内燃机排气消声器自动分析技术及评价技术研究
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摘要
汽车工业发展迅速,使得汽车噪声污染日益严重。减少进排气噪声是降低汽车噪声的关键,而安装消声器作为减少进排气噪声的主要方法,它的设计方法已经引起广泛重视,传统的设计为了满足消声量的要求,必须不断修改结构尺寸进行反复计算和实验,工作量很大,因此如何在缩短设计周期与设计成本的前提下设计出一个性能优良的消声器并预测其性能是需要解决的关键问题。
本文基于传统声学理论,从消声器设计需要出发,以ANSYS软件作为二次开发平台,通过对声学有限元理论和APDL程序参数化语言的学习研究,实现消声器声学性能的自动分析计算,并最终以VB.NET和DirectX9.0为开发工具,初步建立了以用户可视化建模界面为主的消声器设计系统。该系统包含用户参数化建模模块,声学性能自动仿真模块及声学性能评价模块。设计人员只需通过操作系统主界面工具栏中对消声器子结构的组合即可进行消声器的结构设计,并通过后台程序驱动ANSYS仿真计算,所有计算过程都不需要用户干预,计算完毕自动反馈给用户声学性能曲线;用户还可以选择不同频带范围的消声量作为评价指标,以消声器的某些子结构尺寸作为设计变量,进行消声器的灵敏度分析和结构优化。
接着本文在消声器传统声学性能指标基础上,进行了声学性能评价技术的研究。在传声损失评价方面,主要评价参数包括传声损失曲线包围的面积值、任意消声频率范围下的传声损失、比容传声损失、整个频段传声损失曲线存在的消声低谷、消声不足量频带及曲线波动率;在插入损失评价方面,包括各转速下插入损失声压级及消声器出口端噪声A计权总声压级和响度级的线性度。
本文最后通过几个设计实例,把实验得到的传声损失和插入损失曲线与本系统的计算结果对比,发现具有较高的吻合度,从而证明了系统的正确性和工程实用性。
The automobile noise pollution is becoming more and more severe with the development of automobile industry. The critical point of reducing the noise emission is to fix a muffler, the design of which has been extensively emphasized. Traditional design requires people to carry out the simulation and experiment repeatedly with diverse sizes of structures in order to meet the demand of noise loss, which is definitely a very painstaking manual labor. Thus, it quicly become a crutial issue needed to handle ungently that how to shorten the periodic time to obtain the muffler with great performance based on the minimal cost in budget.
Taking three dimensional finite element simulation as the muffler’s design approach, ANSYS is regarded as an second development tool with the support of traditional acoustics theory in this thesis. Through studying on the FEM theory the APDL language, the establishment of finite element model and automatic acoustic simulation of muffler come true. Finallly,by using the VB.NET and DirectX9.0, the muffler design sisyem including the visual modeling module, acustic performance simulation module and evaluation of acoustic behaivor model are building up.Among these different modules, all parameters in visual modeling module are transmitted to the next module with the type of correspond class enclosing.Based on the research in area of automatic analytical technology and evalution technology as well as mutual penetrating in each module,users only operates the toolbars in main interface,which will achieve the purpose of design. Then the outcome of acoustic performance running by ANSY due to the control of programme will present to the user without any manual interruption. After that, choosing trasmission loss in different rang of frequency as evaluation stardard and picking out several structure’s parameters which are used to be design variables, users can implement further research in term of analysis of structures’sensitive degree and structures’optimization.
To continue, this article also focuses on the research regarding to the evaluative technology of acoustic behaivor in term of transmission loss and insertion loss. In the area of transmission loss, the square measure of TL curve, TL value in given frequency range, TL of specific volume, detail about the low point and frequency band of insufficient noise elimination as well as waving rate are presented. In the area of insertion loss, taking the toal value of insertion loss and linear degree of muffler outlet’s sound pressure level into consideration would be a good way to reflect the IL performance. Combining with all parameters mentioned above will achive the comprehensive assessment of muffler’s acoustic behaivor.
At last, the outcome of this system accords with the experiment by comparing with acoustic performance curves in the same muffler, which can prove that the study on this thesis is accurate and meaningful.
