基于面板声学贡献度的封闭空腔结构内声场分析的若干关键问题研究
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摘要
弹性封闭空腔结构在动态载荷激励下产生振动进而形成的空间复杂声场是工程实际中最具代表性的一类声场，如汽车、船舶和飞机的舱内声场。对该类声场的研究一直以来都是振动与噪声控制领域的一个重要研究方向，实现对这类封闭空腔结构内部声场的声学响应预测和分析，具有重要的理论研究意义和广阔的工程应用前景。
根据传递路径分析方法的原理，系统响应可认为是外界激励通过多种不同路径传递到响应点的能量贡献叠加。因此通过识别外界激励载荷和计算结构振动声辐射来解决复杂封闭空腔结构的振动噪声分析与控制问题。
本文以封闭空腔结构受激所形成的内部复杂声场为研究对象，用结构部件的面板声学贡献度代替先前的传递路径贡献量，以预测和控制封闭结构声腔内的声学响应为目标，深入研究结构外界激励载荷的识别和复杂封闭空腔内部声场响应计算两个关键问题。在激励载荷的识别方面，提出了具有一般意义的结构动态载荷时域识别方法，提高了载荷识别的精度和稳定性。在振动声辐射计算求解方面，提出了用于计算复杂封闭结构振动形成的内部空间声场的等效声传递向量法，避免了边界元法的固有缺点，计算效率更高。在封闭空腔结构内声场预测和声学优化方面，提出了一种基于等效源法的内部近场声全息的面板声学贡献度计算方法，该方法可在重建封闭空腔结构内声场的同时，有效识别出各振动板件对封闭声场的声学贡献度。完成的主要研究工作和成果如下：
（1）阐述了封闭空腔结构内部声场分析的研究意义，详细回顾了动态载荷识别方法和封闭空腔结构内部声场计算的研究现状和进展，分析了其中仍然存在的一些值得研究的问题，并以此为基础，确定了本论文所要研究的主要内容。
（2）针对响应中带有噪音时载荷识别的困难，提出了联合奇异熵去噪修正和正则化预优的共轭梯度迭代识别方法。系统的振动响应表示为单位脉冲响应函数与激励载荷的卷积，并离散化一组线性方程组，将载荷识别问题即转化为求解线性方程组的反问题。一方面对含噪信号进行基于奇异熵的去噪处理，提高反问题求解中输入数据的精度。另一方面利用正则化方法对共轭梯度迭代算法进行预优，改善反问题的非适定性。由于从输入的响应数据去噪和正则化算法两方面同时改善动态载荷识别反问题的求解，因此可以有效地抑制噪声，提高识别精度。通过数值算例分析，表明在不同的噪声水平干扰下，其识别精度均优于常规的正则化方法，能够实现有效稳定地识别动态载荷。最后通过实验研究进一步验证了该方法的正确性和有效性。
（3）对封闭空腔结构内声场分析计算问题的数值求解方法进行了详细的论述，推导了求解Helmholtz方程的声学有限元法和声学边界元方法的理论公式，并分析了这两种数值计算方法在实际应用中的不足之处。
（4）推导了基于边界元法的声传递向量的计算公式。提出了用于分析复杂封闭空腔结构内声场的等效声传递向量法，导出了等效声传递向量和面板声学贡献度的理论公式，研究了等效声传递向量法的数值计算误差影响因素。该方法避免了边界元法中复杂的数值计算和奇异积分的处理过程，简化了计算过程，有利于向工程实际推广。分别以三个不同形状结构形成的声腔模型为例进行声场分析，仿真实验结果证明了该方法的正确性和有效性。
（5）基于等效源法的内部声全息技术，提出了一种复杂封闭空腔结构内声场的面板声学贡献度识别方法。首先重构出振动结构表面的法向振速，实现对整个内部封闭声场的预测，再将振动结构的每个面板在腔体内部场点产生的声压分别用位于空腔表面附近的等效源在该点产生的辐射声压代替，将复杂的封闭非自由声场问题转化为简单的内部自由场问题，结合重建出的结构表面法向振速进而识别出封闭振动结构各面板对腔体内任意位置的声学贡献度。研究了等效源的数量及与重建面距离等参数对重建精度的影响，通过复杂结构内声场的数值仿真和实验研究的结果验证了所提方法的正确性和有效性。
（6）总结本文的主要研究成果，指出了需要进一步研究和解决的问题。
The interior sound field in enclosure such as the cabins of automobiles, ships and airplanes, which is induced by the vibrations due to the external excitation, is the most representative in engineering. The research of this kind of sound field has always been an important aspect of noise and vibration control domains. It has important theory significance and wide engineering application prospects to predict and analyze the acoustic response of the interior sound field in enclosure.
According to the principle of transfer path analysis method, the response of the system can be considered as a sum of path contributions that generated by the external excitation through multiple transfer paths. Therefore, for the interior sound field in complex enclosure, identifying the external exciting load and calculating acoustic radiation of structural vibration can be applied to solve the problem of vibration and noise analysis.
In this dissertation, the research is focused on complex enclosure and the interior sound field caused by its vibration, which is regarded as a source-path-receiver system. Based on this model, the transfer path contribution is replaced by the panel acoustic contribution of individual structural component. Aiming at prediction and control the acoustic response of the interior sound field in cavity, the identification method of external dynamic load and calculating method of the interior sound field, the two key problems, have been studied in depth to help one judge whether it is a problem of excitation source or the system itself. In order to obtain the strength of external loads, a general method for dynamic force identification in time domain is proposed, which can be used to improve accuracy and stability of load identification. For the analysis of interior sound field in irregular enclosure, a new method called equivalent acoustic transfer vector is developed, which can avoid the shortcomings of BEM and has higher computational efficiency. For obtaining panel acoustic contribution, by using interior nearfield acoustic holography based on equivalent source method, an identification approach of panel acoustic contribution is presented. This method can be applied to realize reconstruction of the interior sound field in enclosure and identification of the acoustic contribution of each panel to any position in the interior sound field. The detailed research contents of this dissertation are summarized as follows:
(1) The research significance of the analysis of interior sound field in enclosure has been explicated, and the research state and development of identification of dynamic load and calculation of acoustic radiation of the vibrating structure have been reviewed. Then the problems of the above methods have been analyzed. Finally, the main research contents in this dissertation have been determined based on the literature review.
(2) To smooth out the difficulties of the load identification in the presence of noises, a dynamic load identification method is proposed based on the combination of the singular entropy denoising and the regularization-preconditioned conjugate gradient iteration method. The response of the linear system can be obtained by the convolution integral of the unit pulse response function and dynamic loads. Hence, by discretizing the convolution integral into a set of linear algebraic equations, the load identification problem can be transformed into an inverse problem of solution of linear algebraic equations. In order to improve the accuracy of input data in the process of load identification, the singular entropy denoising method is introduced in the noisy response signal. Furthermore, the conjugate gradient iterative algorithm is preconditioned by Tikhonov regularization method to alleviate the ill-posedness of the inverse problem. Since the solution of load identification inverse problem is improved at two respects: the input response data denoising and regularization algorithm, the proposed method can effectively suppress noise and improve the identification accuracy. The numerical simulation result for a given example indicates that the proposed methods are more accurately and stably in the identification of dynamic loads with the interference of different noise levels, compared with the conventional regularization methods. Finally the validity and the effectiveness of the proposed methods are verified by the experiment.
(3) The numerical methods for computating the interior sound field in enclosure have been discussed in detail. The theoretical formulas of acoustic finite element method and boundary element method for solving the Helmholtz equation have been derived, and the shortcomings of these two numerical methods in practical application are analyzed.
(4) The theoretical formulas for solving acoustic transfer vector based on boundary element method are deduced. Based on these, a method called equivalent acoustic transfer vector for the analysis of sound field in irregular enclosure is developed. The calculation formulas of the equivalent acoustic transfer vector and panel acoustic contribution are deduced. Compared with boundary element method, complicated numerical calculation and the singular integrals are avoided in the proposed method, and the calculation process is simplified. Three simulations are conducted by taking different shaped enclosures for example and the results show that the proposed method is correct and effective.
(5) By using interior nearfield acoustic holography based on equivalent source method, an identification approach of panel acoustic contribution is presented. The normal velocities on the surface of vibrating structure have been reconstructed and the interior sound field in enclosure has been predicted. Then the sound pressure produced by each panel at the interested field point is respectively replaced by the radiated pressure of the interior sound field which is formed by the equivalent virtual sources located near the enclosure surface. Combining with the reconstructed normal surface velocities, the acoustic contribution of each panel to any position in enclosure can be obtained by transforming the complex enclosed non-free field into the simple interior free field. The influences of the number of the equivalent sources and the distance between them and the reconstructed surface have been investigated. The numerical simulation and the experiment are used to demonstrate the correctness and validity of this method.
(6) Researches in this dissertation have been summarized, and the topics for further study have been proposed.
根据传递路径分析方法的原理，系统响应可认为是外界激励通过多种不同路径传递到响应点的能量贡献叠加。因此通过识别外界激励载荷和计算结构振动声辐射来解决复杂封闭空腔结构的振动噪声分析与控制问题。
本文以封闭空腔结构受激所形成的内部复杂声场为研究对象，用结构部件的面板声学贡献度代替先前的传递路径贡献量，以预测和控制封闭结构声腔内的声学响应为目标，深入研究结构外界激励载荷的识别和复杂封闭空腔内部声场响应计算两个关键问题。在激励载荷的识别方面，提出了具有一般意义的结构动态载荷时域识别方法，提高了载荷识别的精度和稳定性。在振动声辐射计算求解方面，提出了用于计算复杂封闭结构振动形成的内部空间声场的等效声传递向量法，避免了边界元法的固有缺点，计算效率更高。在封闭空腔结构内声场预测和声学优化方面，提出了一种基于等效源法的内部近场声全息的面板声学贡献度计算方法，该方法可在重建封闭空腔结构内声场的同时，有效识别出各振动板件对封闭声场的声学贡献度。完成的主要研究工作和成果如下：
（1）阐述了封闭空腔结构内部声场分析的研究意义，详细回顾了动态载荷识别方法和封闭空腔结构内部声场计算的研究现状和进展，分析了其中仍然存在的一些值得研究的问题，并以此为基础，确定了本论文所要研究的主要内容。
（2）针对响应中带有噪音时载荷识别的困难，提出了联合奇异熵去噪修正和正则化预优的共轭梯度迭代识别方法。系统的振动响应表示为单位脉冲响应函数与激励载荷的卷积，并离散化一组线性方程组，将载荷识别问题即转化为求解线性方程组的反问题。一方面对含噪信号进行基于奇异熵的去噪处理，提高反问题求解中输入数据的精度。另一方面利用正则化方法对共轭梯度迭代算法进行预优，改善反问题的非适定性。由于从输入的响应数据去噪和正则化算法两方面同时改善动态载荷识别反问题的求解，因此可以有效地抑制噪声，提高识别精度。通过数值算例分析，表明在不同的噪声水平干扰下，其识别精度均优于常规的正则化方法，能够实现有效稳定地识别动态载荷。最后通过实验研究进一步验证了该方法的正确性和有效性。
（3）对封闭空腔结构内声场分析计算问题的数值求解方法进行了详细的论述，推导了求解Helmholtz方程的声学有限元法和声学边界元方法的理论公式，并分析了这两种数值计算方法在实际应用中的不足之处。
（4）推导了基于边界元法的声传递向量的计算公式。提出了用于分析复杂封闭空腔结构内声场的等效声传递向量法，导出了等效声传递向量和面板声学贡献度的理论公式，研究了等效声传递向量法的数值计算误差影响因素。该方法避免了边界元法中复杂的数值计算和奇异积分的处理过程，简化了计算过程，有利于向工程实际推广。分别以三个不同形状结构形成的声腔模型为例进行声场分析，仿真实验结果证明了该方法的正确性和有效性。
（5）基于等效源法的内部声全息技术，提出了一种复杂封闭空腔结构内声场的面板声学贡献度识别方法。首先重构出振动结构表面的法向振速，实现对整个内部封闭声场的预测，再将振动结构的每个面板在腔体内部场点产生的声压分别用位于空腔表面附近的等效源在该点产生的辐射声压代替，将复杂的封闭非自由声场问题转化为简单的内部自由场问题，结合重建出的结构表面法向振速进而识别出封闭振动结构各面板对腔体内任意位置的声学贡献度。研究了等效源的数量及与重建面距离等参数对重建精度的影响，通过复杂结构内声场的数值仿真和实验研究的结果验证了所提方法的正确性和有效性。
（6）总结本文的主要研究成果，指出了需要进一步研究和解决的问题。
The interior sound field in enclosure such as the cabins of automobiles, ships and airplanes, which is induced by the vibrations due to the external excitation, is the most representative in engineering. The research of this kind of sound field has always been an important aspect of noise and vibration control domains. It has important theory significance and wide engineering application prospects to predict and analyze the acoustic response of the interior sound field in enclosure.
