3D-car model are optimized to show the validity and efficiency of the sensitivity analysis and design optimization methods.
In chapter 3, the finite element equations of acoustic-structural coupled systems are given. The static condensation method is used to avoid the singular structural mass matrix. In order to calculate the eigenpairs of non-symmetrical matrix, the adjoint subspace iteration method is given. Also, the relation of the left and right eigenvectors and the normalized orthogonality conditions are confirmed. The responses of coupled systems are calculated using the modal method, direct method and iteration method. Numerical examples are given to illustrate the validity of these methods
In chapter 4, the sensitivity of the eigenfrequency and sound pressure with respect to size and shape design parameters for those coupled systems are derived. Then the design optimization models are also presented. The topology optimization method for the coupled acoustic-structural systems is studied with the topology optimization theory. The sensitivity of acoustic pressure with respect to topology design variables and topology optimization method of stiffener distribution for the acoustic-structural coupled systems are proposed to study the stiffener material distribution of structure for interior sound pressure level (SPL) reduction of the coupled system. Numerical examples are given to show the validity and the efficiency of the sensitivity analysis and design optimization methods.
In the fifth chapter, the interior acoustic-structural coupled systems subjected to random excitations are studied. An iteration method is proposed to improve the efficient and accuracy of the computation. The pseudo-excitation method is used to calculate the random response in iterations. It was found that the pseudo excitation method is more efficiency than traditional random analysis methods for iteration calculation of interior acoustic-structural coupled systems beside its high efficiency.
In chapter 6, the sensitivity analysis formulas for the random responses of coupled acoustic-structural systems are derived and compared with finite difference method. The node sound pressure level (SPL) or average SPL of acoustic pressure power spectral density (PSD) is selected as the objective function with the structural weight constraint. The thickness of the structural plate is chosen as design variables. The design optimization model of the coupled systems subjected to random excitations is proposed. Furthermore, the topology optimization models of the coupled systems subjected to random excitations are presented through improving the SIMP and RAMP topology optimization models. Numerical examples are given to show the validity and efficiency of the sensitivity analysis and design optimization methods.
In the conclusion, the main contributions of the dissertation are summarized and the further work is suggested.
引文
[1]马大猷.噪声与振动控制工程手册.北京:机械工业出版社,2002.
[2]Lueg P.Process of Silencing Sound Oscillations.,US Patent,2043416,June 9,1936.
[3]Olson H.F.Electronic Control of Noise,Vibration and Reverberation.Journal of the Acoustical Society of America,1965,28(5):966-972.
[4]Kempton A.J.The Ambiguity of Acoustic Sources a Possibility for Active Control.Journal of Sound and Vibration,1976,48(2):474-483.
[5]Burgess J.C.Active Adaptive Sound Control in a Duct:a Computer Simulation.The Journal of the Acoustical Society of America,1981,70(3):715-726.
[6]于华民,朱海潮,施引.管道复合噪声主动控制系统及其实现.噪声与振动控制,2003,6(3):34-36.
[7]常振臣.基于神经网络的车内噪声自适应有源控制系统仿真与试验研究,吉林:吉林大学博士学位论文,2003.
[8]Tang W.C.,Zheng H.Low Frequency Sound Transmission through Close Fitting Sandwich Panels.Applied Acoustic,1998,15(1):13-30.
[9]Spannheimer H,Freymann R.infrasound and Low Frequency Noise in the Passenger Compartment of Vehicles.Journal of Low Frequency Noise,Vibration and Active Control,1997,16(4):219-227.
[10]Gladwell G.M.L.,Zimmermann G.on Energy and Complementary Energy Formulation of Acoustic and Structural Vibration Problems.Journal of Sound and Vibration,1966,3(2):233-241.
[11]Mason V.On the Use of Rectangular Finite Elements.Institute of Sound and Vibration Report No.161.1967.
[12]Craggs A.The Transient Response of a Coupled Plate-Acoustic System Using Plate and Acoustic Finite Elements.Journal of Sound and Vibration,1971,15(4):509-528.
[13]Craggs A.The Use of Simple Three-Dimensional Acoustic Finite Elements for Determining the Natural Modes and Frequencies of Complex Shaped Enclosure.Journal of Sound and Vibration,1972,23(3):331-339.
[14]Shuku T.,Ishihara K.The Analysis of the Acoustic Field in Irregular Shaped Rooms by the Finite Element Methods.Journal of Sound and Vibration,1973,29:67-76.
[15]Petyt M.,Lea J.,Koopmann G.H.A Finite Element Method for Determining the Acoustic Modes of Irregular Shaped Cavities.Journal of Sound and Vibration,1976,45(4):495-502.
[16]Wolf J.A.,Nefske Jr.D.J.,Howell L.J.Structure-Acoustic Finite Element Analysis of Automotic Passenger Compartment.Transactions of the Society of Automotive Engineers,1976,85(1):857-864.
[17]Nefshe D.J.,Wolf J.A.,Howell L.J.Structural-Acoustic Finite Element Analysis of the Automobile Passenger Compartment:a Review of Current Practice.Journal of Sound and Vibration,1982,80(2):247-266.
[18]沈壕,孙洪生.工程声学的有限元法.声学学报,1981,7:249-259.
[19]吴国荣,钟伟芳,吴永东等.应用分形有限元方法于外域声场计算,力学与实践,2004。 26(5):52-55.
[20]Seybert A.F.,Soenarko B.,Rizzo F.J.,et al.Application of the BIE Method to Sound Radiation Problems an Isoparametric Element.Journal of Vibration and Acoustics,1984,106:414-420.
[21]Seybert A.F.,Soeuarko B.,Rizzo F.J.,et al.An Advanced Computational Method for Radiation and Scattering of Acoustic Waves in Three Dimensions.Journal of the Acoustical Society of America,1985,77(6):362-368.
[22]Seybert A.F.,Soenarko B.,Rizzo F.J.,et al.A Special Integral Equation Formulation for Acoustic Radiation and Scattering for Axisymmetric Bodies and Boundary Conditions.Journal of the Acoustical Society of America,1986,80(1):1241 - 1247.
[23]Seybert A.F.,Soenarko B.Radiation and Scattering of Acoustic Waves from Bodies of Arbitrary Shape in a Three-Dimensional Half Space.ASME Transactions.J.Vib.Acoust.Stress Rel.Dsgn.,1988,110(3):112-117.
[24]刘鹏,刘更,吴立言等.有限元/边界元方法在卡车驾驶室声学分析中的应用.噪声与振动控制,2005,6(3):25-28.
[25]赵志高,黄其柏,何锃.基于有限元边界元方法的薄板声辐射分析.噪声与振动控制,2008,2(1):39-43.
[26]Warszawski A.,Soares Jr.D.,Mansur W.J.A FEM-BEM Coupling Procedure to Model the Propagation of Interacting Acoustic-Acoustic/Acoustic-Elastic Waves through Axisymmetric Media.Computer Methods in Applied Mechanics and Engineering,2008,in Press.
[27]Tong Z,Zhang Y,Zhang Z,Et Al.Dynamic Behavior and Sound Transmission Analysis of a Fluid-Structure Coupled System Using the Direet-BEM/FEM.Journal of Sound and Vibration,2007,299(3):645-655.
[28]Ute G.,Matthias F.,Lothar G.A Multipole Galerkin Boundary Element Method for Acoustics.Engineering Analysis with Boundary Elements,2004,28(2):155-162.
[29]Lyon R.M.Power Flow between Linearly Coupled Oscillators.Journal of the Acoustical Society of America,1962,34(5):632-639.
[30]Smith Jr.P.W.Response and Radiation of Structural Modes Excited By Sound.Journal of the Acoustical Society of America,1962,34(5):640-647.
[31]Smith Jr.P.W.Coupling of Sound and Panel Vibration below the Critical Frequency.Journal of the Acoustical Society of America,1964,36(5):1516-1520.
[32]Fahy F.J.Response of a Cylinder to Random Sound in the Contained Fluid.Journal of Sound and Vibration,1970,13(2):171-194.
[33]Dowell E.H.Master Plan for Prediction of Vehicle Interior Noise.AIAA.Aeroacoustics Conference,5th,1979,12-14.,
[34]Ma J,Li D.Study of Shipboard Noise Predict Ion With SEA.Journal of Dalian University of Technology,2003,43(5):645-649.
[35]黄其柏,李晓政,王勇.车辆室内噪声的统计能量分析优化仿真,噪声与振动控制,2005,6(3):29-32.
[36]Nefske D.J.,Sung S.H.Power Flow Finite-Element Analysis of Dynamic-Systems:Basic Theory and Application to Beams.Journal of Vibration Acoustics Stress and Reliability in Design,1989, 111(1):94-100.
[37] Wohlever J., Bernhard R.J. Mechanical Energy Flow Models of Rods and Beams. Journal of Sound and Vibration, 1992, 153(1):1-19.
[38] Bouthier O.M. Bernhard RJ. Models of Space-Averaged Energetics of Plates. A1AA Journal, 1992, 30(3):616-623.
[39] Bouthier O.M., Bernhard R.J. Simple Models of the Energetics of Transversely Vibrating Plates. Journal of Sound and Vibration 1995, 182(1): 149 -166.