本文基于传统声学理论,从消声器设计需要出发,以ANSYS软件作为二次开发平台,通过对声学有限元理论和APDL程序参数化语言的学习研究,实现消声器声学性能的自动分析计算,并最终以VB.NET和DirectX9.0为开发工具,初步建立了以用户可视化建模界面为主的消声器设计系统。该系统包含用户参数化建模模块,声学性能自动仿真模块及声学性能评价模块。设计人员只需通过操作系统主界面工具栏中对消声器子结构的组合即可进行消声器的结构设计,并通过后台程序驱动ANSYS仿真计算,所有计算过程都不需要用户干预,计算完毕自动反馈给用户声学性能曲线;用户还可以选择不同频带范围的消声量作为评价指标,以消声器的某些子结构尺寸作为设计变量,进行消声器的灵敏度分析和结构优化。
接着本文在消声器传统声学性能指标基础上,进行了声学性能评价技术的研究。在传声损失评价方面,主要评价参数包括传声损失曲线包围的面积值、任意消声频率范围下的传声损失、比容传声损失、整个频段传声损失曲线存在的消声低谷、消声不足量频带及曲线波动率;在插入损失评价方面,包括各转速下插入损失声压级及消声器出口端噪声A计权总声压级和响度级的线性度。
本文最后通过几个设计实例,把实验得到的传声损失和插入损失曲线与本系统的计算结果对比,发现具有较高的吻合度,从而证明了系统的正确性和工程实用性。
The automobile noise pollution is becoming more and more severe with the development of automobile industry. The critical point of reducing the noise emission is to fix a muffler, the design of which has been extensively emphasized. Traditional design requires people to carry out the simulation and experiment repeatedly with diverse sizes of structures in order to meet the demand of noise loss, which is definitely a very painstaking manual labor. Thus, it quicly become a crutial issue needed to handle ungently that how to shorten the periodic time to obtain the muffler with great performance based on the minimal cost in budget.
Taking three dimensional finite element simulation as the muffler’s design approach, ANSYS is regarded as an second development tool with the support of traditional acoustics theory in this thesis. Through studying on the FEM theory the APDL language, the establishment of finite element model and automatic acoustic simulation of muffler come true. Finallly,by using the VB.NET and DirectX9.0, the muffler design sisyem including the visual modeling module, acustic performance simulation module and evaluation of acoustic behaivor model are building up.Among these different modules, all parameters in visual modeling module are transmitted to the next module with the type of correspond class enclosing.Based on the research in area of automatic analytical technology and evalution technology as well as mutual penetrating in each module,users only operates the toolbars in main interface,which will achieve the purpose of design. Then the outcome of acoustic performance running by ANSY due to the control of programme will present to the user without any manual interruption. After that, choosing trasmission loss in different rang of frequency as evaluation stardard and picking out several structure’s parameters which are used to be design variables, users can implement further research in term of analysis of structures’sensitive degree and structures’optimization.
To continue, this article also focuses on the research regarding to the evaluative technology of acoustic behaivor in term of transmission loss and insertion loss. In the area of transmission loss, the square measure of TL curve, TL value in given frequency range, TL of specific volume, detail about the low point and frequency band of insufficient noise elimination as well as waving rate are presented. In the area of insertion loss, taking the toal value of insertion loss and linear degree of muffler outlet’s sound pressure level into consideration would be a good way to reflect the IL performance. Combining with all parameters mentioned above will achive the comprehensive assessment of muffler’s acoustic behaivor.
At last, the outcome of this system accords with the experiment by comparing with acoustic performance curves in the same muffler, which can prove that the study on this thesis is accurate and meaningful.
引文
[1]方丹群.噪声控制技术[M].上海:上海科学出版社,1986.
[2]何渝生,邓兆祥,陈朝阳.汽车噪声控制[M].北京:机械工业出版社,1999.
[3]马大猷.声学手册[M].北京:科学出版社,1983.
[4] Nishio Y. New approach to low-noise air intake system development[J].SAE Transactions, 1991.
[5] Young C I J C M J. Prediction of transmission loss in mufflers by the finite element method[J]. J.Acoust.Soc.Am, 1975, 57(1): 144-148.
[6] Panicker V.B., Munjal M.L. Aeroacoustic Analysis of Straight-through Mufflers with Simple and Extended Tube Expansion Chambers [J].J.Ind.Inst.Sc,1981,63(A):1-19.
[7] W.Sullivan Joseph, Crocker Malcolm J.Analysis of Concentric-Tube Resonators Having Unpartitioned Cavities [J]. Journal of the Acoustical Society of America, 1978, Vol.64, No.1 July: 207-215.
