用户名: 密码: 验证码:
车用镁合金材料NVH性能研究及镁质仪表板声学优化设计
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
镁合金是目前应用的最轻的结构材料,并以其高阻尼性能、高比强度、高比刚度等特点,在汽车工业中得到日益广泛的应用。当镁合金替换原有的车用金属材料后,必将影响整车的NVH性能。因此开展镁合金车身构件的声学性能研究势在必行。本文针对镁合金材料应用于车身仪表板后遇到的声学问题展开了研究工作。
     采用脉冲响应衰减法测量了镁合金AZ31的阻尼性能。用板件结构的近场辐射声压代替了表面振动信号,避免了接触式振动传感器引入的附加质量和边界约束阻尼的影响,使测试结果更加准确。利用窄带带通滤波器处理近场声压信号,求取了低频段单个模态下的阻尼损耗因子及高频段单个带宽内的平均阻尼损耗因子。镁合金AZ31的阻尼损耗因子在0-3000Hz范围内为2~25×10-4。同时测量了钢的阻尼损耗因子作为对比。实验结果表明镁合金的阻尼性能比钢好。
     在镁合金板件隔声性能的研究上,根据声波在声学介质分界面处的声学边界条件及牛顿定律,推导了平面声波入射场和扩散声波入射场下,单层镁合金板的声阻抗率和隔声量理论计算公式。依靠自行设计、制造的驻波管,测量声波正入射条件下镁合金圆形板件的噪声衰减量,比较了单层板、双层板的测量结果,分析板件厚度、板间空气层厚度及板件放置次序等因素对构件隔声性能的影响。
     本文提出一种预测复杂构件的隔声性能的仿真方法——结构-声耦合分析法,经实验验证,该方法准确可靠。利用结构-声耦合分析法,预测了克莱斯勒Viper仪表板及凯迪拉克CTS仪表板在中低频范围内的隔声性能。研究发现,用镁合金替换原钢质材料,当重量减轻30%-40%时,仪表板的隔声性能不会恶化。且由于阻尼的衰减作用,在低频段隔声性能甚至有所改善。改善仪表板上穿通元件的密封情况,提高边界连接刚度可提高仪表板整体的隔声性能。
     利用面板声贡献量分析法,成功地对镁合金仪表板隔声性能在“关键频率”下的“关键区域”进行定位。以Biot-Allard模型为基础,得到了声学包装起隔声作用时的声学导纳,以此为边界条件,准确地预测了复合镁质仪表板的隔声性能。研究指出,随着吸声材料厚度的增加,复合仪表板的隔声量不是单调增加的,在设计复合结构仪表板时,要同时考虑成本与低频“隔声恶化”的问题,合理选取吸声材料的厚度。
     建立了一整车结构-声耦合有限元模型,计算了复合镁质仪表板五个板件的各层声学包装的厚度对驾驶员耳旁一点声压的结构-声学灵敏度。依据灵敏度分析结果,用“可行方向法”优化目标点声学性能,使目标点声压在整个频率范围内最低。优化后的复合镁质仪表板质量减轻了3.6kg,目标点总声压级由78.1dB降至76.1dB,实现了轻量化、低噪声镁合金仪表板优化设计。
Magnesium alloy is the lightest application structural material at present, and has large specific stiffness, great damping and excellent shock absorption. It had been made into automotive dash successfully. If original automotive metal materials are replaced by magnesium alloy, the vehicle NVH performance must be affected. Hence, researching on acoustic performance of automotive components is imperative. Applying magnesium alloy to automotive dash might meet acoustic problems. In this dissertation, these acoustic problems were investigated.
     Damping performance of magnesium alloy AZ31was researched with the impulse response decay method (IRDM). The sound pressure near the magnesium alloy sheet substituted for vibration signals of sheet surface. It could avoid additional mass and boundary constrained damping caused by contact vibration sensors, and got more accurate test results. The near-field sound pressure signals were filtered by band-pass filter. Based on these filtered signals, damping loss factor(DLF) of one modal in low frequency range and average damping loss factor of one frequency band in high frequency range were calculated. DLF of magnesium alloy AZ31is2-25×10-4in0-3000Hz. DLF of steel was measured meanwhile. The results showed that damping performance of magnesium alloy is better than steel.