[40] Bouthier O.M. Energetics of Vibrating Systems. Ph.D. Thesis, Purdue University, 1992.,
[41] Langley R.S., Heron K.H. Elastic Wave Transmission through Plate/Beam Junctions. Journal of Sound and Vibration, 1990,143(2):241-253.
[42] Cho P.E. Energy Flow Analysis of Coupled Systems. Ph.D. Thesis, Purdue University, 1992.,
[43] Vlahopoulos N., Garze-Rios L.O., Mollo C. Numerical Implementation, Vallidation and Marine Applications of an Energy Finite Element Formulation. Journal of Ship Research, 1999, 43(3): 143-156.
[44] Zhang W., Wang A., Vlahopoulos N. Validation of the EFEA Method through Correlation with Conventional FEA and SEA Results. SAE Noise and Vibration Conference, SAE Paper No. 2001-01-1618,2001,
[45] Wang S. Theory and Applications of a Simplified Energy Finite Element Method and Its Similarity to SEA. Noise Control Engineering Journal, 2002, 50(2):63-72.
[46] Bitsie F. The Structural-Acoustic Energy Finite Element Method and Energy Boundary Element Method. Ph.D. Thesis, Purdue University, 1996.
[47] Zhang W., Wang A., Vlahopoulos N. High-Frequency Vibration Analysis of Thin Elastic Plates under Heavy Fluid Loading by an Energy Finite Element Formulation. Journal of Sound and Vibration, 2003,263(1):21-46.
[48] Bitsie F., Bernhard R.J. Sensitivity Calculations for Structural-Acoustic EFEM Predictions. Noise Control Engineering Journal, 1998,46(3):91-96.
[49] Borlase G.A., Vlahopoulos N. An Energy Finite Element Optimization Process for Reducing High-Frequency Vibration in Large-Scale Structures. Finite Elements in Analysis and Design, 2000,36(1):51-67.
[50] Kim N.H., Dong J., Choi K.K. Energy Flow Analysis and Design Sensitivity Analysis of Structural-Acoustic Problems at High Frequency. Journal of Sound and Vibration, 2004, 269(1-2):213 -250.
[51] Pretlove A.J. Free Vibrations of a Rectangular Panel Backed by a Closed Rectangular Cavity. Journal of Sound and Vibration, 1965,2:197-209.
[52] Wolf J.A., Nefshe D.J., Howell L.T. Structural-Acoustic Finite Element Analysis of the Automobile Passenger Compartment. Transactions of the Society of Automotive Engineers, 1976, 85(1):857-864.
[53] Joseph A., Wolf J.A. Modal Synthesis for Combined Structural-Acoustic Systems. AIAA Journal, 1977,5(5):743-745.
[54] Macneal R.H., Citerley R., Chargin M. A Symmetric Modal Formulation of Fluid-Structure Interaction. ASME Paper 80-C2/PVP-117, 1980.
[55]Nefshe D.J.,Wolf J.A.,Howell L.T.Structural-Acoustic Passenger Compartment:a Review of Current Practice.Journal of Sound and Vibration,1982,80(2):247-266.
[56]Vaieaitis R.,Siazak M.Cabin Noise Control for Twin Engine General Aviation Aircraft.NASA-CR- 165833,1982,
[57]Dowell E.H.,Gormen G.F.,Smith D.A.Acoustoelasticity:General Theory,Acoustic Natural Modes and forced Response to Sinusoidal Excitation,Including Comparison with Experiment.Journal of Sound and Vibration,1977,52(4):519-542.
[58]Adelman H.M.,Haftka R.T.Sensitivity Analysis of Discrete Structural Systems.AIAA Journal,1986,24(5):823-832.
[59]Wang B.P.Improved Approximate Methods for Computing Eigenvector Derivatives in Structural Dynamics.AIAA Journal,1991,29(6):1018-1020.
[60]陈塑寰,刘中生,赵又群.振型一阶导数的高精度截尾模态法,力学学报,1993,25(4):427-434.
[61]刘中生,陈塑寰,赵又群.振动系统特征值和特征向量的一阶导数,宇航学报,1992,4:96-102.
[62]Nelson R.B.Simplified Calculation of Eigenvector Derivatives.AIAA Journal,1976,14(9):1201-1205.
[63]Du K,Wei Y.Structured Pseudospectra and Structured Sensitivity of Eigenvalues.Journal of Computational and Applied Mathematics,2006,197:502-519.
[64]Ma Z.D.,Hagiwara Ⅰ.Improved Mode-Superposition Technique for Modal Frequency Response Analysis of Coupled Acoustic-Structural Systems.AIAA Journal,1991,29(10):1720-1726.
[65]Ma Z.D.,Hagiwara Ⅰ.Sensitivity Analysis Methods for Coupled Acoustic-Structural System,Part Ⅰ:Modal Sensitivity.AIAA Journal,1991,29(11):1787-1795.
[66]Ma Z.D.,Hagiwara Ⅰ.Sensitivity Analysis Methods for Coupled Acoustic-Structural System Part Ⅱ:Direct Frequency Response and Its Sensitivity.AIAA Journal,1991,29(11):1796-1801.
[67]Ma Z.D.,Hagiwara Ⅰ.Sensitivity Calculation for Conducting Modal Frequency Response Analysis of Coupled Acoustic-Structural Systems.JSME International Journal,1992,35(3):14-21.
[68]Hagiwara Ⅰ.,Kozukue W.,Ma Z.D.The Development of Eigenmode Sensitivity Analysis Methods for Coupled Acoustic-Structural Systems and Their Application to Reduction of Vehicle Interior Noise.Finite Elements in Analysis and Design,1993,14(6):235-248.
[69]Scarpa F.,Curti G.A Method for the Parametric Frequency Sensitivity of Interior Acousto-Structural Coupled Systems.Applied Acoustics,1999,58(4):451-467.
[70]Scarpa F.Parametric Sensitivity Analysis of Coupled Acoustic- Structural Systems.Journal of Vibration and Acoustics,2000,122(2):109-115.
[71]Choi K.K.,Shim Ⅰ.,Wang S.Design Sensitivity Analysis of Structure-induced Noise and Vibration.Journal of Vibration and Acoustics,1997,119(3):173-179.
[72]S.Wang.Design Sensitivity Analysis of Noise,Vibration,and Harshness of Vehicle Body Structure.Mechanics of Structures and Machines,1999,27(3):317-336.
[73]王登峰,殷涌光,程悦荪等.拖拉机驾驶室内部噪声响应的灵敏度分析,农业机械学报,1993,24(1):25-30.
[74]吴小清,王登峰,徐诚等.壁面有吸声材料时驾驶室内噪声响应的灵敏度分析,农业机械学 报,1999,15(3):20-24.
[75]Wang H.W.,Gu Y.X.,Gao J.Sensitivity Analysis and Design Optimization for Pressure Level Integral of Structure-Acoustics System.Proceeding of the World Congress of Structural and Multidisciplinary Optimization,June,2001,Dalian,China:120-121.,
[76]Gu Y.X.,Wang H.W.Sensitivity Analysis for Coupled Structural-Acoustic Systems.S.N.Atluri,F.W Brust(Eds.),Tech Science Press,Proc.of ICES2K,2000:1231-1237.,
[77]Gu Y.X.,Wang H.W.The Sensitivity Analysis Methods of Coupled Acoustics- Structure Systems and Application in Interior Noise Reducing.Proc.EPMESC Ⅷ,Shanghai,2001.
[78]孙淦云,王跃方.密闭腔体声.结构耦合系统的动力灵敏度分析.计算力学学报,2005,22(5):550-554.
[79]杨搏,朱平,余海东等.基于模态分析法的车身NV H结构灵敏度分析.中国机械工程,2008,19(3):361-364.
[80]赵冠军,刘更,吴立言.汽车驾驶室声固耦合系统的灵敏度分析.机械设计,2008,25(1):53-55.
[81]Marburg S.Developments in Structural-Acoustic Optimization for Passive Noise Control.Archives of Computational Methods in Engineering,State of the Art Reviews,2002,9(4):291-370.
[82]Lamancusa J.S.,Eschenauer H.A.Design Optimization Methods for Rectangular Panels with Minimal Sound Radiation.AIAA Journal,1994,32(3):472-479.
[83]Crane S.P.,Cunefare K.A.,Engelstad S.P.,Et Al.Comparison of Design Optimization Formulations for Minimization of Noise Transmission in a Cylinder.Journal of Aircraft,1997,34(2):236-243.
[84]Cunefare K.A.,Crane S.P.,Engelstad S.P.,Et Al.Design Minimization of Noise in Stiffened Cylinders Due to Tonal External Excitation.Journal of Aircraft,1999,36(3):563-570.
[85]Engelstad S.P.,Cunefare K.A.,Powell E.A.,Et Al.Stiffener Shape Design to Minimize Interior Noise.Journal of Aircraft,2000,37(1):165-171.
[86]Michell A.G.M.The Limits of Economy of Materials in Frame Structures.Philosophical Magazine,1904,8(47):589-597.