[8] Prased M.G., Crocker M.J. Evaluation of Four-pole Parameters for a Straight Pipe with Mean Glow and a Linear Temperature Gradient [J]. Journal of the Acoustical Society of America, 1981, 69(4): 916-921.
[9] Prased M.G., Crocker.M.J. Studies of Acoustical Performance of a Multi-cylinder Engine Exhaust Muffler System [J]. Journal of Sound and Vibration, 1983, 90(4): 491-508.
[10] Prased M.G., Crocker M.J. Insertion Loss Studies on Models of Automotive Exhaust Systems [J]. Journal of the Acoustical Society of America, 1981, 70(5):384-401.
[11] Peat K.S. A Numerical Decoupling Analysis of Perforated Pipe Silencer Elements [J]. Journal of Sound and Vibration, 1988 123(2): 199-212.
[12] Luo H., Tse C.C., Chen Y.N. Modeling and Application of PartiallyPerforated Intruding Tube Mufflers [J]. Applied Acoustic, Vol.53, 1995.
[13] Munjal M.L. Plane wave analysis of side inlet/out chamber Mufflers with mean flow [J]. Applied Acoustic, Vol.52, 1997.
[14] Barbieri Renato, Barbieri Nilson. Finite element acoustic simulation based shape optimization of a muffler [J].Applied Acoustic,Vol.67, 2006.
[15] Mehdizadeh Omid Z., Paraschivoiu Marius. A three-dimensional finite element approach for predicting the transmission loss in mufflers and silencers with no mean flow [J]. Applied Acoustic, Vol.66, 2005.
[16]赵松龄,盛胜我.抗性消声器中含穿孔管时的声传递矩阵[J].声学技术,2000,19(1):2-5.
[17]赵松龄,盛胜我.管道结构中含同轴穿孔管时的声传播特性[J].声学技术,1999,18(3):103-106.
[18]蔡超,宫镇,赵剑等.拖拉机抗性消声器声学子结构声传递矩阵研究[J].农业机械学报,1994,25(2):65-71.
[19]丁万龙.消声器的数值仿真分析[D].吉林:吉林大学硕士学位论文,2003.3.
[20]陆森林.内燃机排气消声器性能的三维有限元计算及分析[J].内燃机学报,2003,21(5):346-350.
[21]王耀前,陆森林. ANSYS在抗性消声器分析中的应用[J].江苏大学学报(自然科学版),2 003,24(3):53-56.
[22]李丰,黄协清,王少庭.复杂腔体扩张室消声器消声性能数值计算[J].噪声与振动控制,2004,2(l):14-16.
[23]董红亮,邓兆祥,姜艳军等.内燃机排气消声器多物理场分析及改进设计[J].内燃机工程,2008,29(1).
[24]丁律辉,黄其柏,周明刚等..汽车车桥CAE软件设计及接口技术研究[J].设计与研究,2006.
[25]李朔东,马纲.基于ANSYS的模态分析二次开发及应用[J].航天制造技术,2004(10).
[26]张明华,刘强,袁松海.基于ANSYS二次开发的机床主轴单元分析系统[J].机床与液压,2008,36(2).
[27] Heo S.C., J.Kim, Kang B.S. Investigation on determination of loading path to enhance formability in tube hydroforming process using APDL[J]. Journal of Materials Processing Technology, 2006.
[28] Kim C.H., Park J.H. , Kim Chul, Choi J.C. Expert system for process planning of pressure vessel fabrication by deep drawing and ironing[J]. Journal of Materials Processing Technology, 2004.
[29]李林凌,黄其柏,连小珉等.汽车消声器设计方法与评价指标分析[J].农业机械学报,2007,38(5).
[30]夏珩,郑四发,郝鹏等.汽车消声器多工况综合性能的评价方法[J].农业机械学报,2009,40(4).
[31]姜鹏明,富喜,吴帮玉.汽车消声器优化设计与综合评价指数[J].汽车工程,2008,30(3).
[32] Payri F., Torregrosa A.J., Payri R. Evaluation through pressure and mass velocity distributions of the linear acoustical description of I. C. engine exhaust systems[J]. Applied Acoustics, 2000.
[33]丁厚明.空调器噪声客观评价技术的研究与软件开发[D].南京:南京理工大学,2002.
[34]张国胜.基于遗传算法的汽车排气消声器优化设计研究及其软件开发[D].重庆:重庆大学,2005.
[35]于雅丽.消声器设计专家系统的研制[D].重庆:重庆大学,2007.
[36]赵明.汽车排气消声器声学特性研究[D].武汉:华中科技大学,2006.