According to the principle of transfer path analysis method, the response of the system can be considered as a sum of path contributions that generated by the external excitation through multiple transfer paths. Therefore, for the interior sound field in complex enclosure, identifying the external exciting load and calculating acoustic radiation of structural vibration can be applied to solve the problem of vibration and noise analysis.
In this dissertation, the research is focused on complex enclosure and the interior sound field caused by its vibration, which is regarded as a source-path-receiver system. Based on this model, the transfer path contribution is replaced by the panel acoustic contribution of individual structural component. Aiming at prediction and control the acoustic response of the interior sound field in cavity, the identification method of external dynamic load and calculating method of the interior sound field, the two key problems, have been studied in depth to help one judge whether it is a problem of excitation source or the system itself. In order to obtain the strength of external loads, a general method for dynamic force identification in time domain is proposed, which can be used to improve accuracy and stability of load identification. For the analysis of interior sound field in irregular enclosure, a new method called equivalent acoustic transfer vector is developed, which can avoid the shortcomings of BEM and has higher computational efficiency. For obtaining panel acoustic contribution, by using interior nearfield acoustic holography based on equivalent source method, an identification approach of panel acoustic contribution is presented. This method can be applied to realize reconstruction of the interior sound field in enclosure and identification of the acoustic contribution of each panel to any position in the interior sound field. The detailed research contents of this dissertation are summarized as follows:
(1) The research significance of the analysis of interior sound field in enclosure has been explicated, and the research state and development of identification of dynamic load and calculation of acoustic radiation of the vibrating structure have been reviewed. Then the problems of the above methods have been analyzed. Finally, the main research contents in this dissertation have been determined based on the literature review.
(2) To smooth out the difficulties of the load identification in the presence of noises, a dynamic load identification method is proposed based on the combination of the singular entropy denoising and the regularization-preconditioned conjugate gradient iteration method. The response of the linear system can be obtained by the convolution integral of the unit pulse response function and dynamic loads. Hence, by discretizing the convolution integral into a set of linear algebraic equations, the load identification problem can be transformed into an inverse problem of solution of linear algebraic equations. In order to improve the accuracy of input data in the process of load identification, the singular entropy denoising method is introduced in the noisy response signal. Furthermore, the conjugate gradient iterative algorithm is preconditioned by Tikhonov regularization method to alleviate the ill-posedness of the inverse problem. Since the solution of load identification inverse problem is improved at two respects: the input response data denoising and regularization algorithm, the proposed method can effectively suppress noise and improve the identification accuracy. The numerical simulation result for a given example indicates that the proposed methods are more accurately and stably in the identification of dynamic loads with the interference of different noise levels, compared with the conventional regularization methods. Finally the validity and the effectiveness of the proposed methods are verified by the experiment.
(3) The numerical methods for computating the interior sound field in enclosure have been discussed in detail. The theoretical formulas of acoustic finite element method and boundary element method for solving the Helmholtz equation have been derived, and the shortcomings of these two numerical methods in practical application are analyzed.
(4) The theoretical formulas for solving acoustic transfer vector based on boundary element method are deduced. Based on these, a method called equivalent acoustic transfer vector for the analysis of sound field in irregular enclosure is developed. The calculation formulas of the equivalent acoustic transfer vector and panel acoustic contribution are deduced. Compared with boundary element method, complicated numerical calculation and the singular integrals are avoided in the proposed method, and the calculation process is simplified. Three simulations are conducted by taking different shaped enclosures for example and the results show that the proposed method is correct and effective.
(5) By using interior nearfield acoustic holography based on equivalent source method, an identification approach of panel acoustic contribution is presented. The normal velocities on the surface of vibrating structure have been reconstructed and the interior sound field in enclosure has been predicted. Then the sound pressure produced by each panel at the interested field point is respectively replaced by the radiated pressure of the interior sound field which is formed by the equivalent virtual sources located near the enclosure surface. Combining with the reconstructed normal surface velocities, the acoustic contribution of each panel to any position in enclosure can be obtained by transforming the complex enclosed non-free field into the simple interior free field. The influences of the number of the equivalent sources and the distance between them and the reconstructed surface have been investigated. The numerical simulation and the experiment are used to demonstrate the correctness and validity of this method.
(6) Researches in this dissertation have been summarized, and the topics for further study have been proposed.
引文
[1]黄其柏．工程噪声控制学[M]．武汉：华中科技大学出版社，1999．
[2]马大猷．现代声学基础[M]．北京：科学出版社，2003．
[3]应怀樵．现代振动与噪声技术(第2卷)[M]．北京：航空工业出版社，2000．
[4]周新祥．噪声控制技术及其新进展[M]．北京：冶金工业出版社，2007．
[5]何祚镛，赵玉芳．声学理论基础[M]．北京：国防工业出版社，1981．
[6]袁昌明，方云中，华伟进．噪声与振动控制技术[M]．北京：冶金工业出版社，2007．
[7]王伯良．噪声控制理论[M]．武汉：华中理工大学出版社，1990．
[8]靳晓雄，胡子谷．工程机械噪声控制学[M]．上海：同济大学出版社，1997．
[9]何祚镛．结构振动与声辐射[M]．哈尔滨：哈尔滨工程大学出版社，2001．
[10]庞剑，谌刚，何华．汽车噪声与振动—理论与应用[M]．北京：北京理工大学出版社，2006．
[11] Plunt J. Finding and fixing vehicle NVH problems with transfer path analysis [J]. Soundand vibration,2005,39(11):12-17.
[12] De Klerk D., Ossipov A. Operational transfer path analysis: Theory, guidelines and tirenoise application [J]. Mechanical Systems and Signal Processing,2010,24(7):1950-1962.
[13] Janssens K., Gajdatsy P., Gielen L., et al. OPAX: A new transfer path analysis methodbased on parametric load models [J]. Mechanical Systems and Signal Processing,2011,25(4):1321-1338.
[14] Genuit K., Poggenburg J. The design of vehicle interior noise using binaural transferpath analysis [C]. SAE Paper,1999-01-1808.
[15] Unruh J.F., Till P.D., Farwell T.J. Interior noise source/path identification technology[C]. SAE Paper,2000-01-1709.
[16] Kim S.J., Yang H.I., Lee S.K. Prediction of interior noise based on hybrid TPA [C]. SAEInternational Journal of Passenger Cars-Mechanical Systems,2009,2(1):1440-1448.
[17]郝鹏，郑四发，连小珉．运动噪声源的时域传递路径模型及贡献率分析[J]．机械工程学报，2012，48(8)：104-109．
[18] Fabunmi J.A. Effects of structural modes on vibratory force determination by the pseudoinverse technique [J]. AIAA journal,1986,24(3):504-509.
[19] Liu Y., Shepard W.S. Dynamic force identification based on enhanced least squares andtotal least-squares schemes in the frequency domain [J]. Journal of sound and vibration,2005,282(1):37-60.
[20] Parloo E., Verboven P., Guillaume P., et al. Force identification by means of in-operationmodal models [J]. Journal of Sound and Vibration,2003,262(1):161-173.
[21] Law S.S., Chan T.H.T., Zeng Q.H. Moving force identification: a time domain method[J]. Journal of Sound and Vibration,1997,201(1):1-22.
[22] Lin J.H., Guo X.L., Zhi H., et al. Computer simulation of structural random loadingidentification [J]. Computers&Structures,2001,79(4):375-387.
[23] Bartlett F.D., Flannelly W.G. Model verification of force determination for measuringvibratory loads [J]. Journal of the American Helicopter Society,1979,24(2):10-18.
[24] Starkey J.M., Merrill G.L. On the ill-conditioned nature of indirect force-measurementtechniques [J]. Journal of Modal Analysis,1989,4(3):103-108.
[25] Hansen M., Starkey J.M. On predicting and improving the condition ofmodal-model-based indirect force measurement algorithms [J]. Proceedings of the8thIMAC, Kissimmee, FL, USA,1990:115-120.
[26]刘恒春，朱德懋，孙久厚．振动载荷识别的奇异值分解法[J]．振动工程学报，1990，3(1)：24-32．
[27] Karlsson S.E.S. Identification of external structural loads from measured harmonicresponses [J]. Journal of sound and vibration,1996,196(1):59-74.
[28] O'Callahan J., Piergentili F. Force estimation using operational data [J]. Proceedings ofthe14th International Modal Analysis Conference,1996:1586-1592.
[29]顾慧芝，聂君剑．载荷识别的等效点动标定法[J]．振动工程学报，1997，10(3)：329-334．
[30]林家浩，智浩，郭杏林．平稳随机振动荷载识别的逆虚拟激励法(一)[J]．计算力学学报，1998，15(2)：127-136．
[31]智浩，郭杏林，林家浩．平稳随机振动荷载识别的逆虚拟激励法(二)[J]．计算力学学报，1998，15(4)：385-400．
[32]文祥荣，缪龙秀．由实测应变响应识别结构动态载荷[J]．铁道学报，2000，22(6)：36-39．
[33]智浩，文祥荣，缪龙秀，等．动态载荷的频域识别方法[J]．北方交通大学学报，2000，24(4)：5-10．
[34]田燕，王菁，郑海起．多载荷识别频响函数矩阵求逆法的改进算法[J]．军械工程学院学报，2002，14(4)：13-17．
[35]许锋，陈怀海，鲍明．动载荷识别的广义域模态模型及其精度分析研究[J]．计算力学学报，2003，20(2)：218-222．
[36]李东升，郭杏林．逆虚拟激励法随机载荷识别试验研究[J]．工程力学，2004，21(2)：134-139．
[37] Thite A.N., Thompson D.J. Selection of response measurement locations to improveinverse force determination [J]. Applied Acoustics,2006,67(8):797-818.