     In the respect of research on sound insulation of magnesium alloy plate, based on acoustic boundary condition on interface of acoustic medium and Newton's laws, sound impedance radio and sound transmission loss theoretical formulas of single-layer plate in the plane-wave and diffuse incident acoustic field were derived respectively. Noise reduction of circular magnesium alloy plate in normal sound incident field was measured with self-designed standing wave tube. Compare the results of single-layer plate and double-layer plate to analyze the influence factors of sound insulation performance, such as thickness of plate, thickness of air layer between two plates and order of two plates.
     This dissertation advanced a simulation method to be used for predicting sound insulation performance of complex components——structural-acoustic coupling method. Validated by experiments, the method is accurate and reliable. The sound insulation performance of Chrysler Viper dash and Cadillac CTS dash in low-mid frequency range were predicted with this method. The research results showed that replacing steel by magnesium alloy, dash reduced weight by 30%-40%, while acoustic performance didn't deteriorate. Because of damping, sound insulation performance even improved in low frequency range. Improving seal of flanking paths and enhancing connect stiffness can increase overall sound insulation performance of dash.
     Based on panel acoustic contribution analysis,"key regions" in "key frequency" range of magnesium alloy dash for sound insulation were identified successfully. Based on Biot-Allard model, acoustic admittance of sound package (transmission-like condition) was calculated. Applying this admittance to laminated magnesium alloy dash, sound insulation performance of the dash was obtained accurately. Research indicates that sound transmission loss of laminated dash doesn't increase monotonically with the increase of thickness of porous-absorbed material. So when designing laminated dash, cost and "sound insulation performance deterioration" in low frequency range should be taken into account simultaneously and chose appropriate thickness of absorbing material.
     Established structural-acoustic coupling finite element model of a vehicle, and divided the laminated dash into five panels, the structural-acoustic sensitivities of sound pressure at driver's ear position with respect to each layer's thickness of each panel of laminated magnesium alloy dash were calculated. According to the sensitivities, the target point's acoustic performance was optimized with "feasible direction method" to minimize its sound pressure in whole frequency range. The weight of optimized laminated magnesium alloy dash is reduced3.6kg, and overall sound pressure level at target point drops from78.1dB to76.1dB. The light-weight, low-noise design for magnesium alloy dash is achieved.
引文
1. 潘复生,张津,张喜燕等.轻合金材料新技术[M].北京:化学工业出版社,2008:12-17.
    2. 石力开.中国新材料产业发展报告(2004)[M].北京:化学工业出版社,2004:115-140.
    3. 丁文江等.镁合金科学与技术[M].北京:科学出版社,2007:371-376.
    4. 镁合金压铸技术的几个主要问题及其应用前景[OL].2005.12.http://www.mbal 63.com/glwk/hyzt/qchy/200512/16918_5.html
    5. Zhang X N, Wu R J. Damping capacity of pure Mg metal matrix composites[J]. Key Engineering Materials,2003,249:217-222.
    6. 曾荣昌,柯伟,徐永波等.Mg合金的最新发展及应用前景[J].金属学报,2001,37(7):673—685.
    7. Froes F H, Eliezer D, Aghion E. The science, technology and applications of magnesium[J]. JOM,1998(9):30-33.
    8. Kojima Y. Platform science and technology for advanced magnesium alloy [J]. Material Science Forum,2000,350-351:3-12.
    9. Fantozzi G, Esnouf C, Seyed S M, et al. An elastic behavior of plastically deformed high purity magnesium between 10 an 500 K[J]. Acta Metallurgica,1984,32(12): 2175-2183.
    10. Amelinckx S, Gevers R, Nihoul J. Internal Friction of Structural Defects in Crystalline Solids r[M]. North—Holland Pub Co,1972.255.
    11. Koichi Sugimoto, Kazunori Niiya, Taira Okamoto, et al. A study of damping capacity in magnesium alloys [J]. Transactions of Japan Institute Metals,1977(18):277-288.
    12. Granato A, Lucke K. Theory of mechanical damping due to dislocations[J]. Journal of Applied Physics,1956,27(6):583-593.
    13. Granato A, Lucke K. Application of dislocation theory to internal friction phenomena at high frequencies [J]. Journal of Applied Physics,1956,27(7):789-805.