[87]Dorn W.,Gomory R.,Greenberg H.Automatic Design of Optimal Structures.J.De.Mechanique,1964,3(1):25-52.
[88]Schmit L.A.Structural Optimization-Some Ideas and insights.New York:Wileg,1984.
[89]Rozvany G.N,Zhou M.The DCOC Algorithm,Part Ⅱ:Topological,Geometrical and Generalized Shape Optimization.Computer Methods in Applied Mechanics and Engineering,1991,89(1-3):309-336.
[90]Bendsoe M.P,Ben-Tal A,Zowe J.Optimization Methods for Truss Geometry and Topology Design.Structural Optimization,1994,7(3):141-159.
[91]Zhang W.H,Domaszewski M.,Bassir H.Developments of Sizing Sensitivity Analysis With ABAQUS Code.International Journal of Structural Optimization,1999,17(2-3):219-225.
[92]Bendsoe M.P.,Kikuchi N.Generating Optimal Topologies in Structure Design Using Homogenization Method.Computer Methods in Applied Mechanics and Engineering 1988,71(2):197-224.
[93]Bendsoe M.P.,Optimization of Structural Topology.Berlin:Springer,1997.
[94]Bendsoe M.P.,Sigmund O.Topology Optimization:Theory,Methods and Applications.New York:Springer,2003.
[95]张东旭.连续体结构拓扑优化及形状优化若干问题.(博士学位论文).大连:大连理工大学,1992.
[96]杨德庆.连续变量化的结构形状及拓扑优化设计理论和方法研究.(博士学位论文).大连:大连理工大学,1998.
[97]王健.具有形状和应力约束的连续体结构拓扑优化及其在框架结构设计中的应用.工程力学,2002,19(4):99-103.
[98]江允正,曲淑英,初明进.连续体结构拓扑优化.计算力学学报,2003,20(2):146-149.
[99]左孔天.连续体结构拓扑优化理论与应用研究.(博士学位论文).武汉:华中科技大学,2004.
[100]王石刚.组合结构优化理论、方法及工程应用研究.(博士学位论文).武汉:华中科技大学,1993.
[101]程耿东,顾元宪,王健.我国机械优化研究与应用的综述和展望.机械强度,1995,17(2):68-74.
[102]隋允康,建模·变换·优化-结构综合方法新进展.大连:大连理工大学出版社,1996.
[103]杨德庆,刘正兴,隋允康.连续体结构拓扑优化设计的ICM方法.上海交通大学学报,1999,33(6):734-736.
[104]隋允康,杨德庆,孙焕纯.统一骨架与连续体的拓扑优化的ICM理论和方法.计算力学学报,2000,17(1):28-33.
[105]隋允康,任旭春,龙连春.基于ICM方法的刚架拓扑优化.计算力学学报,2003,20(2):286-289.
[106]袁振,吴长春.采用非协调元的连续体拓扑优化设计.力学学报,2003,35(1):176-180.
[107]袁振,吴长春,装守兵.基于杂交元和变密度法的连续体结构的拓扑优化.中国科学技术大学学报,2001,31(6):694-699.
[108]Cheng G.D.,Guo X..E-Relaxed Approach in Structural Topology Optimization.Structural Optimization,1997,13:256-266.
[109]Cheng G.D.,Guo X.a Note on Jellyfish-Liked Feasiable Domain in Structural Topology Optimization.Engineering Optimization,1998,31:1-24.
[110]程耿东.关于桁架结构拓扑优化设计中的奇异最优解.大连理工大学学报,2000,40(1):379-383.
[111]Diaz A.R,Sigmund O.Checkerboard Patterns in Layout Optimization.Structural Optimization,1995,10(1):40-45.
[112]Zhou M,Shyy Yk,Thomas H.Checkerboard and Minimum Member Size Control in Topology Optimization.Structural and Multidiseipline Optimization,2001,21(2):152-158.
[113]Bendsoe M.P,Optimization of Structural Topology,Shape and Material.[M].Berlin:Springer-Verlag,1995.
[114]Sigmund O.Numerical instabilities in Topology Optimization:a Survey on Procedures Dealing With Checkerboard,Mesh Dependencies,Local Minima.Structural Optimization,1998,16(1):68-75.
[115]Petersson J,Sigmund O.Slope Constrained Topology Optimization.International Journal for Numerical Methods in Engineering,1998,41(8):1417- 1434.
[116]Zhang W.,Duysinx P.Dual Approach Using a Variant Perimeter Constraint and Efficient Sub-Iteration Scheme for Topology Optimization.Computers & Structures,2003,81(22-23):2173-2181.
[117]Yang X.Y,Xie Y.M,Liu J.S.Perimeter Control in Bi-Directional Evolutionary Optimization Method.Structural and Multidiscipline Optimization,2003,24(6):430-440.
[118]Pedersen N.Topology Optimization of Laminated Plates With Prestress.Computers & Structures,2002,80(7-8):559-570.
[119]郭中泽,陈裕泽,张卫红等.渐进优化法的一种高阶棋盘格式抑制方法.机械设计,2006,23(5):1-4.
[120]Kozukue W.,Hagiwara I.Development of a Topology Optimization Analysis Method for Coupled Structural-Acoustic System and Application to Vehicle Interior Noise Reduction.JSAE Review,1995,16(3):309.
[121]Kozukue W.,Hagiwara I.Topology Optimization Analysis for Reduction of Interior Noise Using a Homogenization Method for a Mean Eigenvalue.The Journal of the Acoustical Society of America,1996,100(4):2746-2753.
[122]Lee J,Wang S,Dikec A.Topology Optimization for the Radiation and Scattering of Sound From Thin-Body Using Genetic Algorithms.Journal of Sound and Vibration,2004,276:899-918.
[123]Wadbro E.,Berggren M.Topology Optimization of an Acoustic Horn.Computer Methods in Applied Mechanics and Engineering,2006,196:420-436.
[124]Yoon G.H,Jensen J.S.,Ole S.Topology Optimization of Acoustic-Structure Interaction Problems Using a Mixed Finite Element Formulation.International Journal for Numerical Methods in Engineering,2007,70:1049-1075.
[125]Du J.B,Oihoff N.Minimization of Sound Radiation From Vibrating Bi-Materiai Structures Using Topology Optimization.Structural Multidisciplinary Optimization,2007,33(4):305-321.
[126]Luo J.H.,Gea H.C.Optimal Stiffener Design for Interior Sound Reduction Using a Topology Optimization Based Approach.Journal of Vibration and Acoustics,2003,125(3):267-273.
[127]Akl W,A El-Sabbagh,Al-Mitani K,Et Al.Topology Optimization of a Plate Coupled With Acoustic Cavity,Solids and Structures,2008,Accepted Manuscript.
[128]Crandall S.H.,Random Vibration vol.Ⅱ.Cambridge,MA:MIT Press,1963.
[129]Crandall S.H.,Random Vibration vol.Ⅰ.Cambridge,MA:MIT Press,1958.
[130]俞载道,曹国敖.随机振动理论及其应用.上海:同济大学出版社,1988.
[131]欧进萍,王光远.结构随机振动.北京:高等教育出版社,1998.
[132]朱位秋.随机振动.北京:科学出版社,1992.
[133]Ibrahim R.A.Parametric Random Vibration:Research Studies Press Ltd,1985.
[134]李国豪.工程结构抗震动力学.上海:上海科学技术出版社,1980.
[135]Lin J.H.A Fast CQC Algorithm of PSD Matrices for Random Seismic Responses,Computers and Structures,1992,44(3):683-687.
[136]Lin J.H.,Zhao Y.,Zhang Y.H.Accurate and Highly Efficient Algorithms for Structural Stationary/Non-stationary Random Responses,Computer Methods in Applied Mechanics and Engineering,2001,191:103-111.
[137]W.S.Zhang J.H.Lin Structural Responses to Arbitrarily Coherent Stationary Random Excitations,Computers and Structures,1994,50(5):629-633.
[138]Lin J.H.,Zhang W.S.,Williams F.W.Pseudo-excitation Algorithm for Non-stationary Random Seismic Responses,Engineering Structures,1994,16(4):270-276.
[139]Lin J.H.,Shen W.P.,Williams F.W.A High Precision Direct Integration Scheme for Non-stationary Random Seismic Responses of Non-classically Damped Structures,Structural Engineering and Mechanics,1995,3(3):215-228.
[140]林家浩,张亚辉.随机振动的虚拟激励法.北京:科学出版社,2004.
[141]汪梦甫.用虚拟激励法求解非比例阻尼线性体系的非平稳随机地震响应,力学季刊,2006,27(4):598-605.
[142]汪梦甫.非比例阻尼线性体系平稳随机地震响应计算的虚拟激励法,计算力学学报,2008,25(1):94-99.
[143]李建俊.随机地震响应分析的虚拟激励法.(博士学位论文).大连:大连理工大学,1994.
[144]张亚辉.复杂结构在多种荷载工况下的屈曲及动力分析.(博士学位论文).大连:大连理工大学,1999.
[145]孙东科.长跨桥梁三维风振分析.(博士学位论文).大连:大连理工大学,1999.