[38]姜金辉，陈国平，张方．多点平稳随机载荷识别方法研究[J]．振动工程学报，2009，22(2)：162-167．
[39]周林，郑四发，王彬星，等．动态载荷识别位置优化的传递函数相干法[J]．振动工程学报，2011，24(1)：14-19．
[40]许锋，陈怀海，鲍明．机械振动载荷识别研究的现状与未来[J]．中国机械工程，2002，13(6)：526-531．
[41] Desanghere G., Snoeys R. Indirect identification of excitation forces by modalcoordinate transformation [J]. Proceedings of the3rd IMAC.1985,3:685-690.
[42] Ory H., Glaser H., Holzdeppe D. The reconstruction of forcing function based onaeroelasticity and structural dynamics [J]. Proceedings of2nd Int. Symp. OnAeroelasticity and Structural Dynamics, Flaschen, FRG,1985:164-168.
[43] Ory H., Glaser H., Holzdeppe D. Quality of modal analysis and reconstruction of forcingfunction based on measured output data [J]. Proceedings of4th IMAC, New York, USA,1986:350-357.
[44]唐秀近．动态力识别的时域方法[J]．大连理工大学学报，1987，26(4)：21-27．
[45]唐秀近．时域识别动态载荷的精度问题[J]．大连理工大学学报，1990，30(1)：31-37．
[46]初良成，曲乃泗．动态载荷识别的时域正演方法[J]．应用力学学报，1994，11(2)：9-18．
[47]时战，许士斌，初良成，等．利用脉冲响应函数识别载荷的时序法[J]．振动工程学报，1995，8(3)：235-242．
[48]徐倩，文祥荣，孙守光．结构动态载荷识别的精细逐步积分法[J]．计算力学学报，2002，19(1)：53-57．
[49]张运良，林皋，王永学，等．一种改进的动态载荷时域识别方法[J]．计算力学学报，2004，21(2)：209-215．
[50]赵凤遥，张运良，马震岳．动载荷的时域识别方法及其应用[J]．水电能源科学，2005，23(1)：8-11．
[51]蔡元奇，朱以文．基于逆向滤波器的动态载荷时域识别方法[J]．振动工程学报，2006，19(2)：200-205．
[52]瞿伟廉，王锦文．振动结构动态荷载识别综述[J]．华中科技大学学报(城市科学版)，2004，21(4)：1-4．
[53] Kreitinger T.J., Wang M.L., Schreyer H.L. Non-parametric force identification fromstructural response [J]. Soil Dynamics and Earthquake Engineering,1992,11(5):269-277.
[54]路敦勇，吴淼．动态载荷识别的SWAT方法研究[J]．振动与冲击，1999，18(4)：78-81．
[55]张方，朱德懋．动态载荷时域识别的级数方法[J]．振动工程学报，1996，9(1)：1-8．
[56]袁向荣，卜建清，满红高，等．移动荷载识别的函数逼近法[J]．振动与冲击，2000，19(1)：58-70．
[57]陈锋，袁向荣，李明．移动载荷识别的B-样条函数逼近法[J]．石家庄铁道学院学报，2003，16(1)：11-14．
[58]王彦卫，赵玫．一种新的动态载荷识别方法[J]．噪声与振动控制，2003，3：11-13．
[59]袁向荣．梁振动响应曲线滑动拟合法及在移动荷载识别中的应用[J]．噪声与振动控制，2006，26(3)：42-43．
[60]姜增国，孙艳茹．三次样条函数在桥梁移动荷载识别中的应用[J]．振动与冲击，2006，25(6)：124-126．
[61]孙国，郭杏林．基于线性多点逼近的载荷识别方法[J]．计算力学学报，2011，28(B04)：176-181．
[62] Liang Y.C., Zhou C.G., Wang Z.S. Identification of restoring forces in non-linearvibration systems based on neural networks [J]. Journal of sound and vibration,1997,206(1):103-108.
[63]高宝成，张征．基于神经网络的结构荷载识别研究[J]．振动、测试与诊断，1996，16(1)：14-19．
[64]张方，朱德懋．基于神经网络模型的动载荷识别[J]．振动工程学报，1997，10(2)：156-162．
[65]吴大宏，赵人达．基于神经网络的混凝土桥梁荷载识别方法研究[J]．中国铁道科学，2002，23(1)：25-28．
[66]窦春红，林近山，寇兴磊．基于BP神经网络的海洋平台振动载荷识别[J]．石油矿场机械，2007，36(7)：11-15．
[67] Inoue H., Kishimoto K., Shibuya T., et al. Estimation of Impact Load by InverseAnalysis: Optimal Transfer Function for Inverse Analysis [J]. JSME internationaljournal. Ser.1, Solid mechanics, strength of materials,1992,35(4):420-427.
[68]魏星原，宋斌．载荷识别的逆系统方法[J]．振动、测试与诊断，1995，15(3)：35-43．
[69]饶柱石，施勤忠．基于逆系统分析法的多输入—多输出系统动态载荷的优化估计[J]．振动与冲击，2000，19(2)：9-12．
[70]王慧儒，谢晓竹，吴淼．基于逆传系统法的动态载荷识别研究[J]．装甲兵工程学院学报，2005，19(3)：79-82．
[71] Inoue H., Kishimoto K., Shibuya T. Experimental wavelet analysis of flexural waves inbeams [J]. Experimental Mechanics,1996,36(3):212-217.
[72] Doyle J.F. A wavelet deconvolution method for impact force identification [J].Experimental mechanics,1997,37(4):403-408.
[73] Gaul L., Hurlebaus S. Identification of the impact location on a plate using wavelets [J].Mechanical Systems and Signal Processing,1998,12(6):783-795.
[74]赵玉成．动态载荷的小波正交算子变换识别法[J]．机械强度，1998，20(2)：127-130．
[75]郭杏林，毛玉明，赵岩，等．基于Markov参数精细积分法的载荷识别研究[J]．振动与冲击，2009，28(3)：27-30．
[76] Raath A.D., Waveren C.C.V. A time domain approach to load reconstruction fordurability testing [J]. Engineering Failure Analysis,1998,5(2):113-119.
[77] Mao Y.M., Guo X.L., Zhao Y. A state space force identification method based onMarkov parameters precise computation and regularization technique [J]. Journal ofSound and Vibration,2010,329(15):3008-3019.
[78] Esat I.I., Saud M., Naci E.S. A novel method to obtain a real-time control force strategyusing genetic algorithms for dynamic systems subjected to external arbitrary excitations[J]. Journal of Sound and Vibration,2011,330(1):27-48.
[79] Bahra A.S., Greening P.D. Identifying multiple axial load patterns using measuredvibration data [J]. Journal of Sound and Vibration,2011,330(15):3591-3605.
[80] Zheng S., Zhou L., Lian X., et al. Technical note: Coherence analysis of the transferfunction for dynamic force identification [J]. Mechanical Systems and Signal Processing,2011,25(6):2229-2240.
[81] Jang T.S., Baek H., Choi H.S., et al. A new method for measuring nonharmonic periodicexcitation forces in nonlinear damped systems [J]. Mechanical Systems and SignalProcessing,2011,25(6):2219-2228.
[82] Chabchoub M.A., Besset S., Ichchou M.N. Structural sources identification through aninverse mid-high frequency energy method [J]. Mechanical Systems and SignalProcessing,2011,25(8):2948-2961.
[83]王晓军，杨海峰，邱志平，等．基于Green函数的动态载荷区间识别方法研究[J]．固体力学学报，2011，32(1)：95-101．
[84] Ronasi H., Johansson H., Larsson F. A numerical framework for load identification andregularization with application to rolling disc problem [J]. Computers&structures,2011,89(1):38-47.
[85] Li Y.G., Zhang J.P., Wang L.Q., et al. A fault feature extraction method for rotor rubbingbased on load identification and measured impact response [J]. Procedia Engineering,2011,24:793-797.
[86] Zhang J.Y., Ohsaki M. Force identification of prestressed pin-jointed structures [J].Computers&Structures,2011,89(23):2361-2368.
[87] Liu J., Han X., Jiang C., et al. Dynamic load identification foruncertain structures basedon interval analysis and regularization method [J]. International Journal ofComputational Methods,2011,8(04):667-683.
[88] Wang L., Han X., Liu J., et al. An improved iteration regularization method andapplication to reconstruction of dynamic loads on a plate [J]. Journal of computationaland applied mathematics,2011,235(14):4083-4094.
[89] Wang L., Han X., Liu J., et al. A new regularization method and application to dynamicload identification problems [J]. Inverse Problems in Science and Engineering,2011,19(6):765-776.
[90] Zhang E., Antoni J., Feissel P. Bayesian force reconstruction with an uncertain model [J].Journal of Sound and Vibration,2012,331(4):798-814.
[91] Lourens E., Reynders E., De Roeck G., et al. An augmented Kalman filter for forceidentification in structural dynamics [J]. Mechanical Systems and Signal Processing,2012,27:446-460.
[92] Xu B., He J., Rovekamp R., et al. Structural parameters and dynamic loadingidentification from incomplete measurements: Approach and validation [J]. MechanicalSystems and Signal Processing,2012,28:244-257.
[93] Wu S.Q., Law S.S. Statistical moving load identification including uncertainty [J].Probabilistic Engineering Mechanics,2012,29:70-78.
[94] He J., Xu B., Masri S.F. Restoring force and dynamic loadings identification for anonlinear chain-like structure with partially unknown excitations [J]. NonlinearDynamics,2012,69(1-2):231-245.
[95]姚昊萍．基于基本结构声源等效法的复杂结构声辐射建模与特性分析[D]．南京：东南大学，2007．
[96]杜敬涛．任意边界条件下结构振动，封闭声场及其耦合系统建模方法研究[D]．哈尔滨：哈尔滨工程大学，2009．
[97]胡选利，戴德沛．螺旋桨飞机舱内噪声的定量分析和预估[J]．振动工程学报，1988，1(3)：19-29．
[98] Herdic P.C., Houston B.H., Marcus M.H., et al. The vibro-acoustic response and analysisof a full-scale aircraft fuselage section for interior noise reduction [J]. The Journal ofthe Acoustical Society of America,2005,117(6):3667-3678.
[99] Langley R.S. A dynamic stiffness/boundary element method for the prediction of interiornoise levels [J]. Journal of sound and vibration,1993,163(2):207-230.
[100] Steel J.A., Fraser G., Sendall P. A study of exhaust noise in a motor vehicle usingstatistical energy analysis [J]. Proceedings of the Institution of Mechanical Engineers,Part D: Journal of Automobile Engineering,2000,214(1):75-83.
[101]朱才朝，秦大同，李润方．车身结构振动与车内噪声声场耦合分析与控制[J]．机械工程学报，2002，38(8)：54-58．
[102]马天飞，林逸，彭彦宏，等．轿车车内低频噪声的仿真计算及试验研究[J]．中国机械工程，2005，16(16)：1489-1492．
[103] Warburton G.B. Vibration of a cylindrical shell in an acoustic medium [J]. Journal ofMechanical Engineering Science,1961,3(1):69-79.
[104] Dowell E.H., Gorman G.F., Smith D.A. Acoustoelasticity: general theory, acousticnatural modes and forced response to sinusoidal excitation, including comparisons withexperiment [J]. Journal of Sound and Vibration,1977,52(4):519-542.
[105] Sestieri A., Del Vescovo D., Lucibello P. Structural-acoustic coupling in complex shapedcavities [J]. Journal of Sound and Vibration,1984,96(2):219-233.