    14. Koichi Sugimoto, Kuniaki Matsui, Taira Okamoto, et al. Effect of crystal orientation on amplitude-dependent damping in magnesium[J]. Transactions of Japan Institute Metals, 1975(16):647-655.
    15.张小农.金属基复合材料的阻尼行为研究[D].上海交大博士学位论文,1997.
    16. Zhenyan Zhang, Xiaoqin Zeng, Wenjiang Ding. The influence of heat treatment on damping response of AZ91D magnesium alloy[J]. Materials Science and Engineering:A,2005(392): 150-155.
    17.王敬丰,赵亮,胡耀波等.阻尼镁合金的研究现状与发展趋势[J].材料导报.2008,22(7): 103-106.
    18.张平,丁毅,马立群等.镁合金的阻尼性能研究[J].物理学进展.2006(26):419-422.
    19. Richard H. Lyon, Richard G. Dejong. Theory and application of statistical energy analysis[M]. R.H. Lyon Corp,1995.
    20. Maxime Bolduc, Nourddine Atalla, Andrew Wareing. Measurement of SEA damping loss factor for complex structures[J]. SAE,2005-01-2327.
    21. M. Carfagni, M. Pierini. Determining the loss factor by power input method(PIM), Part 1: Numerical investigation[J]. Journal of Vibration and Acoustics.1999(121):417-421.
    22. Lalor N, Wang X. Acquiring SEA parameters on complex structures by a transient test method[R]. ISVR technical report No.192.1991.
    23. Brown K T, Clarkson B L. Average loss factors for use in statistical energy analysis[J]. Vibration Damping Workshop.1984.
    24. M P Norton, R Greenhalgh. On the estimation of loss factors in lightly damped pipeline systems:some measurement techniques and their limitations[J]. Journal of Sound and Vibration.1986,105(3):397-423.
    25. Schroeder M.R. New method of measuring reverberation time[J]. Journal of the Acoustical Society of America.1965(37):409-412.
    26.宁方华,张建.损耗因子测量的Hilbert变换法[J].山东工程学院学报.2002,16(1):17-20.
    27.程广利,关成彬,胡生亮.基于Hilbert变换的结构内损耗因子测试研究[J].噪声与振动控制.2006(4):105-107.
    28.赵跃英,盛胜我.薄壁构件的阻尼振动衰减因子的测量[J].同济大学学报,2002,30(7):900-903.
    29.GBJ75-1984.建筑隔声测量规范[S].北京:中国标准出版社,1984.
    30. Oliviero Olivieri, J. Stuart Bolton, Taewook Yoo. Measurement of transmission loss of materials using a standing wave tube[J]. INTER-NOISE 2006.2006,12. HONOLULU, HAWAII, USA.
    31.朱蓓丽,罗晓辉.驻波管中的隔声量测试方法[J].噪声与振动控制.2000(6):41-43.
    32.曲波,朱蓓丽.驻波管中隔声量的四传感器测量法[J].噪声与振动控制.2002(6):44-46.
    33.彭东立,胡碰,朱蓓丽.驻波管中介质板复透射系数的修正计算方法[J].上海交通大学学报.2007,41(4):649-653.
    34. J. W. S. Rayleigh. The Theory of Sound[M]. London, Macmillan, St. Martin's Street.,1929.
    35. Novikov Ⅱ. Low-frequency sound insulation of thin plates[J]. Applied Acoustics 1998,54: 83-90.
    36. L. Cremer. Theorie der Schalldammung dunner Wande bei Schragem Einfall. Akustische Zeitschrift[J],1942,81-104.
    37. B.H. Sharp. Prediction methods for the sound transmission of building elements [J]. Noise Control Engineering,1978,53-63.
    38. E.C. Sewell. Transmission of reverberant sound through a single-leaf partition surrounded by an infinite rigid baffle[J]. J. Sound Vib.,1970,12:21-32.
    39. J.D. Quirt. Sound transmission through windows, I:single and double glazing[J]. J. Acoust. Soc. Am.,1982,72:834-844.
    40. J.A. Marsh. The airborne Sound insulation of glass, part Ⅰ[J]. Applied Acoust,1971,4: 55-70.
    41. London. Transmission of reverberant sound through double walls[J]. J. Acoust. Soc. Am., 1950,22:270-279.
    42. Leo L. Beranek. Noise reduction[M]. McGraw-Hill,1960.
    43. Fahy F. Foundations of engineering acoustics[M]. Academic Press; 2001.
    44.范玉岭,王敏庆.复合板隔声性能分析[J].噪声与振动控制.2007(2):90-93.