[37]马大猷.噪声控制学[M].北京:科学出版社,1987.
[38]方忠甫.汽车排气消声器的数值分析方法研究[D].合肥:合肥工业大学,2006.
[39]黄其柏.工程噪声控制学[M].武汉:华中科技大学出版社,1999.
[40]方丹群,王文奇,孙加麟.噪声控制[M].北京:北京出版社,1986.
[41]张碧泉,吴国梁.抗性消声器插入损失的传递矩阵计算方法[J].噪声与振动控制,1999,(6):25-27.
[42]王诗恩,高宗英.抗性消声器的插入损失模型及其应用[J].内燃机工程,1996,17(3):35-40
[43]季振林,宋希庚.内燃机排气消声系统声学特性的数值预测[J].内燃机工程,1998,19(3):7-12.
[44]张世杰.排气消声器系统消声量的传递矩阵预测[J].汽车研究与开发,1995,(2):14-20.
[45]朱军,朱传敏,李秀丽.基于尺寸驱动参数化的产品结构设计系统研究[J].制冷空调与电力机械,2006,27:77-79.
[46]金建国,周明华,邬学军.参数化设计综述[J].计算机工程与应用,2003,7:16-18.
[47]潘双夏.基于工程约束的产品参数化建模策略研究[J].计算机辅助设计与图形学学报,2001(9)::840-84.
[48] Pemgt D.B. Resolving Feature Interaction in 3D Part Editing[J].Computer Aided Design.199 7(10) : 687-699.
[49]李浩.基于特征的参数化造型的思想[J].贵州工业大学学报,1999(6).
[50]李迎光,周儒荣.基于主参数信息模型的多实例库设计[J].计算机辅助设计与图形学学报,2006,16(1):135-138.
[51]周宁. ANSYS机械工程应用实例[M].北京:中国水利水电出版社,2006.
[52]周宁. ANSYS_APDL高级工程应用实例分析与二次开发[M].北京:水利水电出版社,2007.9.
[53] ANSYS APDL programmer's guide. ANSYS.Inc, 2002.
[54]博弈创作室编著. APDL参数化有限元分析技术及其应用[M].北京:中国水利水电出版社,2005.11.
[55]美国ANSYS公司. APDL使用指南[Z]. U.S.A: ANSYS INC,2001:1-85.
[56] ANSYS APDL programmer'sguide[M]. ANSYS.Inc, 2002.
[57] Klein Reinhard.Construction of constrained Delaunay triangulation of a polygon domain[J]. CAD System Development: Tools and Mehods, 1995: 313-326.
[58] Sapidis N., Peruchhio R. Delaunay Triangulation of Arbitrarily Shaped Domains[J]. Computer Aided Geometric Design, 1991, 8(6):421-437.
[59]丁永祥,夏巨谌,王英等.任意多边形的Delaunay三角剖分[J].计算机学报,1994,17(4):270~275.
[60]宋超,关振群,顾元宪.三维约束Delaunay三角化的边界恢复和薄元消除方法[J].计算力学学报,2004,21(2):169-196.
[61] Lewis R.W., Yao Z., Usmani A.S. Aspects of Adaptive Mesh Generation Based on Domain Decomposition and Delaunay Triangulation[J]. Finite Elements in Analysis and Design, 1995(20): 47-70.
[62] Barry.J. Construction of three-dimensional Delaunay triangulations using local transformations [J]. Computer Aided Geometric Design, 1991(8): 123-142.
[63]赵松龄.噪声的减低与隔离[M].上海:同济大学出版社,1989.
[64]秦树人,张明洪,罗德扬.机械工程测试原理与技术[M].重庆:重庆大学出版社,2002.8.
[65]范蓉平,孟光,孙旭等.基于心理声学响度分析的高速列车车内噪声评价[J].振动与冲击,2005,24(5).
[66]马大猷.现代声学理论基础[M].北京:科学出版社,2004.3.
[2]何渝生,邓兆祥,陈朝阳.汽车噪声控制[M].北京:机械工业出版社,1999.
[3]马大猷.声学手册[M].北京:科学出版社,1983.
[4] Nishio Y. New approach to low-noise air intake system development[J].SAE Transactions, 1991.
[5] Young C I J C M J. Prediction of transmission loss in mufflers by the finite element method[J]. J.Acoust.Soc.Am, 1975, 57(1): 144-148.