[146]赵岩.桥梁抗震的线性/非线性分析方法研究.(博士学位论文).大连:大连理工大学,2003.
[147]戴新进.复合材料结构随机振动的虚拟激励法及在航空航天领域的应用.(博士学位论文).大连:大连理工大学.2007.
[148]Allen M.J.,Vlahopoulos N.integration of Finite Element and Boundary Element Methods for Calculating the Radiated Sound From a Randomly Excited Structure.Computers and Structures,2000,77:155-169.
[149]Allen M.J.,Sbragio R.,Vlahopoulos N.Structural/Acoustic Sensitivity Analysis of a Structure Subjected to Stochastic Excitation.AIAA Journal,2001,39(7):1270-1279.
[150]童卫华,姜节胜,顾松年.某型导弹振动实验夹具的动力学优化,应用力学学报,1996,13(SI):111-114.
[151]Tong W.H,Jiang J.S,Liu G.R.Dynamic Design of Structures under Random Excitation.Computational Mechanics,1998,22(5):388-394.
[152]杨振兴,荣见华,傅建林.窄带随机激励下的结构动力学拓扑优化设计.振动与冲击,2008,24(6):85-87.
[153]Lambert S,Pagnacco E,Khalij L,Et AI.Topology Optimization of Structures Subject to Random Excitations With Fatigue Life Constraints.European Conference on Computational Mechanics Solids,Structures and Coupled Problems in Engineering,2006,5-8 June:487.
[154]Gu Y.X,Zhang H.W,Guan Z.Q.New Generation Software of Structural Analysis and Design Optimization-JIFEX.Structural Engineering and Mechanics,1999,7(6):589-599.
[155]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.
[156]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.
[157]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.
[158]Craggs A.A Finite Element Method for Free Vibration of Air in Duets and Rooms With Absorbing Walls.Journal of Sound and Vibration,1994,173(4):568-576.
[159]Craggs A.The Free Vibration of Systems With Proportional Or Light Damping.Journal of Sound and Vibration,1994,170(1):130-139.
[160]Easwaran V.,Craggs A.On Further Validation and Use of the Finite Element Method to Room Acoustics.Journal of Sound and Vibration,1995,187(2):195-212.
[161]赵越喆,吴硕贤.小阻尼界面房间声传输函数和声脉冲响应函数的有限元素法.应用声学,2000,19(2):24-30.
[162]许肖梅.声学基础.北京:科学出版社,2003.
[163]Gu Y.X.,Cheng G.D.Structural Modelling and Sensitivity Analysis of Shape Optimization.Structural Optimization,1993,6(1):29-37.
[164]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方法.江汉石油学院学报,1994,16(4):83-89.
[165]顾元宪,程耿东.结构形状优化设计数值方法的研究和应用.计算结构力学及其应用,1993,10(3):321-335.
[166]程耿东.工程结构优化设计基础.北京:水利电力出版社,1984.
[167]Gu Y.X.,Zhang H.W.,Guan Z.Q.New Generation Software of Structural Analysis and Design Optimization-JIFEX,Structural Engineering and Mechanics,1999,7(6):589-599.
[168]Fletcher g.Practical Methods of Optimization.[M].John Wiley & Sons,1980.
[169]Everstine G.C.A Symmetric Potential Formulation for Fluid-Structure Interaction.Journal of Sound and Vibration,1981,79(3):157-160.
[170]Ohayon R.Transient and Modal Analysis of Bounded Medium Fluid Structure Problems.Proceedings of An International Conference,1984,Venice,Nova Sciences Pub inc.
[171]Sandberg G.,Goransson P.A Symmetric Finite Element Formulation for Acoustic Fluid Structure Interaction Analysis.Journal of Sound and Vibration,1988,123(3):507-515.
[172]丁渭平.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,2000,34:58-62.
[173]钟万勰,林家浩.不对称实矩阵的本征对共轭子空间迭代算法.计算结构力学及其应用.1990,7(4):1-10.
[174]Shepard R.,Minkoff M.,Zhou Y.K.Software for Computing Eigenvalue Bounds for Iterative Subspace Matrix Methods.Computer Physics Communications,2005,170:109-114.
[175]Najafi H.S.,Khaleghi E.A New Restarting Method in the Arnoldi Algorithm for Computing the Eigenvalues of a Nonsymmetric Matrix.Applied Mathematics and Computation,2004,156:59-71.
[176]Najafi H.S.,Moosaei H.A New Restarting Method in the Harmonic Projection Algorithm for Computing the Eigenvalues of a Nonsymmetric Matrix.Applied Mathematics and Computation,2008,198:143-149.
[177]Ghazia A.E.,Hajjia S.E.,Giraud L.,Et Al.Newton's Method for the Common Eigenvector Problem.Journal of Computational and Applied Mathematics,2007:Doi:10.1016/J.Cam.2007.11.009.
[178]Najafi H.S.,Ghazvini H.A Modification on Minimum Restarting Method in the Arnoldi Algorithm for Computing the Eigenvalues of a Nonsymmetric Matrix.Applied Mathematics and Computation,2006,181:1455-1461.
[179]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.
[180]林家浩,曲乃泗,孙焕纯.计算结构动力学.北京:高等教育出版社,1989.
[181]Ewins D.J.Estimation of Resonant Peak Amplitudes.Journal of Sound and Vibration,1975,43:595-605.
[182]Ma Z.D.,Hagiwara Ⅰ.Sensitivity Analysis Methods for Coupled Acoustic-Structural System Part Ⅱ:Direct Frequency Response and Its Sensitivities,AIAA Journal,1991,29(11):1796-1801.
[183]Nalecz A.G,Wither J.Design Sensitivity Analysis of Mechanical System in Frequency Domain.Journal of Sound and Vibration,1988,120(2):517-526.
[184]Ting T,Chen T.L.C,Twomey W.J.Finite Element Model Refinement with Actual forced Response of Structures.Finite Elements in Analysis and Design,1992,11(3):213-220.
[185]Livne E,Blando G.D.Structural Dynamic Frequency Response Using Combined Direct and Adjoint Reduced-Order Approximations.AIAA Journal,2003,41(7):1377-1385.
[186]董绍强,廖道训,陆永忠.结构频率响应灵敏度计算及响应修改研究.华中科技大学学报,2001,29(10):56-58.
[187]王秀峰,陈心昭.随机振动结构声辐射的统计边界点法分析.声学技术,2001,20(3):107-110.
[188]刘钊,陈心昭.求解随机振动结构声辐射的统计边界元方法.声学学报,1997,22(6):495-500.
[189]纪刚,张纬康,周其斗.随机力作用下的水下结构物声辐射分析.中国造船,2004,12:182-188.
[190]张军.声学.结构灵敏度及结构.声学优化设计研究.(博士学位论文).大连:大连交通大学,2006.
[191]林家浩,钟万勰.关于虚拟激励法与结构随机响应的注记.计算力学学报,1998,15(2):217-223.
[192]林家浩,易平.线性随机结构的平稳随机响应.计算力学学报,2001,18(4):402-408.
[193]Elishak I,Lin Y K,Zhu L P.Probabilistic and Convex Modeling of Acoustically Excited Structures.Elsevier,Amsterdam,1994.
[194]Simiu E,Scanlan R.H.Wing Effects on Structures:An introduction to Wind Engineering.John Wiley & Sons,New York,1978.
[195]Clough R.W,Penzien J.Dynamics of Structures.Mcgraw-Hill Book Company,1975.
[196]Bendat J.S,Piersol A.G.Random Data:Analysis and Measurement Procedures.New York Wiley,2000.
[197]Socha L.The Sensitivity Analysis of Stochastic Non-Linear Dynamic Systems.Journal of Sound and Vibration,1986,110:271-296.
[198]Szopa J.Sensitivity of Stochastic Systems to initial Conditions.Journal of Sound and Vibration,1984,97:645-649.
[199]Benfratelio S,Caddemi S,Muscolino G.Gaussian and Non-Gaussian Stochastic Sensitivity Analysis of Discrete Structural System.Computers & Structures,2000,78:425-434.
[200]Bhattaeharyya B,Chakraborty S.Stochastic Dynamic Sensitivity of Uncertain Structures Subjected to Random Earthquake Loading.Journal of Sound and Vibration,2002,249(3):543-556.
[201]Caceiola P,Colajanni P,Muscolino G.A Modal Approach for the Evaluation of the Response Sensitivity of Structural Systems Subjected to Non-Stationary Random Processes.Computer Methods in Applied Mechanics and Engineering,2005,194:4344-4361.
[202]姚昌仁,麻永平.结构随机激励的响应灵敏度分析.力学学报,1990,22(4):438-445.
[203]童卫华,姜节胜,顾松年.一种以均方响应作为约束的动力学设计方法.应用力学学报,1996,13(3):94-98.
[204]童卫华,姜节胜.结构在随机激励下的一种动力学设计方法.机械强度,1996,18(2):6-10.
[205]乔红威,吕震宙.随机结构随机激励下的响应灵敏度分析.振动与冲击,2008,27(3):60-62.
[206]陈建兵,李杰.结构随机动力非线性反应的整体灵敏度分析.计算力学学报,2008,25(2):169-176.