[106] Succi G.P. The interior acoustic field of an automobile cabin [J]. The Journal of theAcoustical Society of America,1987,81(6):1688-1694.
[107] Missaoui J., Cheng L. A combined integro-modal approach for predicting acousticproperties of irregular-shaped cavities [J]. The Journal of the Acoustical Society ofAmerica,1997,101(6):3313-3321.
[108] Pan J. The forced response of an acoustic‐structural coupled system [J]. The Journal ofthe Acoustical Society of America,1992,91(2):949-956.
[109] Luo C., Zhao M., Rao Z. The analysis of structural-acoustic coupling of an enclosureusing Green’s function method [J]. The International Journal of AdvancedManufacturing Technology,2005,27(3-4):242-247.
[110] Gladwell G.M.L, Zimmermann G. On energy and complementary energy formulations ofacoustic and structural vibration problems [J]. Journal of Sound and Vibration,1966,3(3):233-241.
[111] Gladwell G.M.L. A variational formulation of damped acousto structural vibrationproblems [J]. Journal of Sound and Vibration,1966,4(2):172-186.
[112] Craggs A. The transient response of a coupled plate-acoustic system using plate andacoustic finite elements [J]. Journal of Sound and Vibration,1971,15(4):509-528.
[113] Petyt M., Lea J., Koopmann G.H. A finite element method for determining the acousticmodes of irregular shaped cavities [J]. Journal of Sound and Vibration,1976,45(4):495-502.
[114] Petyt M., Lim S.P. Finite element analysis of the noise inside a mechanically excitedcylinder [J]. International Journal for Numerical Methods in Engineering,1978,13(1):109-122.
[115] Joppa P.D., Fyfe I.M. A finite element analysis of the impedance properties of irregularshaped cavities with absorptive boundaries [J]. Journal of Sound and Vibration,1978,56(1):61-69.
[116] Richards T.L., Jha S.K. A simplified finite element method for studying acousticcharacteristics inside a car cavity [J]. Journal of Sound and Vibration,1979,63(1):61-72.
[117] Unruh J.F. Finite element subvolume technique for structural-borne interior noiseprediction [J]. Journal of Aircraft,1980,17(6):434-441.
[118] Tetambe R.P., Rajakumar C. Estimation of error in finite element acoustic analysis [J].Computers&structures,1996,61(1):13-19.
[119] Nefske D.J., Wolf Jr J.A., Howell L.J. Structural-acoustic finite element analysis of theautomobile passenger compartment: a review of current practice [J]. Journal of Soundand Vibration,1982,80(2):247-266.
[120] Kropp A., Heiserer D. Efficient broadband vibro-acoustic analysis of passenger carbodies using an FE-based component mode synthesis approach [J]. Journal ofComputational Acoustics,2003,11(2):139-157.
[121] Sandberg G., G ransson P. A symmetric finite element formulation for acousticfluid-structure interaction analysis [J]. Journal of sound and vibration,1988,123(3):507-515.
[122] Wyckaert K., Augusztinovicz F., Sas P. Vibro-acoustical modal analysis: reciprocity,modal symmetry and model validity [J]. Journal of the Acoustical Society of America,1996,100(5):3172-3181.
[123] Kanarachos A., Antoniadis I. Symmetric variational principles and modal methods influid-structure interaction problems [J]. Journal of sound and vibration,1988,121(1):77-104.
[124] Everstine G.C. A symmetric potential formulation for fluid-structure interaction [J].Journal of Sound and Vibration,1981,79(1):157-160.
[125]曹友强，邓兆祥，李昌敏．车内耦合声场振动噪声预测研究[J]．汽车工程，2008，30(6)：483-487．
[126]马天飞，林逸，闵海涛，等．轻型客车NVH特性的刚弹耦合、声固耦合仿真研究[J]．汽车工程，2005，27(1)：72-76．
[127]马天飞，林逸，张建伟．轿车车室声固耦合系统的模态分析[J]．机械工程学报，2005，41(7)：225-230．
[128]赵冠军，刘更，吴立言．基于模态叠加法的声固耦合噪声仿真与实验[J]．机械科学与技术，2007，26(12)：1633-1636．
[129]惠巍，刘更，吴立言．轿车声固耦合低频噪声的有限元分析[J]．汽车工程，2006，28(12)：1070-1077．
[130] Brebbia C.A. The boundary element method for engineers [M]. London: Pentech Press,1978.
[131] Chertock G. Sound radiation from vibrating surfaces [J]. The Journal of the AcousticalSociety of America,1964,36(7):1305-1313.
[132] Copley L.G. Integral equation method for radiation from vibrating bodies [J]. TheJournal of the Acoustical Society of America,1967,41(4A):807-816.
[133] Schenck H.A. Improved integral formulation for acoustic radiation problems [J]. TheJournal of the Acoustical Society of America,1968,44(1):41-58.
[134] Li W.L., Wu T.W., Seybert A.F. A half-space boundary element method for acousticproblems with a reflecting plane of arbitrary impedance [J]. Journal of sound andvibration,1994,171(2):173-184.
[135] Park J.M., Eversman W. A boundary element method for propagation over absorbingboundaries [J]. Journal of sound and vibration,1994,175(2):197-218.
[136] Vlahopoulos N. A numerical structure-borne noise prediction scheme based on theboundary element method, with a new formulation for the singular integrals [J].Computers&structures,1994,50(1):97-109.
[137] Chandler-Wilde S.N., Hothersall D.C. A uniformly valid far field asymptotic expansionof the Green function for two-dimensional propagation above a homogeneousimpedance plane [J]. Journal of sound and vibration,1995,182(5):665-675.
[138] Chandler-Wilde S.N., Hothersall D.C. Efficient calculation of the Green function foracoustic propagation above a homogeneous impedance plane [J]. Journal of Sound andVibration,1995,180(5):705-724.
[139] Mohanty A.R., St Pierre B.D., Suruli-Narayanasami P. Structure-borne noise reductionin a truck cab interior using numerical techniques [J]. Applied Acoustics,2000,59(1):1-17.
[140] Ochmann M. The complex equivalent source method for sound propagation over animpedance plane [J]. The Journal of the Acoustical Society of America,2004,116(6):3304-3311.
[141] Chen Z.S., Waubke H. A formulation of the boundary element method for acousticradiation and scattering from two-dimensional structures [J]. Journal of ComputationalAcoustics,2007,15(3):333-352.
[142] Suzuki S., Maruyama S., Ido H. Boundary element analysis of cavity noise problemswith complicated boundary conditions [J]. Journal of Sound and Vibration,1989,130(1):79-96.
[143] Cheng C.Y.R., Seybert A.F., Wu T.W. A multidomain boundary element solution forsilencer and muffler performance prediction [J]. Journal of Sound and Vibration,1991,151(1):119-129.
[144] Wu T.W. A direct boundary element method for acoustic radiation and scattering frommixed regular and thin bodies [J]. The Journal of the Acoustical Society of America,1995,97(1):84-91.
[145] Wu T.W., Cheng C.Y.R, Zhang P. A direct mixed-body boundary element method forpacked silencers [J]. The Journal of the Acoustical Society of America,2002,111(6):2566-2572.
[146] Liu Y. Fast multipole boundary element method: theory and applications in engineering
[M]. Cambridge; New York: Cambridge University Press,2009.
[147] Chen Z.S., Waubke H., Kreuzer W. A formulation of the fast multipole boundaryelement method (FMBEM) for acoustic radiation and scattering from three-dimensionalstructures [J]. Journal of Computational Acoustics,2008,16(2):303-320.
[148] Fischer M., Gaul L. Application of the fast multipole BEM for structural–acousticsimulations [J]. Journal of Computational Acoustics,2005,13(1):87-98.
[149] Chappell D.J., Harris P.J., Henwood D., et al. A stable boundary element method formodeling transient acoustic radiation [J]. The Journal of the Acoustical Society ofAmerica,2006,120(1):74-80.
[150] Hargreaves J.A., Cox T. A transient boundary element method for acoustic scatteringfrom mixed regular and thin rigid bodies [J]. Acta Acustica united with Acustica,2009,95(4):678-689.
[151]赵键，汪鸿振，朱物华．边界元法计算已知振速封闭面的声辐射[J]．声学学报，1989，14(4)：250-257．
[152]黎胜，赵德有．用边界元法计算结构振动辐射声场[J]．大连理工大学学报，2000，40(4)：391-394．
[153]黎胜，赵德有．用有限元/边界元方法进行结构声辐射的模态分析[J]．声学学报，2001，26(2)：174-179．
[154]张胜勇，陈心昭．应用三次B样条函数插值的边界元法计算结构振动声辐射问题[J]．声学技术，1998，17(1)：20-23．
[155] Coyette J.P., Fyfe K.R. An improved formulation for acoustic eigenmode extractionfrom boundary element models [J]. ASME Transactions Journal of Vibration Acoustics,1990,112(3):392-397.
[156]赵志高．结构声辐射的机理与数值方法研究[D]．武汉：华中科技大学，2005．
[157] Langley R.S., Smith J.R.D., Fahy F.J. Statistical energy analysis of periodically stiffeneddamped plate structures [J]. Journal of Sound and Vibration,1997,208(3):407-426.
[158] Langley R.S. On the modal density and energy flow characteristics of periodic structures[J]. Journal of sound and vibration,1994,172(4):491-511.
[159] Norton M.P., Greenhalgh R. On the estimation of loss factors in lightly damped pipelinesystems: some measurement techniques and their limitations [J]. Journal of sound andvibration,1986,105(3):397-423.
[160] Wentang R., Attenborough K. Prediction of sound fields in rooms using statisticalenergy analysis [J]. Applied Acoustics,1991,34(3):207-220.
[161] Misaji K., Tada H., Yamashita T., et al. Testing uniqueness of a hybrid SEA modelingsolution for a passenger car [C]. SAE Paper,2009-01-1408.
[162] Moore J.A., Powell R., Bharj T. Development of condensed SEA models of passengervehicles [C]. SAE Technical Paper,1999-01-1699.
[163] Lee J., Powell R., Ni A., et al. Integration of SEA tire model with vehicle model [C].SAE Technical Paper,1999-01-1700.
[164] Chen H., O'Keefe M., Bremner P. A comparison of test-based and analytic SEA modelsfor vibro-acoustics of a light truck [C]. SAE Technical Paper,951329.
[165] Manning J.E. SEA models to predict structureborne noise in vehicles [C]. SAETechnical Paper,2003-01-1542.
[166] Moron P., Musser C. Use of SEA for vehicle target setting and efficient realization ofvehicle acoustic goals [C]. SAE Technical Paper,2006-01-1096.
[167] Musser C., Manning J., Peng G.C. Prediction of vehicle interior sound pressuredistribution with SEA [C]. SAE Technical Paper,2011-01-1705.
[168] Vaz I., Washburn K., DeVries L. Improvement of an SEA model of cab interior soundlevels through use of a hybrid FE/SEA method [C]. SAE Technical Paper2011-01-1706.