    45.陈卫松,邱小军.多层板的隔声特性研究[J].南京大学学报(自然科学).2005,41(1):91-97.
    46. Panneton R, Atalla N. Numerical prediction of sound transmission through finite multilayer systems with poroelastic materials[J]. J Acoust Soc Am 1996,100(1):346-354.
    47. Sgard FC, Atalla N, Nicolas J. A numerical model for the low frequency diffuse field sound transmission loss of double-wall sound barriers with elastic porous linings[J]. J Acoust Soc Am 2000,108(6):2865-2872.
    48.曲波.用有限元法分析声学材料的声学性能[D].硕士学位论文.上海:上海交通大学2003.2.
    49.王英敏,胡碰,朱蓓丽.单层薄板在共振频率区隔声性能的有限元分析[J].噪声与振动控制.2006(4):55-58.
    50. A.J. Price, M.J. Crocker. Sound transmission through double panels using statistical energy analysis[J]. J. Acoust. Soc. Am.,1970,47:683-693.
    51. Terence Connelly, James D. Knittel, Ramkumar Krishnan et al. The Use of in Vehicle STL Testing to Correlate Subsystem Level SEA Models [J]. SAE,2003-01-1564.
    52. Qijun Zhang, Alan Parrett, Michelle Wood. Vehicle Dash Mat SEA Modeling and Correlation[J]. SAE,2007-01-2310.
    53. Charpentier, D. Blanchet, K. Fukui. Full Vehicle SEA Model Uses Detailed Sound Package Definition to Predict Driver's Headspace Acoustic Response[C]. The 33rd International Congress and Exposition on Noise Control Engineering.2004.
    54.叶武平,易明,靳晓雄等.运用统计能量分析法进行轿车内室噪声的仿真[J].同济大学学报.2001,29(9):1066-1071.
    55.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.
    56.宫镇,夏恒,曾发林等.高速车辆内部气流噪声的统计能量分析[J].农业机械学报.2003,34(2):7-1 0.
    57. MSC.Nastran Design Sensitivity and Optimization User's Guide,2004.
    58. Zheng-Dong Ma, Ichiro Hagiwara. Sensitivity Analysis Methods for Coupled Acoustic-Structural System, Part Ⅰ:Modal Sensitivity[J]. AIAA journal.1991,29(5): 113-125.
    59. Zheng-Dong Ma, Ichiro Hagiwara. Sensitivity Analysis Methods for Coupled Acoustic-Structural System, Part Ⅱ:Direct frequency response and its sensitivities[J]. JSME International Journal.1992,35 (3):14-21.
    60. K. K. Choi, I. Shim, S. Wang. Design sensitivity analysis of structure-induced noise and vibration[J]. J. Vib. Acoust.1997,119(3):173-179.
    61. S. Wang. Design sensitivity analysis of noise, vibration, and harshness of vehicle body structure[J]. Mech. Struct. Mach.1999,27 (3):317-336.
    62. Semyung Wang, Jeawon Lee. Acoustic Design Sensitivity Analysis and Optimization for Reduced Exterior Noise [J]. AIAA Journal.2001,39(4):1237-1245.
    63.张永斌,毕传兴,陈剑等.基于波叠加的结构-声学灵敏度分析的伴随变量方法[J].机械工程学报.2009,45(4):177-182.
    64.陈剑,程昊,高煜等.基于多域边界元法的声学形状灵敏度分析[J].振动工程学报.2008,21(3):319-322.
    65.吴小清,王登峰,徐诚等.壁面有吸声材料时驾驶室内噪声响应的灵敏度分析[J].农业工程学报.1999,15(3):151-155.
    66.邓江华,刘献栋,李兴虎等.车身阻尼层结构的声灵敏度分析及优化[J].噪声与振动控制.2009,1:54-58.
    67.丁文江等.镁合金科学与技术[M].北京:科学出版社,2007,179-181.
    68.田铁.镁合金阻尼特性的实验研究[D].硕士学位论文.重庆:重庆理工大学.2008,9-11.