[207]李晓峰,张军,兆文忠等.随机激励结构.声场耦合振动声学数值仿真研究.系统仿真学报,2007,19(8):1683-1685.
[208]Fox R.L,Kapoor M.D.Rates of Change of Eigenvalues and Eigenvectors.AIAA Journal,1968,6(12):2426-2429.
[209]Nelson K.B.Simplified Calculation of Eigenvector Derivative.AIAA Journal,1976,14(9):1201-1205.
[210]Wang B.P.Improved Approximate Methods for Computing of Eigenvector Derivative in Structural Dynamics.AIAA Journal,1991,29(6):1018-1020.
[211]Rozvany G.I.N.,Kirsch U.,Bendsoe M.P.,Sigmund O.Layout optimization of structures.Apply Mechanics Review,1995,48:41-119.
[212]Rietz A.sufficiency of a Finite Exponent in SIMP(Power Law) Method.Structural and Multidiseipline Optimization,2001,21:159-163.
[213]Stolpe M.,Svanberg K.An Alternative Interpolation Scheme for Minimum Compliance Topology Optimization.Structural and Multidiscipline Optimization,2001,22:116-124
[2]Lueg P.Process of Silencing Sound Oscillations.,US Patent,2043416,June 9,1936.
[3]Olson H.F.Electronic Control of Noise,Vibration and Reverberation.Journal of the Acoustical Society of America,1965,28(5):966-972.
[4]Kempton A.J.The Ambiguity of Acoustic Sources a Possibility for Active Control.Journal of Sound and Vibration,1976,48(2):474-483.
[5]Burgess J.C.Active Adaptive Sound Control in a Duct:a Computer Simulation.The Journal of the Acoustical Society of America,1981,70(3):715-726.
[6]于华民,朱海潮,施引.管道复合噪声主动控制系统及其实现.噪声与振动控制,2003,6(3):34-36.
[7]常振臣.基于神经网络的车内噪声自适应有源控制系统仿真与试验研究,吉林:吉林大学博士学位论文,2003.
[8]Tang W.C.,Zheng H.Low Frequency Sound Transmission through Close Fitting Sandwich Panels.Applied Acoustic,1998,15(1):13-30.
[9]Spannheimer H,Freymann R.infrasound and Low Frequency Noise in the Passenger Compartment of Vehicles.Journal of Low Frequency Noise,Vibration and Active Control,1997,16(4):219-227.
[10]Gladwell G.M.L.,Zimmermann G.on Energy and Complementary Energy Formulation of Acoustic and Structural Vibration Problems.Journal of Sound and Vibration,1966,3(2):233-241.
[11]Mason V.On the Use of Rectangular Finite Elements.Institute of Sound and Vibration Report No.161.1967.
[12]Craggs A.The Transient Response of a Coupled Plate-Acoustic System Using Plate and Acoustic Finite Elements.Journal of Sound and Vibration,1971,15(4):509-528.
[13]Craggs A.The Use of Simple Three-Dimensional Acoustic Finite Elements for Determining the Natural Modes and Frequencies of Complex Shaped Enclosure.Journal of Sound and Vibration,1972,23(3):331-339.
[14]Shuku T.,Ishihara K.The Analysis of the Acoustic Field in Irregular Shaped Rooms by the Finite Element Methods.Journal of Sound and Vibration,1973,29:67-76.
[15]Petyt M.,Lea J.,Koopmann G.H.A Finite Element Method for Determining the Acoustic Modes of Irregular Shaped Cavities.Journal of Sound and Vibration,1976,45(4):495-502.
[16]Wolf J.A.,Nefske Jr.D.J.,Howell L.J.Structure-Acoustic Finite Element Analysis of Automotic Passenger Compartment.Transactions of the Society of Automotive Engineers,1976,85(1):857-864.
[17]Nefshe D.J.,Wolf J.A.,Howell L.J.Structural-Acoustic Finite Element Analysis of the Automobile Passenger Compartment:a Review of Current Practice.Journal of Sound and Vibration,1982,80(2):247-266.
[18]沈壕,孙洪生.工程声学的有限元法.声学学报,1981,7:249-259.
[19]吴国荣,钟伟芳,吴永东等.应用分形有限元方法于外域声场计算,力学与实践,2004。 26(5):52-55.
[20]Seybert A.F.,Soenarko B.,Rizzo F.J.,et al.Application of the BIE Method to Sound Radiation Problems an Isoparametric Element.Journal of Vibration and Acoustics,1984,106:414-420.
[21]Seybert A.F.,Soeuarko B.,Rizzo F.J.,et al.An Advanced Computational Method for Radiation and Scattering of Acoustic Waves in Three Dimensions.Journal of the Acoustical Society of America,1985,77(6):362-368.
[22]Seybert A.F.,Soenarko B.,Rizzo F.J.,et al.A Special Integral Equation Formulation for Acoustic Radiation and Scattering for Axisymmetric Bodies and Boundary Conditions.Journal of the Acoustical Society of America,1986,80(1):1241 - 1247.
[23]Seybert A.F.,Soenarko B.Radiation and Scattering of Acoustic Waves from Bodies of Arbitrary Shape in a Three-Dimensional Half Space.ASME Transactions.J.Vib.Acoust.Stress Rel.Dsgn.,1988,110(3):112-117.
[24]刘鹏,刘更,吴立言等.有限元/边界元方法在卡车驾驶室声学分析中的应用.噪声与振动控制,2005,6(3):25-28.
[25]赵志高,黄其柏,何锃.基于有限元边界元方法的薄板声辐射分析.噪声与振动控制,2008,2(1):39-43.
[26]Warszawski A.,Soares Jr.D.,Mansur W.J.A FEM-BEM Coupling Procedure to Model the Propagation of Interacting Acoustic-Acoustic/Acoustic-Elastic Waves through Axisymmetric Media.Computer Methods in Applied Mechanics and Engineering,2008,in Press.
[27]Tong Z,Zhang Y,Zhang Z,Et Al.Dynamic Behavior and Sound Transmission Analysis of a Fluid-Structure Coupled System Using the Direet-BEM/FEM.Journal of Sound and Vibration,2007,299(3):645-655.
[28]Ute G.,Matthias F.,Lothar G.A Multipole Galerkin Boundary Element Method for Acoustics.Engineering Analysis with Boundary Elements,2004,28(2):155-162.
[29]Lyon R.M.Power Flow between Linearly Coupled Oscillators.Journal of the Acoustical Society of America,1962,34(5):632-639.
[30]Smith Jr.P.W.Response and Radiation of Structural Modes Excited By Sound.Journal of the Acoustical Society of America,1962,34(5):640-647.
[31]Smith Jr.P.W.Coupling of Sound and Panel Vibration below the Critical Frequency.Journal of the Acoustical Society of America,1964,36(5):1516-1520.
[32]Fahy F.J.Response of a Cylinder to Random Sound in the Contained Fluid.Journal of Sound and Vibration,1970,13(2):171-194.
[33]Dowell E.H.Master Plan for Prediction of Vehicle Interior Noise.AIAA.Aeroacoustics Conference,5th,1979,12-14.,
[34]Ma J,Li D.Study of Shipboard Noise Predict Ion With SEA.Journal of Dalian University of Technology,2003,43(5):645-649.
[35]黄其柏,李晓政,王勇.车辆室内噪声的统计能量分析优化仿真,噪声与振动控制,2005,6(3):29-32.
[36]Nefske D.J.,Sung S.H.Power Flow Finite-Element Analysis of Dynamic-Systems:Basic Theory and Application to Beams.Journal of Vibration Acoustics Stress and Reliability in Design,1989, 111(1):94-100.
[37] Wohlever J., Bernhard R.J. Mechanical Energy Flow Models of Rods and Beams. Journal of Sound and Vibration, 1992, 153(1):1-19.
[38] Bouthier O.M. Bernhard RJ. Models of Space-Averaged Energetics of Plates. A1AA Journal, 1992, 30(3):616-623.
[39] Bouthier O.M., Bernhard R.J. Simple Models of the Energetics of Transversely Vibrating Plates. Journal of Sound and Vibration 1995, 182(1): 149 -166.
[40] Bouthier O.M. Energetics of Vibrating Systems. Ph.D. Thesis, Purdue University, 1992.,
[41] Langley R.S., Heron K.H. Elastic Wave Transmission through Plate/Beam Junctions. Journal of Sound and Vibration, 1990,143(2):241-253.
[42] Cho P.E. Energy Flow Analysis of Coupled Systems. Ph.D. Thesis, Purdue University, 1992.,
[43] Vlahopoulos N., Garze-Rios L.O., Mollo C. Numerical Implementation, Vallidation and Marine Applications of an Energy Finite Element Formulation. Journal of Ship Research, 1999, 43(3): 143-156.
[44] Zhang W., Wang A., Vlahopoulos N. Validation of the EFEA Method through Correlation with Conventional FEA and SEA Results. SAE Noise and Vibration Conference, SAE Paper No. 2001-01-1618,2001,
[45] Wang S. Theory and Applications of a Simplified Energy Finite Element Method and Its Similarity to SEA. Noise Control Engineering Journal, 2002, 50(2):63-72.