[169]靳晓雄，叶武平，丁玉兰．基于统计能量分析法的轿车内室噪声优化与控制[J]．同济大学学报，2002，30(7)：862-867．
[170]朱桂华，宫镇，胡均平，等．统计能量分析用于工程机械驾驶室噪声预估[J]．中南工业大学学报，2003，34(2)：166-166．
[171]王登峰，陈书明，曲伟，等．车内噪声统计能量分析预测与试验[J]．吉林大学学报，2009，39(1)：68-73．
[172]张肃，陈南，李普，等．基于小波迦辽金法的复杂封闭空腔结构—声耦合场分析[J]．机械工程学报，2008，44(6)：155-160．
[173]吴九汇．车辆内腔声固耦合分析的覆盖域方法研究[D]．西安：西安交通大学，2001．
[174] Wu J.H., Chen H.L., An W.B. A method to predict sound radiation from a plate-endedcylindrical shell excited by an external force [J]. Journal of sound and vibration,2000,237(5):793-803.
[175]吴九汇，陈花玲．任意开头封闭薄壳内部声场计算的一种新方法研究[J]．声学学报，2000，25(5)：468-471．
[176] Djamaa M.C., Ouelaa N., Pezeratb C., et al. Reconstruction of a distributed forceapplied on a thin cylindrical shell by an inverse method and spatial filtering [J]. Journalof Sound and Vibration,2007,301(3):560-575.
[177] Jang T.S., Sung H.G., Han S.L., et al. Inverse determination of the loading source of theinfinite beam on elastic foundation [J]. Journal of Mechanical Science and Technology,2008,22(12):2350-2356.
[178] Hansen P.C. Truncated SVD solution to discrete ill-posed problems with ill-determinednumerical rank [J]. SIAM Journal on Scientific and Statistical Computing,1990,11(3):503-518.
[179] Tikhonov A.N., Arsenin V.Y. Methods for solving ill-posed problems [M]. John Wileyand Sons, Inc,1977.
[180]肖庭延，于慎根，王彦飞．反问题的数值解法[M]．北京：科学出版社，2003．
[181]杨文献，任兴民，姜节胜．基于奇异熵的信号降噪技术研究[J]．西北工业大学学报，2001，19(3)：368-371．
[182] Morozov V.A. The error principle in the solution of operational equations by theregularization method [J]. USSR Computational Mathematics and Mathematical Physics,1968,8(2):63-87.
[183] Hansen P.C. Analysis of discrete ill-posed problems by means of the L-curve [J]. SIAMreview,1992,34(4):561-580.
[184] Golub G.H., Heath M., Wahba G. Generalized CROSS-validation as a method forchoosing a good ridge parameter [J].Technometracs,1979,21(2):215-222.
[185] Citarella R., Federico L., Cicatiello A. Model acoustic transfer vector approach in aFEM-BEM vibro-acoustic analysis [J]. Engineering Analysis with Boundary Elements,2007,31(3):248-258.
[186]张伟，刘献栋，单颖春，等．基于声传递向量法的路面激励引起车内噪声的仿真研究[J]．振动工程学报，2010，23(6)：39-43．
[187] Koopmann G.H., Song L., Fahnline J. A method for computing acoustic fields based onthe principle of wave superposition [J]. The Journal of the Acoustical Society ofAmerica,1989,86(5):2433-2438.
[188] Kim S.M., Brennan M.J. A compact matrix formulation using the impedance andmobility approach for the analysis of structural-acoustic system [J]. Journal of Soundand Vibration,1999,223(1):97-113.
[189] Ding W.P., Chen H.L. Research on the interior noise contributed from a local panel’svibration of an elastic thin-walled cavity [J]. Applied Acoustics,2002,63(1):95-102.
[190] Thite A.N., Thompson D.J. The quantification of structure-borne transmission paths byinverse methods. Part2: Use of regularization techniques [J]. Journal of Sound andVibration,2003,264:411-431.
[191] Verheij J.W. Inverse and reciprocity methods for machinery noise sourcecharacterization and sound path quantification [J]. International Journal of Acousticsand Vibration,1997,2(1):11-20.
[192] Fahy F.J. Some applications of the reciprocity principle in experimental vibroacoustics[J]. Acoustical Physics,2003,49(2):217-229.
[193] Williams E.G., Maynard J.D. Holographic imaging without the wavelength resolutionlimit [J]. Physical Review Letters,1980,45(7):554-557.
[194] Williams E.G. Fourier acoustics: sound radiation and nearfield acoustical holography[M]. Academic Press,1999.
[195] Veronesi W.A., Maynard J.D. Digital holographic reconstruction of sources witharbitrarily shaped surfaces [J]. The Journal of the Acoustical Society of America,1989,85(2):588-598.
[196]李加庆，陈进，史重九．基于声全息的故障诊断方法[J]．机械工程学报，2009，45(5)：34-38．
[197]邓江华，顾灿松，刘献栋，等．基于声阵列技术的汽车噪声源识别及贡献量分析[J]．振动工程学报，2010，23(006)：630-635．
[198]鲁文波，蒋伟康．基于近场声全息的故障诊断方法及系统实现[J]．振动与冲击，2013，32(5)：48-51．
[199] Maynard J.D., Williams E.G., Lee Y. Nearfield acoustic holography: I. Theory ofgeneralized holography and the development of NAH [J]. The Journal of the AcousticalSociety of America,1985,78(4):1395-1413.
[200] Veronesi W.A., Maynard J.D. Digital holographic reconstruction of sources witharbitrarily shaped surfaces [J]. The Journal of the Acoustical Society of America,1989,85(2):588-598.
[201] Williams E.G., Houston B.H. Interior near-field acoustical holography in flight [J]. TheJournal of the Acoustical Society of America,2000,108(4):1451-1463.
[202] Wu S.F., Yu J. Reconstructing interior acoustic pressure field via Helmholtz equationleast-squares method [J]. The Journal of the Acoustical Society of America,1998,104(4):2054-2060.
[203] Wu S.F. On reconstruction of acoustic pressure fields using the Helmholtz least squaresmethod [J]. The Journal of the Acoustical Society of America,2000,107(5):2511-2522.
[204] Ochmann M. The source simulation technique for acoustic radiation problems [J]. ActaAcustica united with Acustica,1995,81(6):512-527.
[205] Zhang Y.B., Jacobsen F., Bi C.X., et al. Near field acoustic holography based on theequivalent source method and pressure-velocity transducers [J]. The Journal of theAcoustical Society of America,2009,126(3):1257-1263.
[206] Wu S.F., Natarajan L.K. Panel acoustic contribution analysis [J]. The Journal of theAcoustical Society of America,2013,133(2):799-809.
[207] Song L., Koopmann G.H., Fahnline J.B. Numerical errors associated with the method ofsuperposition for computing acoustic fields [J]. The Journal of the Acoustical Society ofAmerica,1991,89(6):2625-2633.
[208] Fahnline J.B., Koopmann G.H. A numerical solution for the general radiation problembased on the combined methods of superposition and singular‐value decomposition [J].The Journal of the Acoustical Society of America,1991,90(5):2808-2819.
[209] Jeans R., Mathews I.C. The wave superposition method as a robust technique forcomputing acoustic fields [J]. The Journal of the Acoustical Society of America,1992,92(2):1156-1166.
[210]陈鸿洋，商德江，李琪，等．声场匹配波叠加法的水下结构声辐射预报[J]．声学学报，2013，38(2)：137-146．
[211]毕传兴，陈心昭，陈剑，等．基于等效源法的近场声全息技术[J]．中国科学(E辑)，2005，35(5)：535-548．
[212]李卫兵，陈剑，毕传兴，等．联合波叠加法的全息理论与实验研究[J]．物理学报，2006，55(3)：1264-1270．
[213]毕传兴，陈心昭，徐亮，等．基于等效源法的Patch近场声全息[J]．中国科学(E辑)，2007，37(9)：1205-1213．
[214]徐亮，毕传兴，陈剑，等．基于波叠加法的Patch近场声全息及其实验研究[J]．物理学报，2007，56(5)：2776-2783．
[215]张永斌，毕传兴，陈剑，等．基于等效源法的平面近场声全息及其实验研究[J]．声学学报，2007，32(6)：489-496．
[216]于飞，陈剑，李卫兵，等．腔体内三维声场重构与预测的波叠加方法[J]．自然科学进展，2005，15(1)：90-96．
[217] Sarkissian A. Method of superposition applied to patch near-field acoustic holography[J]. The Journal of the Acoustical Society of America,2005,118(2):671-678.
[218] Valdivia N.P., Williams E.G. Study of the comparison of the methods of equivalentsources and boundary element methods for near-field acoustic holography [J]. TheJournal of the Acoustical Society of America,2006,120(6):3694-3705.
[219] Bai M.R., Chen C.C., Lin J.H. On optimal retreat distance for the equivalent sourcemethod-based nearfield acoustical holography [J]. The Journal of the Acoustical Societyof America,2011,129(3):1407-1416.
[220]李加庆，陈进，杨超等．波叠加声场重构精度的影响因素分析[J]．物理学报，2008，57(7)：4258-4264．
[2]马大猷．现代声学基础[M]．北京：科学出版社，2003．
[3]应怀樵．现代振动与噪声技术(第2卷)[M]．北京：航空工业出版社，2000．
[4]周新祥．噪声控制技术及其新进展[M]．北京：冶金工业出版社，2007．
[5]何祚镛，赵玉芳．声学理论基础[M]．北京：国防工业出版社，1981．
[6]袁昌明，方云中，华伟进．噪声与振动控制技术[M]．北京：冶金工业出版社，2007．
[7]王伯良．噪声控制理论[M]．武汉：华中理工大学出版社，1990．
[8]靳晓雄，胡子谷．工程机械噪声控制学[M]．上海：同济大学出版社，1997．
[9]何祚镛．结构振动与声辐射[M]．哈尔滨：哈尔滨工程大学出版社，2001．
[10]庞剑，谌刚，何华．汽车噪声与振动—理论与应用[M]．北京：北京理工大学出版社，2006．
[11] Plunt J. Finding and fixing vehicle NVH problems with transfer path analysis [J]. Soundand vibration,2005,39(11):12-17.
[12] De Klerk D., Ossipov A. Operational transfer path analysis: Theory, guidelines and tirenoise application [J]. Mechanical Systems and Signal Processing,2010,24(7):1950-1962.
[13] Janssens K., Gajdatsy P., Gielen L., et al. OPAX: A new transfer path analysis methodbased on parametric load models [J]. Mechanical Systems and Signal Processing,2011,25(4):1321-1338.
[14] Genuit K., Poggenburg J. The design of vehicle interior noise using binaural transferpath analysis [C]. SAE Paper,1999-01-1808.
[15] Unruh J.F., Till P.D., Farwell T.J. Interior noise source/path identification technology[C]. SAE Paper,2000-01-1709.
[16] Kim S.J., Yang H.I., Lee S.K. Prediction of interior noise based on hybrid TPA [C]. SAEInternational Journal of Passenger Cars-Mechanical Systems,2009,2(1):1440-1448.
[17]郝鹏，郑四发，连小珉．运动噪声源的时域传递路径模型及贡献率分析[J]．机械工程学报，2012，48(8)：104-109．
[18] Fabunmi J.A. Effects of structural modes on vibratory force determination by the pseudoinverse technique [J]. AIAA journal,1986,24(3):504-509.
[19] Liu Y., Shepard W.S. Dynamic force identification based on enhanced least squares andtotal least-squares schemes in the frequency domain [J]. Journal of sound and vibration,2005,282(1):37-60.
[20] Parloo E., Verboven P., Guillaume P., et al. Force identification by means of in-operationmodal models [J]. Journal of Sound and Vibration,2003,262(1):161-173.