    69.程耀东,李培玉.机械振动学(线性系统)[M].杭州:浙江大学出版社.2005,36-42.
    70. Brandon C. Bloss, Mohan D. Rao. Estimation of frequency-averaged loss factors by the power injection and the impulse response decay methods [J]. Journal of Acoustical Society of America,2004,117(1):240-249.
    71.姚德源,王其政.统计能量分析[M].北京:北京理工大学出版社.1995,76-79.
    72. Maxime Bolduc, Nourddine Atalla. Measurement of SEA Damping Loss Factor for Complex Structures [J]. SAE,2005-01-2327
    73.莫尔斯PM,英格特K U.理论声学:上册[M].北京:科学出版社,1984.
    74.张津,陶艳玲,孙智富等.镁合金AZ91D的阻尼减振性能[J].机械工程学报,2006,42(10):186-189.
    75.王济,胡晓MATLAB在振动信号处理中的应用[M].北京:中国水利水电出版社2006:69-82.
    76.陈馨蕊,郝志勇,杨陈.镁合金AZ31阻尼性能的实验研究[J].浙江大学学报(工学版),2010,44(1):19-22.
    77.刘楚明,纪仁峰,周海涛等.镁及镁合金阻尼特性的研究进展[J].中国有色金属学报,2005,15(9):1319-1325.
    78.訾炳涛,王辉.镁合金及其在工业中的应用[J].稀有金属,2004,28(1):229-232.
    79.岳岩,刘继生.铁路客车车窗玻璃结构型式对隔声效果的影响[J].铁道车辆,2000,38(10):18-20.
    80.许林云,蒋本浩,李明才等.汽车发动机隔声仓的设计[J].江苏理工大学学报,1995,16(4):13-18.
    81.何琳,朱海潮,邱小军等.声学理论与工程应用[M].北京:科学出版社.2006,173-182,168-169.
    82.杜功焕,朱哲民,龚秀芬.声学基础[M]南京:南京大学出版社.2001,106-108.
    83.沈山豪.声学测量[M].科学出版社,1986.
    84. Beranek Leo Leroy. Acoustic Measurements. Wiley, New York,1949, pp.844.-847.
    85.冯璃正.轻结构隔声原理与应用技术[M].科学出版社,1987.
    86.李晓敏.压铸镁合金在汽车中的应用及其发展前景[J].世界有色金属,2001,9:16-18.
    87.陈力禾.镁合金压铸及其在汽车工业中的应用[J].铸造.1999(10):45-47.
    88.黎胜,赵德有.用耦合有限元/边界元方法研究加筋板的声传输[J].振动工程学报.2001,14(3):364-367.
    89. S. Suziki, M. lmai, and S. lshiyama. Boundary element analysis of structural-acoustic problems[M]. Bounday Elements VI (Springer-Verlag, New York,).1984:27-35.
    90. V. B. Bokil. Modal analysis of gyroscopically coupled sound-structure interaction problems[D]. Old Dominion University, Norfolk, Virginia,1992.
    91. A.F. Seybert, N. T.W. Wu, W.L. Li. A Coupled FEM/BEM for Fluid-structure Interaction Using Ritz Vectors and Eigenvectors [J]. Trans. ASME. J. Vibr. Acoust.,1993 (115): 152-158.
    92.徐张明,沈荣瀛,华宏星.利用FEM/IBEM计算流体介质中的壳体的结构声耦合问题[J].振动工程学报.2002,15(3):363-367.
    93.杨景义,王信义.试验模态分析[M].北京:北京理工大学出版社,1990.
    94.陈馨蕊,郝志勇,杨陈等.结构-声耦合法在汽车仪表板隔声性能仿真分析中的应用[J].振动与冲击,2009,28(8):154-157.
    95. Kin. L. Hong and S. T. Raveendra. Sound Transmission Loss Analysis of an Automotive Dash by Finite Element Method[J]. SAE,2003-01-1613.
    96.张新安,振动吸声理论及声学设计[M].西安:西安交通大学出版社.2007:77-80.
    97. Allard J F. Propagation of sound in porous media modeling sound absorbing materials [M]. New York:Elsevier Applied Science,1993:76-77.
    98. Biot M A. Theory of propagation of elastic waves in a fluid-saturated porous solid [J]. J Acoustic Soc Am,1955,28(2):168-191.