[46] Bitsie F. The Structural-Acoustic Energy Finite Element Method and Energy Boundary Element Method. Ph.D. Thesis, Purdue University, 1996.
[47] Zhang W., Wang A., Vlahopoulos N. High-Frequency Vibration Analysis of Thin Elastic Plates under Heavy Fluid Loading by an Energy Finite Element Formulation. Journal of Sound and Vibration, 2003,263(1):21-46.
[48] Bitsie F., Bernhard R.J. Sensitivity Calculations for Structural-Acoustic EFEM Predictions. Noise Control Engineering Journal, 1998,46(3):91-96.
[49] Borlase G.A., Vlahopoulos N. An Energy Finite Element Optimization Process for Reducing High-Frequency Vibration in Large-Scale Structures. Finite Elements in Analysis and Design, 2000,36(1):51-67.
[50] Kim N.H., Dong J., Choi K.K. Energy Flow Analysis and Design Sensitivity Analysis of Structural-Acoustic Problems at High Frequency. Journal of Sound and Vibration, 2004, 269(1-2):213 -250.
[51] Pretlove A.J. Free Vibrations of a Rectangular Panel Backed by a Closed Rectangular Cavity. Journal of Sound and Vibration, 1965,2:197-209.
[52] Wolf J.A., Nefshe D.J., Howell L.T. Structural-Acoustic Finite Element Analysis of the Automobile Passenger Compartment. Transactions of the Society of Automotive Engineers, 1976, 85(1):857-864.
[53] Joseph A., Wolf J.A. Modal Synthesis for Combined Structural-Acoustic Systems. AIAA Journal, 1977,5(5):743-745.
[54] Macneal R.H., Citerley R., Chargin M. A Symmetric Modal Formulation of Fluid-Structure Interaction. ASME Paper 80-C2/PVP-117, 1980.
[55]Nefshe D.J.,Wolf J.A.,Howell L.T.Structural-Acoustic Passenger Compartment:a Review of Current Practice.Journal of Sound and Vibration,1982,80(2):247-266.
[56]Vaieaitis R.,Siazak M.Cabin Noise Control for Twin Engine General Aviation Aircraft.NASA-CR- 165833,1982,
[57]Dowell E.H.,Gormen G.F.,Smith D.A.Acoustoelasticity:General Theory,Acoustic Natural Modes and forced Response to Sinusoidal Excitation,Including Comparison with Experiment.Journal of Sound and Vibration,1977,52(4):519-542.
[58]Adelman H.M.,Haftka R.T.Sensitivity Analysis of Discrete Structural Systems.AIAA Journal,1986,24(5):823-832.
[59]Wang B.P.Improved Approximate Methods for Computing Eigenvector Derivatives in Structural Dynamics.AIAA Journal,1991,29(6):1018-1020.
[60]陈塑寰,刘中生,赵又群.振型一阶导数的高精度截尾模态法,力学学报,1993,25(4):427-434.
[61]刘中生,陈塑寰,赵又群.振动系统特征值和特征向量的一阶导数,宇航学报,1992,4:96-102.
[62]Nelson R.B.Simplified Calculation of Eigenvector Derivatives.AIAA Journal,1976,14(9):1201-1205.
[63]Du K,Wei Y.Structured Pseudospectra and Structured Sensitivity of Eigenvalues.Journal of Computational and Applied Mathematics,2006,197:502-519.
[64]Ma Z.D.,Hagiwara Ⅰ.Improved Mode-Superposition Technique for Modal Frequency Response Analysis of Coupled Acoustic-Structural Systems.AIAA Journal,1991,29(10):1720-1726.
[65]Ma Z.D.,Hagiwara Ⅰ.Sensitivity Analysis Methods for Coupled Acoustic-Structural System,Part Ⅰ:Modal Sensitivity.AIAA Journal,1991,29(11):1787-1795.
[66]Ma Z.D.,Hagiwara Ⅰ.Sensitivity Analysis Methods for Coupled Acoustic-Structural System Part Ⅱ:Direct Frequency Response and Its Sensitivity.AIAA Journal,1991,29(11):1796-1801.
[67]Ma Z.D.,Hagiwara Ⅰ.Sensitivity Calculation for Conducting Modal Frequency Response Analysis of Coupled Acoustic-Structural Systems.JSME International Journal,1992,35(3):14-21.
[68]Hagiwara Ⅰ.,Kozukue W.,Ma Z.D.The Development of Eigenmode Sensitivity Analysis Methods for Coupled Acoustic-Structural Systems and Their Application to Reduction of Vehicle Interior Noise.Finite Elements in Analysis and Design,1993,14(6):235-248.
[69]Scarpa F.,Curti G.A Method for the Parametric Frequency Sensitivity of Interior Acousto-Structural Coupled Systems.Applied Acoustics,1999,58(4):451-467.
[70]Scarpa F.Parametric Sensitivity Analysis of Coupled Acoustic- Structural Systems.Journal of Vibration and Acoustics,2000,122(2):109-115.
[71]Choi K.K.,Shim Ⅰ.,Wang S.Design Sensitivity Analysis of Structure-induced Noise and Vibration.Journal of Vibration and Acoustics,1997,119(3):173-179.
[72]S.Wang.Design Sensitivity Analysis of Noise,Vibration,and Harshness of Vehicle Body Structure.Mechanics of Structures and Machines,1999,27(3):317-336.
[73]王登峰,殷涌光,程悦荪等.拖拉机驾驶室内部噪声响应的灵敏度分析,农业机械学报,1993,24(1):25-30.
[74]吴小清,王登峰,徐诚等.壁面有吸声材料时驾驶室内噪声响应的灵敏度分析,农业机械学 报,1999,15(3):20-24.
[75]Wang H.W.,Gu Y.X.,Gao J.Sensitivity Analysis and Design Optimization for Pressure Level Integral of Structure-Acoustics System.Proceeding of the World Congress of Structural and Multidisciplinary Optimization,June,2001,Dalian,China:120-121.,
[76]Gu Y.X.,Wang H.W.Sensitivity Analysis for Coupled Structural-Acoustic Systems.S.N.Atluri,F.W Brust(Eds.),Tech Science Press,Proc.of ICES2K,2000:1231-1237.,
[77]Gu Y.X.,Wang H.W.The Sensitivity Analysis Methods of Coupled Acoustics- Structure Systems and Application in Interior Noise Reducing.Proc.EPMESC Ⅷ,Shanghai,2001.
[78]孙淦云,王跃方.密闭腔体声.结构耦合系统的动力灵敏度分析.计算力学学报,2005,22(5):550-554.
[79]杨搏,朱平,余海东等.基于模态分析法的车身NV H结构灵敏度分析.中国机械工程,2008,19(3):361-364.
[80]赵冠军,刘更,吴立言.汽车驾驶室声固耦合系统的灵敏度分析.机械设计,2008,25(1):53-55.
[81]Marburg S.Developments in Structural-Acoustic Optimization for Passive Noise Control.Archives of Computational Methods in Engineering,State of the Art Reviews,2002,9(4):291-370.
[82]Lamancusa J.S.,Eschenauer H.A.Design Optimization Methods for Rectangular Panels with Minimal Sound Radiation.AIAA Journal,1994,32(3):472-479.
[83]Crane S.P.,Cunefare K.A.,Engelstad S.P.,Et Al.Comparison of Design Optimization Formulations for Minimization of Noise Transmission in a Cylinder.Journal of Aircraft,1997,34(2):236-243.
[84]Cunefare K.A.,Crane S.P.,Engelstad S.P.,Et Al.Design Minimization of Noise in Stiffened Cylinders Due to Tonal External Excitation.Journal of Aircraft,1999,36(3):563-570.
[85]Engelstad S.P.,Cunefare K.A.,Powell E.A.,Et Al.Stiffener Shape Design to Minimize Interior Noise.Journal of Aircraft,2000,37(1):165-171.
[86]Michell A.G.M.The Limits of Economy of Materials in Frame Structures.Philosophical Magazine,1904,8(47):589-597.
[87]Dorn W.,Gomory R.,Greenberg H.Automatic Design of Optimal Structures.J.De.Mechanique,1964,3(1):25-52.
[88]Schmit L.A.Structural Optimization-Some Ideas and insights.New York:Wileg,1984.
[89]Rozvany G.N,Zhou M.The DCOC Algorithm,Part Ⅱ:Topological,Geometrical and Generalized Shape Optimization.Computer Methods in Applied Mechanics and Engineering,1991,89(1-3):309-336.
[90]Bendsoe M.P,Ben-Tal A,Zowe J.Optimization Methods for Truss Geometry and Topology Design.Structural Optimization,1994,7(3):141-159.
[91]Zhang W.H,Domaszewski M.,Bassir H.Developments of Sizing Sensitivity Analysis With ABAQUS Code.International Journal of Structural Optimization,1999,17(2-3):219-225.
[92]Bendsoe M.P.,Kikuchi N.Generating Optimal Topologies in Structure Design Using Homogenization Method.Computer Methods in Applied Mechanics and Engineering 1988,71(2):197-224.
[93]Bendsoe M.P.,Optimization of Structural Topology.Berlin:Springer,1997.