[21] Law S.S., Chan T.H.T., Zeng Q.H. Moving force identification: a time domain method[J]. Journal of Sound and Vibration,1997,201(1):1-22.
[22] Lin J.H., Guo X.L., Zhi H., et al. Computer simulation of structural random loadingidentification [J]. Computers&Structures,2001,79(4):375-387.
[23] Bartlett F.D., Flannelly W.G. Model verification of force determination for measuringvibratory loads [J]. Journal of the American Helicopter Society,1979,24(2):10-18.
[24] Starkey J.M., Merrill G.L. On the ill-conditioned nature of indirect force-measurementtechniques [J]. Journal of Modal Analysis,1989,4(3):103-108.
[25] Hansen M., Starkey J.M. On predicting and improving the condition ofmodal-model-based indirect force measurement algorithms [J]. Proceedings of the8thIMAC, Kissimmee, FL, USA,1990:115-120.
[26]刘恒春，朱德懋，孙久厚．振动载荷识别的奇异值分解法[J]．振动工程学报，1990，3(1)：24-32．
[27] Karlsson S.E.S. Identification of external structural loads from measured harmonicresponses [J]. Journal of sound and vibration,1996,196(1):59-74.
[28] O'Callahan J., Piergentili F. Force estimation using operational data [J]. Proceedings ofthe14th International Modal Analysis Conference,1996:1586-1592.
[29]顾慧芝，聂君剑．载荷识别的等效点动标定法[J]．振动工程学报，1997，10(3)：329-334．
[30]林家浩，智浩，郭杏林．平稳随机振动荷载识别的逆虚拟激励法(一)[J]．计算力学学报，1998，15(2)：127-136．
[31]智浩，郭杏林，林家浩．平稳随机振动荷载识别的逆虚拟激励法(二)[J]．计算力学学报，1998，15(4)：385-400．
[32]文祥荣，缪龙秀．由实测应变响应识别结构动态载荷[J]．铁道学报，2000，22(6)：36-39．
[33]智浩，文祥荣，缪龙秀，等．动态载荷的频域识别方法[J]．北方交通大学学报，2000，24(4)：5-10．
[34]田燕，王菁，郑海起．多载荷识别频响函数矩阵求逆法的改进算法[J]．军械工程学院学报，2002，14(4)：13-17．
[35]许锋，陈怀海，鲍明．动载荷识别的广义域模态模型及其精度分析研究[J]．计算力学学报，2003，20(2)：218-222．
[36]李东升，郭杏林．逆虚拟激励法随机载荷识别试验研究[J]．工程力学，2004，21(2)：134-139．
[37] Thite A.N., Thompson D.J. Selection of response measurement locations to improveinverse force determination [J]. Applied Acoustics,2006,67(8):797-818.
[38]姜金辉，陈国平，张方．多点平稳随机载荷识别方法研究[J]．振动工程学报，2009，22(2)：162-167．
[39]周林，郑四发，王彬星，等．动态载荷识别位置优化的传递函数相干法[J]．振动工程学报，2011，24(1)：14-19．
[40]许锋，陈怀海，鲍明．机械振动载荷识别研究的现状与未来[J]．中国机械工程，2002，13(6)：526-531．
[41] Desanghere G., Snoeys R. Indirect identification of excitation forces by modalcoordinate transformation [J]. Proceedings of the3rd IMAC.1985,3:685-690.
[42] Ory H., Glaser H., Holzdeppe D. The reconstruction of forcing function based onaeroelasticity and structural dynamics [J]. Proceedings of2nd Int. Symp. OnAeroelasticity and Structural Dynamics, Flaschen, FRG,1985:164-168.
[43] Ory H., Glaser H., Holzdeppe D. Quality of modal analysis and reconstruction of forcingfunction based on measured output data [J]. Proceedings of4th IMAC, New York, USA,1986:350-357.
[44]唐秀近．动态力识别的时域方法[J]．大连理工大学学报，1987，26(4)：21-27．
[45]唐秀近．时域识别动态载荷的精度问题[J]．大连理工大学学报，1990，30(1)：31-37．
[46]初良成，曲乃泗．动态载荷识别的时域正演方法[J]．应用力学学报，1994，11(2)：9-18．
[47]时战，许士斌，初良成，等．利用脉冲响应函数识别载荷的时序法[J]．振动工程学报，1995，8(3)：235-242．
[48]徐倩，文祥荣，孙守光．结构动态载荷识别的精细逐步积分法[J]．计算力学学报，2002，19(1)：53-57．
[49]张运良，林皋，王永学，等．一种改进的动态载荷时域识别方法[J]．计算力学学报，2004，21(2)：209-215．
[50]赵凤遥，张运良，马震岳．动载荷的时域识别方法及其应用[J]．水电能源科学，2005，23(1)：8-11．
[51]蔡元奇，朱以文．基于逆向滤波器的动态载荷时域识别方法[J]．振动工程学报，2006，19(2)：200-205．
[52]瞿伟廉，王锦文．振动结构动态荷载识别综述[J]．华中科技大学学报(城市科学版)，2004，21(4)：1-4．
[53] Kreitinger T.J., Wang M.L., Schreyer H.L. Non-parametric force identification fromstructural response [J]. Soil Dynamics and Earthquake Engineering,1992,11(5):269-277.
[54]路敦勇，吴淼．动态载荷识别的SWAT方法研究[J]．振动与冲击，1999，18(4)：78-81．
[55]张方，朱德懋．动态载荷时域识别的级数方法[J]．振动工程学报，1996，9(1)：1-8．
[56]袁向荣，卜建清，满红高，等．移动荷载识别的函数逼近法[J]．振动与冲击，2000，19(1)：58-70．
[57]陈锋，袁向荣，李明．移动载荷识别的B-样条函数逼近法[J]．石家庄铁道学院学报，2003，16(1)：11-14．
[58]王彦卫，赵玫．一种新的动态载荷识别方法[J]．噪声与振动控制，2003，3：11-13．
[59]袁向荣．梁振动响应曲线滑动拟合法及在移动荷载识别中的应用[J]．噪声与振动控制，2006，26(3)：42-43．
[60]姜增国，孙艳茹．三次样条函数在桥梁移动荷载识别中的应用[J]．振动与冲击，2006，25(6)：124-126．
[61]孙国，郭杏林．基于线性多点逼近的载荷识别方法[J]．计算力学学报，2011，28(B04)：176-181．
[62] Liang Y.C., Zhou C.G., Wang Z.S. Identification of restoring forces in non-linearvibration systems based on neural networks [J]. Journal of sound and vibration,1997,206(1):103-108.
[63]高宝成，张征．基于神经网络的结构荷载识别研究[J]．振动、测试与诊断，1996，16(1)：14-19．
[64]张方，朱德懋．基于神经网络模型的动载荷识别[J]．振动工程学报，1997，10(2)：156-162．
[65]吴大宏，赵人达．基于神经网络的混凝土桥梁荷载识别方法研究[J]．中国铁道科学，2002，23(1)：25-28．
[66]窦春红，林近山，寇兴磊．基于BP神经网络的海洋平台振动载荷识别[J]．石油矿场机械，2007，36(7)：11-15．
[67] Inoue H., Kishimoto K., Shibuya T., et al. Estimation of Impact Load by InverseAnalysis: Optimal Transfer Function for Inverse Analysis [J]. JSME internationaljournal. Ser.1, Solid mechanics, strength of materials,1992,35(4):420-427.
[68]魏星原，宋斌．载荷识别的逆系统方法[J]．振动、测试与诊断，1995，15(3)：35-43．
[69]饶柱石，施勤忠．基于逆系统分析法的多输入—多输出系统动态载荷的优化估计[J]．振动与冲击，2000，19(2)：9-12．
[70]王慧儒，谢晓竹，吴淼．基于逆传系统法的动态载荷识别研究[J]．装甲兵工程学院学报，2005，19(3)：79-82．
[71] Inoue H., Kishimoto K., Shibuya T. Experimental wavelet analysis of flexural waves inbeams [J]. Experimental Mechanics,1996,36(3):212-217.
[72] Doyle J.F. A wavelet deconvolution method for impact force identification [J].Experimental mechanics,1997,37(4):403-408.
[73] Gaul L., Hurlebaus S. Identification of the impact location on a plate using wavelets [J].Mechanical Systems and Signal Processing,1998,12(6):783-795.
[74]赵玉成．动态载荷的小波正交算子变换识别法[J]．机械强度，1998，20(2)：127-130．
[75]郭杏林，毛玉明，赵岩，等．基于Markov参数精细积分法的载荷识别研究[J]．振动与冲击，2009，28(3)：27-30．
[76] Raath A.D., Waveren C.C.V. A time domain approach to load reconstruction fordurability testing [J]. Engineering Failure Analysis,1998,5(2):113-119.
[77] Mao Y.M., Guo X.L., Zhao Y. A state space force identification method based onMarkov parameters precise computation and regularization technique [J]. Journal ofSound and Vibration,2010,329(15):3008-3019.
[78] Esat I.I., Saud M., Naci E.S. A novel method to obtain a real-time control force strategyusing genetic algorithms for dynamic systems subjected to external arbitrary excitations[J]. Journal of Sound and Vibration,2011,330(1):27-48.
[79] Bahra A.S., Greening P.D. Identifying multiple axial load patterns using measuredvibration data [J]. Journal of Sound and Vibration,2011,330(15):3591-3605.
[80] Zheng S., Zhou L., Lian X., et al. Technical note: Coherence analysis of the transferfunction for dynamic force identification [J]. Mechanical Systems and Signal Processing,2011,25(6):2229-2240.
[81] Jang T.S., Baek H., Choi H.S., et al. A new method for measuring nonharmonic periodicexcitation forces in nonlinear damped systems [J]. Mechanical Systems and SignalProcessing,2011,25(6):2219-2228.
[82] Chabchoub M.A., Besset S., Ichchou M.N. Structural sources identification through aninverse mid-high frequency energy method [J]. Mechanical Systems and SignalProcessing,2011,25(8):2948-2961.
[83]王晓军，杨海峰，邱志平，等．基于Green函数的动态载荷区间识别方法研究[J]．固体力学学报，2011，32(1)：95-101．
[84] Ronasi H., Johansson H., Larsson F. A numerical framework for load identification andregularization with application to rolling disc problem [J]. Computers&structures,2011,89(1):38-47.
[85] Li Y.G., Zhang J.P., Wang L.Q., et al. A fault feature extraction method for rotor rubbingbased on load identification and measured impact response [J]. Procedia Engineering,2011,24:793-797.
[86] Zhang J.Y., Ohsaki M. Force identification of prestressed pin-jointed structures [J].Computers&Structures,2011,89(23):2361-2368.
[87] Liu J., Han X., Jiang C., et al. Dynamic load identification foruncertain structures basedon interval analysis and regularization method [J]. International Journal ofComputational Methods,2011,8(04):667-683.
[88] Wang L., Han X., Liu J., et al. An improved iteration regularization method andapplication to reconstruction of dynamic loads on a plate [J]. Journal of computationaland applied mathematics,2011,235(14):4083-4094.
[89] Wang L., Han X., Liu J., et al. A new regularization method and application to dynamicload identification problems [J]. Inverse Problems in Science and Engineering,2011,19(6):765-776.
[90] Zhang E., Antoni J., Feissel P. Bayesian force reconstruction with an uncertain model [J].Journal of Sound and Vibration,2012,331(4):798-814.