[6] Panicker V.B., Munjal M.L. Aeroacoustic Analysis of Straight-through Mufflers with Simple and Extended Tube Expansion Chambers [J].J.Ind.Inst.Sc,1981,63(A):1-19.
[7] W.Sullivan Joseph, Crocker Malcolm J.Analysis of Concentric-Tube Resonators Having Unpartitioned Cavities [J]. Journal of the Acoustical Society of America, 1978, Vol.64, No.1 July: 207-215.
[8] Prased M.G., Crocker M.J. Evaluation of Four-pole Parameters for a Straight Pipe with Mean Glow and a Linear Temperature Gradient [J]. Journal of the Acoustical Society of America, 1981, 69(4): 916-921.
[9] Prased M.G., Crocker.M.J. Studies of Acoustical Performance of a Multi-cylinder Engine Exhaust Muffler System [J]. Journal of Sound and Vibration, 1983, 90(4): 491-508.
[10] Prased M.G., Crocker M.J. Insertion Loss Studies on Models of Automotive Exhaust Systems [J]. Journal of the Acoustical Society of America, 1981, 70(5):384-401.
[11] Peat K.S. A Numerical Decoupling Analysis of Perforated Pipe Silencer Elements [J]. Journal of Sound and Vibration, 1988 123(2): 199-212.
[12] Luo H., Tse C.C., Chen Y.N. Modeling and Application of PartiallyPerforated Intruding Tube Mufflers [J]. Applied Acoustic, Vol.53, 1995.
[13] Munjal M.L. Plane wave analysis of side inlet/out chamber Mufflers with mean flow [J]. Applied Acoustic, Vol.52, 1997.
[14] Barbieri Renato, Barbieri Nilson. Finite element acoustic simulation based shape optimization of a muffler [J].Applied Acoustic,Vol.67, 2006.
[15] Mehdizadeh Omid Z., Paraschivoiu Marius. A three-dimensional finite element approach for predicting the transmission loss in mufflers and silencers with no mean flow [J]. Applied Acoustic, Vol.66, 2005.
[16]赵松龄,盛胜我.抗性消声器中含穿孔管时的声传递矩阵[J].声学技术,2000,19(1):2-5.
[17]赵松龄,盛胜我.管道结构中含同轴穿孔管时的声传播特性[J].声学技术,1999,18(3):103-106.
[18]蔡超,宫镇,赵剑等.拖拉机抗性消声器声学子结构声传递矩阵研究[J].农业机械学报,1994,25(2):65-71.
[19]丁万龙.消声器的数值仿真分析[D].吉林:吉林大学硕士学位论文,2003.3.
[20]陆森林.内燃机排气消声器性能的三维有限元计算及分析[J].内燃机学报,2003,21(5):346-350.
[21]王耀前,陆森林. ANSYS在抗性消声器分析中的应用[J].江苏大学学报(自然科学版),2 003,24(3):53-56.
[22]李丰,黄协清,王少庭.复杂腔体扩张室消声器消声性能数值计算[J].噪声与振动控制,2004,2(l):14-16.
[23]董红亮,邓兆祥,姜艳军等.内燃机排气消声器多物理场分析及改进设计[J].内燃机工程,2008,29(1).
[24]丁律辉,黄其柏,周明刚等..汽车车桥CAE软件设计及接口技术研究[J].设计与研究,2006.
[25]李朔东,马纲.基于ANSYS的模态分析二次开发及应用[J].航天制造技术,2004(10).
[26]张明华,刘强,袁松海.基于ANSYS二次开发的机床主轴单元分析系统[J].机床与液压,2008,36(2).
[27] Heo S.C., J.Kim, Kang B.S. Investigation on determination of loading path to enhance formability in tube hydroforming process using APDL[J]. Journal of Materials Processing Technology, 2006.
[28] Kim C.H., Park J.H. , Kim Chul, Choi J.C. Expert system for process planning of pressure vessel fabrication by deep drawing and ironing[J]. Journal of Materials Processing Technology, 2004.
[29]李林凌,黄其柏,连小珉等.汽车消声器设计方法与评价指标分析[J].农业机械学报,2007,38(5).
[30]夏珩,郑四发,郝鹏等.汽车消声器多工况综合性能的评价方法[J].农业机械学报,2009,40(4).
[31]姜鹏明,富喜,吴帮玉.汽车消声器优化设计与综合评价指数[J].汽车工程,2008,30(3).