[94]Bendsoe M.P.,Sigmund O.Topology Optimization:Theory,Methods and Applications.New York:Springer,2003.
[95]张东旭.连续体结构拓扑优化及形状优化若干问题.(博士学位论文).大连:大连理工大学,1992.
[96]杨德庆.连续变量化的结构形状及拓扑优化设计理论和方法研究.(博士学位论文).大连:大连理工大学,1998.
[97]王健.具有形状和应力约束的连续体结构拓扑优化及其在框架结构设计中的应用.工程力学,2002,19(4):99-103.
[98]江允正,曲淑英,初明进.连续体结构拓扑优化.计算力学学报,2003,20(2):146-149.
[99]左孔天.连续体结构拓扑优化理论与应用研究.(博士学位论文).武汉:华中科技大学,2004.
[100]王石刚.组合结构优化理论、方法及工程应用研究.(博士学位论文).武汉:华中科技大学,1993.
[101]程耿东,顾元宪,王健.我国机械优化研究与应用的综述和展望.机械强度,1995,17(2):68-74.
[102]隋允康,建模·变换·优化-结构综合方法新进展.大连:大连理工大学出版社,1996.
[103]杨德庆,刘正兴,隋允康.连续体结构拓扑优化设计的ICM方法.上海交通大学学报,1999,33(6):734-736.
[104]隋允康,杨德庆,孙焕纯.统一骨架与连续体的拓扑优化的ICM理论和方法.计算力学学报,2000,17(1):28-33.
[105]隋允康,任旭春,龙连春.基于ICM方法的刚架拓扑优化.计算力学学报,2003,20(2):286-289.
[106]袁振,吴长春.采用非协调元的连续体拓扑优化设计.力学学报,2003,35(1):176-180.
[107]袁振,吴长春,装守兵.基于杂交元和变密度法的连续体结构的拓扑优化.中国科学技术大学学报,2001,31(6):694-699.
[108]Cheng G.D.,Guo X..E-Relaxed Approach in Structural Topology Optimization.Structural Optimization,1997,13:256-266.
[109]Cheng G.D.,Guo X.a Note on Jellyfish-Liked Feasiable Domain in Structural Topology Optimization.Engineering Optimization,1998,31:1-24.
[110]程耿东.关于桁架结构拓扑优化设计中的奇异最优解.大连理工大学学报,2000,40(1):379-383.
[111]Diaz A.R,Sigmund O.Checkerboard Patterns in Layout Optimization.Structural Optimization,1995,10(1):40-45.
[112]Zhou M,Shyy Yk,Thomas H.Checkerboard and Minimum Member Size Control in Topology Optimization.Structural and Multidiseipline Optimization,2001,21(2):152-158.
[113]Bendsoe M.P,Optimization of Structural Topology,Shape and Material.[M].Berlin:Springer-Verlag,1995.
[114]Sigmund O.Numerical instabilities in Topology Optimization:a Survey on Procedures Dealing With Checkerboard,Mesh Dependencies,Local Minima.Structural Optimization,1998,16(1):68-75.
[115]Petersson J,Sigmund O.Slope Constrained Topology Optimization.International Journal for Numerical Methods in Engineering,1998,41(8):1417- 1434.
[116]Zhang W.,Duysinx P.Dual Approach Using a Variant Perimeter Constraint and Efficient Sub-Iteration Scheme for Topology Optimization.Computers & Structures,2003,81(22-23):2173-2181.
[117]Yang X.Y,Xie Y.M,Liu J.S.Perimeter Control in Bi-Directional Evolutionary Optimization Method.Structural and Multidiscipline Optimization,2003,24(6):430-440.
[118]Pedersen N.Topology Optimization of Laminated Plates With Prestress.Computers & Structures,2002,80(7-8):559-570.
[119]郭中泽,陈裕泽,张卫红等.渐进优化法的一种高阶棋盘格式抑制方法.机械设计,2006,23(5):1-4.
[120]Kozukue W.,Hagiwara I.Development of a Topology Optimization Analysis Method for Coupled Structural-Acoustic System and Application to Vehicle Interior Noise Reduction.JSAE Review,1995,16(3):309.
[121]Kozukue W.,Hagiwara I.Topology Optimization Analysis for Reduction of Interior Noise Using a Homogenization Method for a Mean Eigenvalue.The Journal of the Acoustical Society of America,1996,100(4):2746-2753.
[122]Lee J,Wang S,Dikec A.Topology Optimization for the Radiation and Scattering of Sound From Thin-Body Using Genetic Algorithms.Journal of Sound and Vibration,2004,276:899-918.
[123]Wadbro E.,Berggren M.Topology Optimization of an Acoustic Horn.Computer Methods in Applied Mechanics and Engineering,2006,196:420-436.
[124]Yoon G.H,Jensen J.S.,Ole S.Topology Optimization of Acoustic-Structure Interaction Problems Using a Mixed Finite Element Formulation.International Journal for Numerical Methods in Engineering,2007,70:1049-1075.
[125]Du J.B,Oihoff N.Minimization of Sound Radiation From Vibrating Bi-Materiai Structures Using Topology Optimization.Structural Multidisciplinary Optimization,2007,33(4):305-321.
[126]Luo J.H.,Gea H.C.Optimal Stiffener Design for Interior Sound Reduction Using a Topology Optimization Based Approach.Journal of Vibration and Acoustics,2003,125(3):267-273.
[127]Akl W,A El-Sabbagh,Al-Mitani K,Et Al.Topology Optimization of a Plate Coupled With Acoustic Cavity,Solids and Structures,2008,Accepted Manuscript.
[128]Crandall S.H.,Random Vibration vol.Ⅱ.Cambridge,MA:MIT Press,1963.
[129]Crandall S.H.,Random Vibration vol.Ⅰ.Cambridge,MA:MIT Press,1958.
[130]俞载道,曹国敖.随机振动理论及其应用.上海:同济大学出版社,1988.
[131]欧进萍,王光远.结构随机振动.北京:高等教育出版社,1998.
[132]朱位秋.随机振动.北京:科学出版社,1992.
[133]Ibrahim R.A.Parametric Random Vibration:Research Studies Press Ltd,1985.
[134]李国豪.工程结构抗震动力学.上海:上海科学技术出版社,1980.
[135]Lin J.H.A Fast CQC Algorithm of PSD Matrices for Random Seismic Responses,Computers and Structures,1992,44(3):683-687.
[136]Lin J.H.,Zhao Y.,Zhang Y.H.Accurate and Highly Efficient Algorithms for Structural Stationary/Non-stationary Random Responses,Computer Methods in Applied Mechanics and Engineering,2001,191:103-111.
[137]W.S.Zhang J.H.Lin Structural Responses to Arbitrarily Coherent Stationary Random Excitations,Computers and Structures,1994,50(5):629-633.
[138]Lin J.H.,Zhang W.S.,Williams F.W.Pseudo-excitation Algorithm for Non-stationary Random Seismic Responses,Engineering Structures,1994,16(4):270-276.
[139]Lin J.H.,Shen W.P.,Williams F.W.A High Precision Direct Integration Scheme for Non-stationary Random Seismic Responses of Non-classically Damped Structures,Structural Engineering and Mechanics,1995,3(3):215-228.
[140]林家浩,张亚辉.随机振动的虚拟激励法.北京:科学出版社,2004.
[141]汪梦甫.用虚拟激励法求解非比例阻尼线性体系的非平稳随机地震响应,力学季刊,2006,27(4):598-605.
[142]汪梦甫.非比例阻尼线性体系平稳随机地震响应计算的虚拟激励法,计算力学学报,2008,25(1):94-99.
[143]李建俊.随机地震响应分析的虚拟激励法.(博士学位论文).大连:大连理工大学,1994.
[144]张亚辉.复杂结构在多种荷载工况下的屈曲及动力分析.(博士学位论文).大连:大连理工大学,1999.
[145]孙东科.长跨桥梁三维风振分析.(博士学位论文).大连:大连理工大学,1999.
[146]赵岩.桥梁抗震的线性/非线性分析方法研究.(博士学位论文).大连:大连理工大学,2003.
[147]戴新进.复合材料结构随机振动的虚拟激励法及在航空航天领域的应用.(博士学位论文).大连:大连理工大学.2007.
[148]Allen M.J.,Vlahopoulos N.integration of Finite Element and Boundary Element Methods for Calculating the Radiated Sound From a Randomly Excited Structure.Computers and Structures,2000,77:155-169.
[149]Allen M.J.,Sbragio R.,Vlahopoulos N.Structural/Acoustic Sensitivity Analysis of a Structure Subjected to Stochastic Excitation.AIAA Journal,2001,39(7):1270-1279.
[150]童卫华,姜节胜,顾松年.某型导弹振动实验夹具的动力学优化,应用力学学报,1996,13(SI):111-114.
[151]Tong W.H,Jiang J.S,Liu G.R.Dynamic Design of Structures under Random Excitation.Computational Mechanics,1998,22(5):388-394.
[152]杨振兴,荣见华,傅建林.窄带随机激励下的结构动力学拓扑优化设计.振动与冲击,2008,24(6):85-87.