[91] Lourens E., Reynders E., De Roeck G., et al. An augmented Kalman filter for forceidentification in structural dynamics [J]. Mechanical Systems and Signal Processing,2012,27:446-460.
[92] Xu B., He J., Rovekamp R., et al. Structural parameters and dynamic loadingidentification from incomplete measurements: Approach and validation [J]. MechanicalSystems and Signal Processing,2012,28:244-257.
[93] Wu S.Q., Law S.S. Statistical moving load identification including uncertainty [J].Probabilistic Engineering Mechanics,2012,29:70-78.
[94] He J., Xu B., Masri S.F. Restoring force and dynamic loadings identification for anonlinear chain-like structure with partially unknown excitations [J]. NonlinearDynamics,2012,69(1-2):231-245.
[95]姚昊萍．基于基本结构声源等效法的复杂结构声辐射建模与特性分析[D]．南京：东南大学，2007．
[96]杜敬涛．任意边界条件下结构振动，封闭声场及其耦合系统建模方法研究[D]．哈尔滨：哈尔滨工程大学，2009．
[97]胡选利，戴德沛．螺旋桨飞机舱内噪声的定量分析和预估[J]．振动工程学报，1988，1(3)：19-29．
[98] Herdic P.C., Houston B.H., Marcus M.H., et al. The vibro-acoustic response and analysisof a full-scale aircraft fuselage section for interior noise reduction [J]. The Journal ofthe Acoustical Society of America,2005,117(6):3667-3678.
[99] Langley R.S. A dynamic stiffness/boundary element method for the prediction of interiornoise levels [J]. Journal of sound and vibration,1993,163(2):207-230.
[100] Steel J.A., Fraser G., Sendall P. A study of exhaust noise in a motor vehicle usingstatistical energy analysis [J]. Proceedings of the Institution of Mechanical Engineers,Part D: Journal of Automobile Engineering,2000,214(1):75-83.
[101]朱才朝，秦大同，李润方．车身结构振动与车内噪声声场耦合分析与控制[J]．机械工程学报，2002，38(8)：54-58．
[102]马天飞，林逸，彭彦宏，等．轿车车内低频噪声的仿真计算及试验研究[J]．中国机械工程，2005，16(16)：1489-1492．
[103] Warburton G.B. Vibration of a cylindrical shell in an acoustic medium [J]. Journal ofMechanical Engineering Science,1961,3(1):69-79.
[104] Dowell E.H., Gorman G.F., Smith D.A. Acoustoelasticity: general theory, acousticnatural modes and forced response to sinusoidal excitation, including comparisons withexperiment [J]. Journal of Sound and Vibration,1977,52(4):519-542.
[105] Sestieri A., Del Vescovo D., Lucibello P. Structural-acoustic coupling in complex shapedcavities [J]. Journal of Sound and Vibration,1984,96(2):219-233.
[106] Succi G.P. The interior acoustic field of an automobile cabin [J]. The Journal of theAcoustical Society of America,1987,81(6):1688-1694.
[107] Missaoui J., Cheng L. A combined integro-modal approach for predicting acousticproperties of irregular-shaped cavities [J]. The Journal of the Acoustical Society ofAmerica,1997,101(6):3313-3321.
[108] Pan J. The forced response of an acoustic‐structural coupled system [J]. The Journal ofthe Acoustical Society of America,1992,91(2):949-956.
[109] Luo C., Zhao M., Rao Z. The analysis of structural-acoustic coupling of an enclosureusing Green’s function method [J]. The International Journal of AdvancedManufacturing Technology,2005,27(3-4):242-247.
[110] Gladwell G.M.L, Zimmermann G. On energy and complementary energy formulations ofacoustic and structural vibration problems [J]. Journal of Sound and Vibration,1966,3(3):233-241.
[111] Gladwell G.M.L. A variational formulation of damped acousto structural vibrationproblems [J]. Journal of Sound and Vibration,1966,4(2):172-186.
[112] Craggs A. The transient response of a coupled plate-acoustic system using plate andacoustic finite elements [J]. Journal of Sound and Vibration,1971,15(4):509-528.
[113] Petyt M., Lea J., Koopmann G.H. A finite element method for determining the acousticmodes of irregular shaped cavities [J]. Journal of Sound and Vibration,1976,45(4):495-502.
[114] Petyt M., Lim S.P. Finite element analysis of the noise inside a mechanically excitedcylinder [J]. International Journal for Numerical Methods in Engineering,1978,13(1):109-122.
[115] Joppa P.D., Fyfe I.M. A finite element analysis of the impedance properties of irregularshaped cavities with absorptive boundaries [J]. Journal of Sound and Vibration,1978,56(1):61-69.
[116] Richards T.L., Jha S.K. A simplified finite element method for studying acousticcharacteristics inside a car cavity [J]. Journal of Sound and Vibration,1979,63(1):61-72.
[117] Unruh J.F. Finite element subvolume technique for structural-borne interior noiseprediction [J]. Journal of Aircraft,1980,17(6):434-441.
[118] Tetambe R.P., Rajakumar C. Estimation of error in finite element acoustic analysis [J].Computers&structures,1996,61(1):13-19.
[119] Nefske D.J., Wolf Jr J.A., Howell L.J. Structural-acoustic finite element analysis of theautomobile passenger compartment: a review of current practice [J]. Journal of Soundand Vibration,1982,80(2):247-266.
[120] Kropp A., Heiserer D. Efficient broadband vibro-acoustic analysis of passenger carbodies using an FE-based component mode synthesis approach [J]. Journal ofComputational Acoustics,2003,11(2):139-157.
[121] Sandberg G., G ransson P. A symmetric finite element formulation for acousticfluid-structure interaction analysis [J]. Journal of sound and vibration,1988,123(3):507-515.
[122] Wyckaert K., Augusztinovicz F., Sas P. Vibro-acoustical modal analysis: reciprocity,modal symmetry and model validity [J]. Journal of the Acoustical Society of America,1996,100(5):3172-3181.
[123] Kanarachos A., Antoniadis I. Symmetric variational principles and modal methods influid-structure interaction problems [J]. Journal of sound and vibration,1988,121(1):77-104.
[124] Everstine G.C. A symmetric potential formulation for fluid-structure interaction [J].Journal of Sound and Vibration,1981,79(1):157-160.
[125]曹友强，邓兆祥，李昌敏．车内耦合声场振动噪声预测研究[J]．汽车工程，2008，30(6)：483-487．
[126]马天飞，林逸，闵海涛，等．轻型客车NVH特性的刚弹耦合、声固耦合仿真研究[J]．汽车工程，2005，27(1)：72-76．
[127]马天飞，林逸，张建伟．轿车车室声固耦合系统的模态分析[J]．机械工程学报，2005，41(7)：225-230．
[128]赵冠军，刘更，吴立言．基于模态叠加法的声固耦合噪声仿真与实验[J]．机械科学与技术，2007，26(12)：1633-1636．
[129]惠巍，刘更，吴立言．轿车声固耦合低频噪声的有限元分析[J]．汽车工程，2006，28(12)：1070-1077．
[130] Brebbia C.A. The boundary element method for engineers [M]. London: Pentech Press,1978.
[131] Chertock G. Sound radiation from vibrating surfaces [J]. The Journal of the AcousticalSociety of America,1964,36(7):1305-1313.
[132] Copley L.G. Integral equation method for radiation from vibrating bodies [J]. TheJournal of the Acoustical Society of America,1967,41(4A):807-816.
[133] Schenck H.A. Improved integral formulation for acoustic radiation problems [J]. TheJournal of the Acoustical Society of America,1968,44(1):41-58.
[134] Li W.L., Wu T.W., Seybert A.F. A half-space boundary element method for acousticproblems with a reflecting plane of arbitrary impedance [J]. Journal of sound andvibration,1994,171(2):173-184.
[135] Park J.M., Eversman W. A boundary element method for propagation over absorbingboundaries [J]. Journal of sound and vibration,1994,175(2):197-218.
[136] Vlahopoulos N. A numerical structure-borne noise prediction scheme based on theboundary element method, with a new formulation for the singular integrals [J].Computers&structures,1994,50(1):97-109.
[137] Chandler-Wilde S.N., Hothersall D.C. A uniformly valid far field asymptotic expansionof the Green function for two-dimensional propagation above a homogeneousimpedance plane [J]. Journal of sound and vibration,1995,182(5):665-675.
[138] Chandler-Wilde S.N., Hothersall D.C. Efficient calculation of the Green function foracoustic propagation above a homogeneous impedance plane [J]. Journal of Sound andVibration,1995,180(5):705-724.
[139] Mohanty A.R., St Pierre B.D., Suruli-Narayanasami P. Structure-borne noise reductionin a truck cab interior using numerical techniques [J]. Applied Acoustics,2000,59(1):1-17.
[140] Ochmann M. The complex equivalent source method for sound propagation over animpedance plane [J]. The Journal of the Acoustical Society of America,2004,116(6):3304-3311.
[141] Chen Z.S., Waubke H. A formulation of the boundary element method for acousticradiation and scattering from two-dimensional structures [J]. Journal of ComputationalAcoustics,2007,15(3):333-352.
[142] Suzuki S., Maruyama S., Ido H. Boundary element analysis of cavity noise problemswith complicated boundary conditions [J]. Journal of Sound and Vibration,1989,130(1):79-96.
[143] Cheng C.Y.R., Seybert A.F., Wu T.W. A multidomain boundary element solution forsilencer and muffler performance prediction [J]. Journal of Sound and Vibration,1991,151(1):119-129.
[144] Wu T.W. A direct boundary element method for acoustic radiation and scattering frommixed regular and thin bodies [J]. The Journal of the Acoustical Society of America,1995,97(1):84-91.
[145] Wu T.W., Cheng C.Y.R, Zhang P. A direct mixed-body boundary element method forpacked silencers [J]. The Journal of the Acoustical Society of America,2002,111(6):2566-2572.
[146] Liu Y. Fast multipole boundary element method: theory and applications in engineering
[M]. Cambridge; New York: Cambridge University Press,2009.
[147] Chen Z.S., Waubke H., Kreuzer W. A formulation of the fast multipole boundaryelement method (FMBEM) for acoustic radiation and scattering from three-dimensionalstructures [J]. Journal of Computational Acoustics,2008,16(2):303-320.
[148] Fischer M., Gaul L. Application of the fast multipole BEM for structural–acousticsimulations [J]. Journal of Computational Acoustics,2005,13(1):87-98.
[149] Chappell D.J., Harris P.J., Henwood D., et al. A stable boundary element method formodeling transient acoustic radiation [J]. The Journal of the Acoustical Society ofAmerica,2006,120(1):74-80.
[150] Hargreaves J.A., Cox T. A transient boundary element method for acoustic scatteringfrom mixed regular and thin rigid bodies [J]. Acta Acustica united with Acustica,2009,95(4):678-689.
[151]赵键，汪鸿振，朱物华．边界元法计算已知振速封闭面的声辐射[J]．声学学报，1989，14(4)：250-257．
[152]黎胜，赵德有．用边界元法计算结构振动辐射声场[J]．大连理工大学学报，2000，40(4)：391-394．
[153]黎胜，赵德有．用有限元/边界元方法进行结构声辐射的模态分析[J]．声学学报，2001，26(2)：174-179．
[154]张胜勇，陈心昭．应用三次B样条函数插值的边界元法计算结构振动声辐射问题[J]．声学技术，1998，17(1)：20-23．
[155] Coyette J.P., Fyfe K.R. An improved formulation for acoustic eigenmode extractionfrom boundary element models [J]. ASME Transactions Journal of Vibration Acoustics,1990,112(3):392-397.
[156]赵志高．结构声辐射的机理与数值方法研究[D]．武汉：华中科技大学，2005．
[157] Langley R.S., Smith J.R.D., Fahy F.J. Statistical energy analysis of periodically stiffeneddamped plate structures [J]. Journal of Sound and Vibration,1997,208(3):407-426.
[158] Langley R.S. On the modal density and energy flow characteristics of periodic structures[J]. Journal of sound and vibration,1994,172(4):491-511.
[159] Norton M.P., Greenhalgh R. On the estimation of loss factors in lightly damped pipelinesystems: some measurement techniques and their limitations [J]. Journal of sound andvibration,1986,105(3):397-423.
[160] Wentang R., Attenborough K. Prediction of sound fields in rooms using statisticalenergy analysis [J]. Applied Acoustics,1991,34(3):207-220.
[161] Misaji K., Tada H., Yamashita T., et al. Testing uniqueness of a hybrid SEA modelingsolution for a passenger car [C]. SAE Paper,2009-01-1408.
[162] Moore J.A., Powell R., Bharj T. Development of condensed SEA models of passengervehicles [C]. SAE Technical Paper,1999-01-1699.
[163] Lee J., Powell R., Ni A., et al. Integration of SEA tire model with vehicle model [C].SAE Technical Paper,1999-01-1700.
[164] Chen H., O'Keefe M., Bremner P. A comparison of test-based and analytic SEA modelsfor vibro-acoustics of a light truck [C]. SAE Technical Paper,951329.
[165] Manning J.E. SEA models to predict structureborne noise in vehicles [C]. SAETechnical Paper,2003-01-1542.
[166] Moron P., Musser C. Use of SEA for vehicle target setting and efficient realization ofvehicle acoustic goals [C]. SAE Technical Paper,2006-01-1096.
[167] Musser C., Manning J., Peng G.C. Prediction of vehicle interior sound pressuredistribution with SEA [C]. SAE Technical Paper,2011-01-1705.
[168] Vaz I., Washburn K., DeVries L. Improvement of an SEA model of cab interior soundlevels through use of a hybrid FE/SEA method [C]. SAE Technical Paper2011-01-1706.
[169]靳晓雄，叶武平，丁玉兰．基于统计能量分析法的轿车内室噪声优化与控制[J]．同济大学学报，2002，30(7)：862-867．
[170]朱桂华，宫镇，胡均平，等．统计能量分析用于工程机械驾驶室噪声预估[J]．中南工业大学学报，2003，34(2)：166-166．
[171]王登峰，陈书明，曲伟，等．车内噪声统计能量分析预测与试验[J]．吉林大学学报，2009，39(1)：68-73．
[172]张肃，陈南，李普，等．基于小波迦辽金法的复杂封闭空腔结构—声耦合场分析[J]．机械工程学报，2008，44(6)：155-160．
[173]吴九汇．车辆内腔声固耦合分析的覆盖域方法研究[D]．西安：西安交通大学，2001．
[174] Wu J.H., Chen H.L., An W.B. A method to predict sound radiation from a plate-endedcylindrical shell excited by an external force [J]. Journal of sound and vibration,2000,237(5):793-803.
[175]吴九汇，陈花玲．任意开头封闭薄壳内部声场计算的一种新方法研究[J]．声学学报，2000，25(5)：468-471．
[176] Djamaa M.C., Ouelaa N., Pezeratb C., et al. Reconstruction of a distributed forceapplied on a thin cylindrical shell by an inverse method and spatial filtering [J]. Journalof Sound and Vibration,2007,301(3):560-575.
[177] Jang T.S., Sung H.G., Han S.L., et al. Inverse determination of the loading source of theinfinite beam on elastic foundation [J]. Journal of Mechanical Science and Technology,2008,22(12):2350-2356.
[178] Hansen P.C. Truncated SVD solution to discrete ill-posed problems with ill-determinednumerical rank [J]. SIAM Journal on Scientific and Statistical Computing,1990,11(3):503-518.
[179] Tikhonov A.N., Arsenin V.Y. Methods for solving ill-posed problems [M]. John Wileyand Sons, Inc,1977.
[180]肖庭延，于慎根，王彦飞．反问题的数值解法[M]．北京：科学出版社，2003．
[181]杨文献，任兴民，姜节胜．基于奇异熵的信号降噪技术研究[J]．西北工业大学学报，2001，19(3)：368-371．
[182] Morozov V.A. The error principle in the solution of operational equations by theregularization method [J]. USSR Computational Mathematics and Mathematical Physics,1968,8(2):63-87.
[183] Hansen P.C. Analysis of discrete ill-posed problems by means of the L-curve [J]. SIAMreview,1992,34(4):561-580.
[184] Golub G.H., Heath M., Wahba G. Generalized CROSS-validation as a method forchoosing a good ridge parameter [J].Technometracs,1979,21(2):215-222.
[185] Citarella R., Federico L., Cicatiello A. Model acoustic transfer vector approach in aFEM-BEM vibro-acoustic analysis [J]. Engineering Analysis with Boundary Elements,2007,31(3):248-258.
[186]张伟，刘献栋，单颖春，等．基于声传递向量法的路面激励引起车内噪声的仿真研究[J]．振动工程学报，2010，23(6)：39-43．
[187] Koopmann G.H., Song L., Fahnline J. A method for computing acoustic fields based onthe principle of wave superposition [J]. The Journal of the Acoustical Society ofAmerica,1989,86(5):2433-2438.
[188] Kim S.M., Brennan M.J. A compact matrix formulation using the impedance andmobility approach for the analysis of structural-acoustic system [J]. Journal of Soundand Vibration,1999,223(1):97-113.
[189] Ding W.P., Chen H.L. Research on the interior noise contributed from a local panel’svibration of an elastic thin-walled cavity [J]. Applied Acoustics,2002,63(1):95-102.
[190] Thite A.N., Thompson D.J. The quantification of structure-borne transmission paths byinverse methods. Part2: Use of regularization techniques [J]. Journal of Sound andVibration,2003,264:411-431.
[191] Verheij J.W. Inverse and reciprocity methods for machinery noise sourcecharacterization and sound path quantification [J]. International Journal of Acousticsand Vibration,1997,2(1):11-20.
[192] Fahy F.J. Some applications of the reciprocity principle in experimental vibroacoustics[J]. Acoustical Physics,2003,49(2):217-229.
[193] Williams E.G., Maynard J.D. Holographic imaging without the wavelength resolutionlimit [J]. Physical Review Letters,1980,45(7):554-557.
[194] Williams E.G. Fourier acoustics: sound radiation and nearfield acoustical holography[M]. Academic Press,1999.
[195] Veronesi W.A., Maynard J.D. Digital holographic reconstruction of sources witharbitrarily shaped surfaces [J]. The Journal of the Acoustical Society of America,1989,85(2):588-598.
[196]李加庆，陈进，史重九．基于声全息的故障诊断方法[J]．机械工程学报，2009，45(5)：34-38．
[197]邓江华，顾灿松，刘献栋，等．基于声阵列技术的汽车噪声源识别及贡献量分析[J]．振动工程学报，2010，23(006)：630-635．
[198]鲁文波，蒋伟康．基于近场声全息的故障诊断方法及系统实现[J]．振动与冲击，2013，32(5)：48-51．
[199] Maynard J.D., Williams E.G., Lee Y. Nearfield acoustic holography: I. Theory ofgeneralized holography and the development of NAH [J]. The Journal of the AcousticalSociety of America,1985,78(4):1395-1413.
[200] Veronesi W.A., Maynard J.D. Digital holographic reconstruction of sources witharbitrarily shaped surfaces [J]. The Journal of the Acoustical Society of America,1989,85(2):588-598.
[201] Williams E.G., Houston B.H. Interior near-field acoustical holography in flight [J]. TheJournal of the Acoustical Society of America,2000,108(4):1451-1463.
[202] Wu S.F., Yu J. Reconstructing interior acoustic pressure field via Helmholtz equationleast-squares method [J]. The Journal of the Acoustical Society of America,1998,104(4):2054-2060.
[203] Wu S.F. On reconstruction of acoustic pressure fields using the Helmholtz least squaresmethod [J]. The Journal of the Acoustical Society of America,2000,107(5):2511-2522.
[204] Ochmann M. The source simulation technique for acoustic radiation problems [J]. ActaAcustica united with Acustica,1995,81(6):512-527.
[205] Zhang Y.B., Jacobsen F., Bi C.X., et al. Near field acoustic holography based on theequivalent source method and pressure-velocity transducers [J]. The Journal of theAcoustical Society of America,2009,126(3):1257-1263.
[206] Wu S.F., Natarajan L.K. Panel acoustic contribution analysis [J]. The Journal of theAcoustical Society of America,2013,133(2):799-809.
[207] Song L., Koopmann G.H., Fahnline J.B. Numerical errors associated with the method ofsuperposition for computing acoustic fields [J]. The Journal of the Acoustical Society ofAmerica,1991,89(6):2625-2633.
[208] Fahnline J.B., Koopmann G.H. A numerical solution for the general radiation problembased on the combined methods of superposition and singular‐value decomposition [J].The Journal of the Acoustical Society of America,1991,90(5):2808-2819.
[209] Jeans R., Mathews I.C. The wave superposition method as a robust technique forcomputing acoustic fields [J]. The Journal of the Acoustical Society of America,1992,92(2):1156-1166.
[210]陈鸿洋，商德江，李琪，等．声场匹配波叠加法的水下结构声辐射预报[J]．声学学报，2013，38(2)：137-146．
[211]毕传兴，陈心昭，陈剑，等．基于等效源法的近场声全息技术[J]．中国科学(E辑)，2005，35(5)：535-548．
[212]李卫兵，陈剑，毕传兴，等．联合波叠加法的全息理论与实验研究[J]．物理学报，2006，55(3)：1264-1270．
[213]毕传兴，陈心昭，徐亮，等．基于等效源法的Patch近场声全息[J]．中国科学(E辑)，2007，37(9)：1205-1213．
[214]徐亮，毕传兴，陈剑，等．基于波叠加法的Patch近场声全息及其实验研究[J]．物理学报，2007，56(5)：2776-2783．
[215]张永斌，毕传兴，陈剑，等．基于等效源法的平面近场声全息及其实验研究[J]．声学学报，2007，32(6)：489-496．
[216]于飞，陈剑，李卫兵，等．腔体内三维声场重构与预测的波叠加方法[J]．自然科学进展，2005，15(1)：90-96．
[217] Sarkissian A. Method of superposition applied to patch near-field acoustic holography[J]. The Journal of the Acoustical Society of America,2005,118(2):671-678.
[218] Valdivia N.P., Williams E.G. Study of the comparison of the methods of equivalentsources and boundary element methods for near-field acoustic holography [J]. TheJournal of the Acoustical Society of America,2006,120(6):3694-3705.
[219] Bai M.R., Chen C.C., Lin J.H. On optimal retreat distance for the equivalent sourcemethod-based nearfield acoustical holography [J]. The Journal of the Acoustical Societyof America,2011,129(3):1407-1416.
[220]李加庆，陈进，杨超等．波叠加声场重构精度的影响因素分析[J]．物理学报，2008，57(7)：4258-4264．
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