    99.张波,陈天宁.烧结金属纤维材料的吸声模型研究[J].西安交通大学学报,2008,42(3):328-332.
    100.Zhang Y K, Lee M R, Stanecki P J, et al. Vehicle noise and weight reduction using panel acoustic contribution analysis [J].SAE Paper 951338,1995:2411-2421.
    101.Mohanty A R, St Pierre B D, Suruli-Narayanasami P. Structure-borne noise reduction in a truck cab interior using numerical techniques [J].Applied Acoustics,2000,59(1):1-17.
    102.Wolff O, Sottek R. Panel contribution analysis——An alternative window method [J].SAE Paper,2005-01-2274.
    103.靳晓雄,白胜勇,丁玉兰等.车身板件振动声学贡献的计算机模拟[J].汽车工程,2000,22(4):235-239.
    104.Ding W, Chen H. Research on the interior noise contributed from a local panel's vibration of an elastic thin-walled cavity [J].Applied Acoustics,2002,63(1):95-102.
    105.梁新华,朱平,林忠钦,等.基于有限元法和边界元法的轻量化车身声学分析[J].上海交通大学学报,2006,40(1):177-180.
    106.Kim K C, Kim C M. Process of designing body structures for the reduction of rear seat noise in passenger car [J].International Journal of Automotive Technology,2007,8(1): 67-73
    107.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.
    108.李增刚SYSNOISE Rev5.6详解[M].北京:国防工业出版社.2005:168-169.
    109.C F McCulloch, Dr L Cremers, P Guisset. PREDICTIVE MODELS OF TRANSMISSION LOSS OF PANELS WITH MULTI-LAYER TREATMENTS[R]. LMS International, Interleuvenlaan 68, B-3001 Leuven, Belgium.1997.
    110.陈馨蕊,郝志勇,刘迟.汽车镁质复合仪表板传声损失的实验及仿真研究[J].振动与冲击,2010,29(11):40-43.
    111.HAMBRIC S A. Sensitivity calculation for broadband acoustic radiated noise design optimization problems[J]. J. Vib. Acoust.1995,117(1):136-144.
    112.CHOI K K, SHIM I, WANG S. Design sensitivity analysis of structure-induced noise and vibration[J]. J.Vib.Acoust.1997,119(3):173-179.
    113.WANG S. Design sensitivity analysis of noise, vibration, and harshness of vehicle body structure[J]. Mech. Struct. Mach.1999,27 (3):317-336.
    114.白杨,汪鸿振.声学—结构设计灵敏度分析[J].振动与冲击.2003,22(3):43-45.
    115.张军.声学—结构灵敏度及结构—声学优化设计研究[D].大连:大连交通大学.2006:64-77.
    116.江爱川.结构优化设计[M].北京:清华大学出版社.1986:9-10,237-241.
    117.袁亚湘.非线性规划数值方法[M].上海:上海科学技术出版社.1993:200-203.
    118.D.Q. MAYNE, E. POLAK. FEASIBLE DIRECTIONS ALGORITHMS FOR OPTIMIZATION PROBLEMS WITH EQUALITY AND INEQUALITY CONSTRAINTS[J]. Mathematical Programming.1976,11:67-80.
    119.LAMANCUSA J S. Numerical optimization techniques for structural-acoustic design of rectangular panels[J]. Computer and Structures.1993,48 (4):661-675.
    120.陈馨蕊,郝志勇,杨陈.仪表板的结构-声灵敏度分析及声学优化设计[J].浙江大学学报(工学版).2010, 44(11):2154-2158.
    121.杨德庆,柳拥军.自由阻尼层结构阻尼材料配置优化的拓扑敏度法[J].振动工程学报.2003,16(4):420-425.
    122.臧献国,于德介,姚凌云等.基于模态振型的自由阻尼层厚度分布优化[J].中国机械工程.2010,21(5):515-518.
    123.隋允康,杜家政,彭细荣MSC.Nastran有限元动力分析与优化设计使用教程[M].北京:科学出版社.2004:166-174.
    124.李增刚Nastran快速入门与实例[M].北京:国防工业出版社.2007:156-166.
    125.MSC.Nastran Version 70, Advanced Dynamic Analysis User's Guide.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700