[32] Payri F., Torregrosa A.J., Payri R. Evaluation through pressure and mass velocity distributions of the linear acoustical description of I. C. engine exhaust systems[J]. Applied Acoustics, 2000.
[33]丁厚明.空调器噪声客观评价技术的研究与软件开发[D].南京:南京理工大学,2002.
[34]张国胜.基于遗传算法的汽车排气消声器优化设计研究及其软件开发[D].重庆:重庆大学,2005.
[35]于雅丽.消声器设计专家系统的研制[D].重庆:重庆大学,2007.
[36]赵明.汽车排气消声器声学特性研究[D].武汉:华中科技大学,2006.
[37]马大猷.噪声控制学[M].北京:科学出版社,1987.
[38]方忠甫.汽车排气消声器的数值分析方法研究[D].合肥:合肥工业大学,2006.
[39]黄其柏.工程噪声控制学[M].武汉:华中科技大学出版社,1999.
[40]方丹群,王文奇,孙加麟.噪声控制[M].北京:北京出版社,1986.
[41]张碧泉,吴国梁.抗性消声器插入损失的传递矩阵计算方法[J].噪声与振动控制,1999,(6):25-27.
[42]王诗恩,高宗英.抗性消声器的插入损失模型及其应用[J].内燃机工程,1996,17(3):35-40
[43]季振林,宋希庚.内燃机排气消声系统声学特性的数值预测[J].内燃机工程,1998,19(3):7-12.
[44]张世杰.排气消声器系统消声量的传递矩阵预测[J].汽车研究与开发,1995,(2):14-20.
[45]朱军,朱传敏,李秀丽.基于尺寸驱动参数化的产品结构设计系统研究[J].制冷空调与电力机械,2006,27:77-79.
[46]金建国,周明华,邬学军.参数化设计综述[J].计算机工程与应用,2003,7:16-18.
[47]潘双夏.基于工程约束的产品参数化建模策略研究[J].计算机辅助设计与图形学学报,2001(9)::840-84.
[48] Pemgt D.B. Resolving Feature Interaction in 3D Part Editing[J].Computer Aided Design.199 7(10) : 687-699.
[49]李浩.基于特征的参数化造型的思想[J].贵州工业大学学报,1999(6).
[50]李迎光,周儒荣.基于主参数信息模型的多实例库设计[J].计算机辅助设计与图形学学报,2006,16(1):135-138.
[51]周宁. ANSYS机械工程应用实例[M].北京:中国水利水电出版社,2006.
[52]周宁. ANSYS_APDL高级工程应用实例分析与二次开发[M].北京:水利水电出版社,2007.9.
[53] ANSYS APDL programmer's guide. ANSYS.Inc, 2002.
[54]博弈创作室编著. APDL参数化有限元分析技术及其应用[M].北京:中国水利水电出版社,2005.11.
[55]美国ANSYS公司. APDL使用指南[Z]. U.S.A: ANSYS INC,2001:1-85.
[56] ANSYS APDL programmer'sguide[M]. ANSYS.Inc, 2002.
[57] Klein Reinhard.Construction of constrained Delaunay triangulation of a polygon domain[J]. CAD System Development: Tools and Mehods, 1995: 313-326.
[58] Sapidis N., Peruchhio R. Delaunay Triangulation of Arbitrarily Shaped Domains[J]. Computer Aided Geometric Design, 1991, 8(6):421-437.
[59]丁永祥,夏巨谌,王英等.任意多边形的Delaunay三角剖分[J].计算机学报,1994,17(4):270~275.
[60]宋超,关振群,顾元宪.三维约束Delaunay三角化的边界恢复和薄元消除方法[J].计算力学学报,2004,21(2):169-196.
[61] Lewis R.W., Yao Z., Usmani A.S. Aspects of Adaptive Mesh Generation Based on Domain Decomposition and Delaunay Triangulation[J]. Finite Elements in Analysis and Design, 1995(20): 47-70.
[62] Barry.J. Construction of three-dimensional Delaunay triangulations using local transformations [J]. Computer Aided Geometric Design, 1991(8): 123-142.
[63]赵松龄.噪声的减低与隔离[M].上海:同济大学出版社,1989.
[64]秦树人,张明洪,罗德扬.机械工程测试原理与技术[M].重庆:重庆大学出版社,2002.8.
[65]范蓉平,孟光,孙旭等.基于心理声学响度分析的高速列车车内噪声评价[J].振动与冲击,2005,24(5).
[66]马大猷.现代声学理论基础[M].北京:科学出版社,2004.3.