[153]Lambert S,Pagnacco E,Khalij L,Et AI.Topology Optimization of Structures Subject to Random Excitations With Fatigue Life Constraints.European Conference on Computational Mechanics Solids,Structures and Coupled Problems in Engineering,2006,5-8 June:487.
[154]Gu Y.X,Zhang H.W,Guan Z.Q.New Generation Software of Structural Analysis and Design Optimization-JIFEX.Structural Engineering and Mechanics,1999,7(6):589-599.
[155]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.
[156]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.
[157]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.
[158]Craggs A.A Finite Element Method for Free Vibration of Air in Duets and Rooms With Absorbing Walls.Journal of Sound and Vibration,1994,173(4):568-576.
[159]Craggs A.The Free Vibration of Systems With Proportional Or Light Damping.Journal of Sound and Vibration,1994,170(1):130-139.
[160]Easwaran V.,Craggs A.On Further Validation and Use of the Finite Element Method to Room Acoustics.Journal of Sound and Vibration,1995,187(2):195-212.
[161]赵越喆,吴硕贤.小阻尼界面房间声传输函数和声脉冲响应函数的有限元素法.应用声学,2000,19(2):24-30.
[162]许肖梅.声学基础.北京:科学出版社,2003.
[163]Gu Y.X.,Cheng G.D.Structural Modelling and Sensitivity Analysis of Shape Optimization.Structural Optimization,1993,6(1):29-37.
[164]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方法.江汉石油学院学报,1994,16(4):83-89.
[165]顾元宪,程耿东.结构形状优化设计数值方法的研究和应用.计算结构力学及其应用,1993,10(3):321-335.
[166]程耿东.工程结构优化设计基础.北京:水利电力出版社,1984.
[167]Gu Y.X.,Zhang H.W.,Guan Z.Q.New Generation Software of Structural Analysis and Design Optimization-JIFEX,Structural Engineering and Mechanics,1999,7(6):589-599.
[168]Fletcher g.Practical Methods of Optimization.[M].John Wiley & Sons,1980.
[169]Everstine G.C.A Symmetric Potential Formulation for Fluid-Structure Interaction.Journal of Sound and Vibration,1981,79(3):157-160.
[170]Ohayon R.Transient and Modal Analysis of Bounded Medium Fluid Structure Problems.Proceedings of An International Conference,1984,Venice,Nova Sciences Pub inc.
[171]Sandberg G.,Goransson P.A Symmetric Finite Element Formulation for Acoustic Fluid Structure Interaction Analysis.Journal of Sound and Vibration,1988,123(3):507-515.
[172]丁渭平.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,2000,34:58-62.
[173]钟万勰,林家浩.不对称实矩阵的本征对共轭子空间迭代算法.计算结构力学及其应用.1990,7(4):1-10.
[174]Shepard R.,Minkoff M.,Zhou Y.K.Software for Computing Eigenvalue Bounds for Iterative Subspace Matrix Methods.Computer Physics Communications,2005,170:109-114.
[175]Najafi H.S.,Khaleghi E.A New Restarting Method in the Arnoldi Algorithm for Computing the Eigenvalues of a Nonsymmetric Matrix.Applied Mathematics and Computation,2004,156:59-71.
[176]Najafi H.S.,Moosaei H.A New Restarting Method in the Harmonic Projection Algorithm for Computing the Eigenvalues of a Nonsymmetric Matrix.Applied Mathematics and Computation,2008,198:143-149.
[177]Ghazia A.E.,Hajjia S.E.,Giraud L.,Et Al.Newton's Method for the Common Eigenvector Problem.Journal of Computational and Applied Mathematics,2007:Doi:10.1016/J.Cam.2007.11.009.
[178]Najafi H.S.,Ghazvini H.A Modification on Minimum Restarting Method in the Arnoldi Algorithm for Computing the Eigenvalues of a Nonsymmetric Matrix.Applied Mathematics and Computation,2006,181:1455-1461.
[179]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.
[180]林家浩,曲乃泗,孙焕纯.计算结构动力学.北京:高等教育出版社,1989.
[181]Ewins D.J.Estimation of Resonant Peak Amplitudes.Journal of Sound and Vibration,1975,43:595-605.
[182]Ma Z.D.,Hagiwara Ⅰ.Sensitivity Analysis Methods for Coupled Acoustic-Structural System Part Ⅱ:Direct Frequency Response and Its Sensitivities,AIAA Journal,1991,29(11):1796-1801.
[183]Nalecz A.G,Wither J.Design Sensitivity Analysis of Mechanical System in Frequency Domain.Journal of Sound and Vibration,1988,120(2):517-526.
[184]Ting T,Chen T.L.C,Twomey W.J.Finite Element Model Refinement with Actual forced Response of Structures.Finite Elements in Analysis and Design,1992,11(3):213-220.
[185]Livne E,Blando G.D.Structural Dynamic Frequency Response Using Combined Direct and Adjoint Reduced-Order Approximations.AIAA Journal,2003,41(7):1377-1385.
[186]董绍强,廖道训,陆永忠.结构频率响应灵敏度计算及响应修改研究.华中科技大学学报,2001,29(10):56-58.
[187]王秀峰,陈心昭.随机振动结构声辐射的统计边界点法分析.声学技术,2001,20(3):107-110.
[188]刘钊,陈心昭.求解随机振动结构声辐射的统计边界元方法.声学学报,1997,22(6):495-500.
[189]纪刚,张纬康,周其斗.随机力作用下的水下结构物声辐射分析.中国造船,2004,12:182-188.
[190]张军.声学.结构灵敏度及结构.声学优化设计研究.(博士学位论文).大连:大连交通大学,2006.
[191]林家浩,钟万勰.关于虚拟激励法与结构随机响应的注记.计算力学学报,1998,15(2):217-223.
[192]林家浩,易平.线性随机结构的平稳随机响应.计算力学学报,2001,18(4):402-408.
[193]Elishak I,Lin Y K,Zhu L P.Probabilistic and Convex Modeling of Acoustically Excited Structures.Elsevier,Amsterdam,1994.
[194]Simiu E,Scanlan R.H.Wing Effects on Structures:An introduction to Wind Engineering.John Wiley & Sons,New York,1978.
[195]Clough R.W,Penzien J.Dynamics of Structures.Mcgraw-Hill Book Company,1975.
[196]Bendat J.S,Piersol A.G.Random Data:Analysis and Measurement Procedures.New York Wiley,2000.
[197]Socha L.The Sensitivity Analysis of Stochastic Non-Linear Dynamic Systems.Journal of Sound and Vibration,1986,110:271-296.
[198]Szopa J.Sensitivity of Stochastic Systems to initial Conditions.Journal of Sound and Vibration,1984,97:645-649.
[199]Benfratelio S,Caddemi S,Muscolino G.Gaussian and Non-Gaussian Stochastic Sensitivity Analysis of Discrete Structural System.Computers & Structures,2000,78:425-434.
[200]Bhattaeharyya B,Chakraborty S.Stochastic Dynamic Sensitivity of Uncertain Structures Subjected to Random Earthquake Loading.Journal of Sound and Vibration,2002,249(3):543-556.
[201]Caceiola P,Colajanni P,Muscolino G.A Modal Approach for the Evaluation of the Response Sensitivity of Structural Systems Subjected to Non-Stationary Random Processes.Computer Methods in Applied Mechanics and Engineering,2005,194:4344-4361.
[202]姚昌仁,麻永平.结构随机激励的响应灵敏度分析.力学学报,1990,22(4):438-445.
[203]童卫华,姜节胜,顾松年.一种以均方响应作为约束的动力学设计方法.应用力学学报,1996,13(3):94-98.
[204]童卫华,姜节胜.结构在随机激励下的一种动力学设计方法.机械强度,1996,18(2):6-10.
[205]乔红威,吕震宙.随机结构随机激励下的响应灵敏度分析.振动与冲击,2008,27(3):60-62.
[206]陈建兵,李杰.结构随机动力非线性反应的整体灵敏度分析.计算力学学报,2008,25(2):169-176.
[207]李晓峰,张军,兆文忠等.随机激励结构.声场耦合振动声学数值仿真研究.系统仿真学报,2007,19(8):1683-1685.
[208]Fox R.L,Kapoor M.D.Rates of Change of Eigenvalues and Eigenvectors.AIAA Journal,1968,6(12):2426-2429.
[209]Nelson K.B.Simplified Calculation of Eigenvector Derivative.AIAA Journal,1976,14(9):1201-1205.
[210]Wang B.P.Improved Approximate Methods for Computing of Eigenvector Derivative in Structural Dynamics.AIAA Journal,1991,29(6):1018-1020.
[211]Rozvany G.I.N.,Kirsch U.,Bendsoe M.P.,Sigmund O.Layout optimization of structures.Apply Mechanics Review,1995,48:41-119.
[212]Rietz A.sufficiency of a Finite Exponent in SIMP(Power Law) Method.Structural and Multidiseipline Optimization,2001,21:159-163.
[213]Stolpe M.,Svanberg K.An Alternative Interpolation Scheme for Minimum Compliance Topology Optimization.Structural and Multidiscipline Optimization,2001,22:116-124
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |