基于Lamb波的结构损伤识别试验研究
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摘要
结构健康监测是设备状态监测和故障诊断的基础,智能材料与结构的应用是进行结构健康监测的重点。PZT(锆钛酸铅压电陶瓷)能广泛应用于智能材料结构中。PZT能与基体材料很好结合,具有正压电效应和逆压电效应,在智能材料结构中既能用作传感元件又能用作驱动元件。PZT还具有较好的机电耦合系数、压电常数、机械品质因数、居里温度和稳定性等。
本文充分发挥PZT既可作为传感器又可作为驱动器的优势,进行铝板损伤检测的试验研究。主要研究内容包括:首先,采用数值方法对Lamb波进行建模,并对Lamb波激励进行优化。其次,基于压电基本理论,介绍PZT电压感知机理和阻抗感知机理,以及PZT压电陶瓷各种性能参数对PZT材料特性的影响;研究PZT驱动、感知元件的制作与粘贴工艺,建立结构主动健康监测试验平台。第三,通过试验,研究PZT用于铝板结构裂缝损伤的检测。验证Lamb波群速度频散曲线;研究基于最小二乘法的峰值损伤因子;应用波传播时间延迟和能量-时间谱的衰减,结合板的对称性,对单一裂缝损伤、单一有蜡填充裂缝损伤、多处裂缝损伤进行损伤检测进而精确定位,试验结果证实该方法是切实可行的。最后,探讨了损伤率用于判断结构健康状况的方法。
Structural Health Monitoring is the base of equipment status monitoring and failure diagnosing with focus on the application of smart materials and structure in which PZT is widely used.Adhering well to the matrix, Piezoelectric ceramics have piezoelectric effect and inverse piezoelectric effect and can function as both sensor component and driving component in the smart materials and structure. There are also advantages of PZT in electromechanical coupling coefficient, piezoelectric constant, mechanical quality factor, curie temperature and stability etc.
Giving full play to the advantages of PZT used as both sensor component and driving component, this thesis carries out research on the identification of the aluminum plate damages, including the followings: Firstly, Lamb waves travelling in the aluminum plate is modeled through numerical methods, and the optimization of the Lamb waves incentive is done. Secondly, based on the piezoelectric theory, this thesis introduces the PZT voltage sensing mechanism, the impedance sensing mechanism and the impacts which various performance parameters of PZT exert on the characteristics of PZT material. The experiment platform is also founded for the active structural health monitoring and reseach is done on the making and sticking of PZT sensors and actuators.Thirdly, PZT for the identification of the aluminum plate crack is studied through the experiment. The dispersion curve of the group velocity of Lamb waves is drawn, which agrees largely with the theoretical curve. The peak damage factors are studied based on the least-squares method. With the application of the delay time of wave propagation and the attenuation of the energy-time spectrum, the identification and precise positioning of damages are conducted on a single crack damage, a single wax-filled crack and multiple cracks employing the symmetry of the square board. This experiment method has been proved to be feasible. Finally, this thesis explores the damage index on the judgement of the health situation of the structure.
本文充分发挥PZT既可作为传感器又可作为驱动器的优势,进行铝板损伤检测的试验研究。主要研究内容包括:首先,采用数值方法对Lamb波进行建模,并对Lamb波激励进行优化。其次,基于压电基本理论,介绍PZT电压感知机理和阻抗感知机理,以及PZT压电陶瓷各种性能参数对PZT材料特性的影响;研究PZT驱动、感知元件的制作与粘贴工艺,建立结构主动健康监测试验平台。第三,通过试验,研究PZT用于铝板结构裂缝损伤的检测。验证Lamb波群速度频散曲线;研究基于最小二乘法的峰值损伤因子;应用波传播时间延迟和能量-时间谱的衰减,结合板的对称性,对单一裂缝损伤、单一有蜡填充裂缝损伤、多处裂缝损伤进行损伤检测进而精确定位,试验结果证实该方法是切实可行的。最后,探讨了损伤率用于判断结构健康状况的方法。
Structural Health Monitoring is the base of equipment status monitoring and failure diagnosing with focus on the application of smart materials and structure in which PZT is widely used.Adhering well to the matrix, Piezoelectric ceramics have piezoelectric effect and inverse piezoelectric effect and can function as both sensor component and driving component in the smart materials and structure. There are also advantages of PZT in electromechanical coupling coefficient, piezoelectric constant, mechanical quality factor, curie temperature and stability etc.
Giving full play to the advantages of PZT used as both sensor component and driving component, this thesis carries out research on the identification of the aluminum plate damages, including the followings: Firstly, Lamb waves travelling in the aluminum plate is modeled through numerical methods, and the optimization of the Lamb waves incentive is done. Secondly, based on the piezoelectric theory, this thesis introduces the PZT voltage sensing mechanism, the impedance sensing mechanism and the impacts which various performance parameters of PZT exert on the characteristics of PZT material. The experiment platform is also founded for the active structural health monitoring and reseach is done on the making and sticking of PZT sensors and actuators.Thirdly, PZT for the identification of the aluminum plate crack is studied through the experiment. The dispersion curve of the group velocity of Lamb waves is drawn, which agrees largely with the theoretical curve. The peak damage factors are studied based on the least-squares method. With the application of the delay time of wave propagation and the attenuation of the energy-time spectrum, the identification and precise positioning of damages are conducted on a single crack damage, a single wax-filled crack and multiple cracks employing the symmetry of the square board. This experiment method has been proved to be feasible. Finally, this thesis explores the damage index on the judgement of the health situation of the structure.
引文
1谢礼立.防灾减灾工程在国民经济建设中的应用.学术报告. 2002.04.湖北武汉
2 Sohn H, Farrar C R, Hemez F. A Review of Structural Health Monitoring Literature: 1996-2001, Los Alamos National Laboratory Report, LA-13976-MS, 2003
3 Aktan A E, Tsikos C J, Catbas F N. Challenges and Opportunities in Bridge Health Monitoring 2000, Stanford University, Palo Alto, Califonia, 1999: 461-473
4 Matsuzaki Yuji. Smart Structures Research in Japan, Review Article. Smart Materials and Structures. 1997, 6(4): 1-10
5 Ko J,Chan T. Dynamics Monitoring of Structural Health in Cable Supported Bridge. Smart Structures and Materials 1999: Smart Systems for Bridges, Structures, and Highways. Proceedings of SPIE. 1999, 3(671): 161-172
6欧进萍,肖仪清,黄虎杰.海洋平台结构实时安全监测系统.海洋工程. 2001, 19(2): 1-6
7 H..Lamb. On the Waves in an Elastic Plate. Proceedings of the Royal Society of London. 1917: 293-312
8 [美]阿肯巴赫著.徐植信,洪锦如译.弹性固体中波的传播.上海:同济大学出版社. 1994: 125-130
9 D.E.Chienti, R.W.Martin. Nondestructive Evaluation of Composite Lamin-ates by Leaky Lamb Waves. Ultrasonics. 1991, 29(5): 13-21
10 Igor Aleksandrovich Viktorov.Rayleigh and Lamb Waves. [M]. New York: Plenum Press. 1967: 67-77
11 T Kundu, T Ghosh, K Maslov. Detection of Kissing Bonds Lamb Waves. [J]. Ultrasonics. 1998, 35 (8): 573-580
12 Zhongqing Su, LinYe, Xiongzhu Bu. A Damage Technique for CF/EP Composite Laminates Using Distributed Piezoelectric Transducers. [J]. Composite Structures. 2002, 57(14): 465~471
13 Ivan Bartoli, Mahmood Fateh, Erasmo Viola. Modeling Guided Wave Propagation with Appilcation to the Longrang Defection in Rail Road Tracks.[J]. NDT&E International. 2005, 38 (5):325~334
14 D.C.Worlton. Experimental Confirmation of Lamb Waves at Megacycle Frequencies. Journal of Applied Physics. 1961, 32(6): 967-971
15李申.超声兰姆波探伤研究与应用.机械设计与制造. 2001, 42(6): 85-87
16 Victory I V. Rayleigh and Lamb Waves Physical Theory and Applications. Plenum Press. New Yrok. 1967: 336-341
17 W.Sachse, Y.H.Pao. On the Determination of Phase and Group Velocities of Dispersive Waves in Solids. [J]. Appl. Phys. 1978, 49(8): 4320-4327
18 Saravanos D.A.,P.R. Heyliger. Coupled Layerwise Analysis of Composite Beams with Embedded Piezoelectric Sensors and Actuators. Journal of Intelligent Material Systems and Structures. 1995, (6): 350-362
19 Saravanos D.A., Birman V., D.A.Hopkins. Detection of Delaminations in Composite Beams Using Piezoelectric Sensors. Proceedings of the 35th Structure, Structural Dyamics and Materials Conference of the AIAA. 1994: 181-191
20 Percival W.J., E.A.Birt. Insight: Non-Destructive Testing and Condition Monitoring. 1997vol. 39: 728-735
21 Kercel, Klein. Separation of Lamb Waves in Laser Ultrasonics. In Applications and Science of Computation Intelligence. III Proceedings of SPIE. 2000. Vol. 4055: 350-361
22 Quan Wang, Xiaomin Deng. Damage Detection with Spatial Wave1ets. International Journal of Solids and Structures. 1999: 3443-3468
23 K.Worden,G.Manson, D.Allman. Experimental Validation of a Structural Health Monitroing Methodology: Part I. Novelty Detection on a Laboratory Structure. Journal of Sound and Vibration. 2003, Volume.259 Issue 2, 323-343
24 M.J.Sundaresan, P.F.Pai, A.Ghoshal. Methods of Distributed Sensing for Health Monitoring of Composite Material Structures Composites. 2001: 1357-1374
25 Demma, A. Cawley, P. Lowe. The Reflection of Guided Waves from Notches in Pipes: A Guide for lnterpreting Corrosion Measurements. NDT&E Internatinoal. 2004, Vol.37.pp:167-180
26 Monkhouse R S C., Wilcox P W. The Rapid Monitoring of Structures UsingInterdigital Llamb Wave Transducers. Smart Materials and Structures. 2000, 9: 304-309
27 Valdez S H D, Soutis C. Structural Intergrity Monitoring of CFRP Laminates Using Piezoelectric Devices. Proceedings of the European Conference on Composite Materials. Brighton, UK. 2000: 1560-1577
28 Andrein.Zagral and Victor Giurgiutiu. Electro-Mechanical Impedance Method for Crack Detection in Thin Wall Structures. In Proc.of the 3rd Inter.Work Shop on Structural Health Monitoring. Stanford: CRC Press. 2001: 176~186
29 V Giurgiutiu, Andrei Zagrai, Jingjing Bao. Embedded Active Sensors for In-situ Structural Health Monitoring of Thin-wall Structures. ASME. 2002, Vol. 124: 293-302
30 Tua P S, Quek S T and Wang Q. Detection of Cracks in Plates Using Piezo-actuated Lamb waves. Smart Mater. Struct. 2004, 13: 643-660
31 Tua P S, Quek S T and Wang Q, Detection of Crack in Cylindrical Pipes and Plates Using Piezo-actuated Lamb Waves. Smart Mater.Struct. 2005, 14: 1325-1342
32 Tua P S, Quek S T and Wang Q. Detection of Crack in Thin Cylindrical Pipes and Plates Using Piezo-actuated Lamb Waves. [J]. Smart Mater. Struct. 2005: 820-831
33 Wang L, Yuan F G.. Damage Identification in a Composite Plate Using Prestack Reverse-time Migration Technique. [J]. Structural Health Monitoring. 2005, 4 (3): 195-211
34 Wang CH, Rose JT, Chang F K. A Synthetic Time-reversal Imaging Method for Structural Health Monitoring. [J]. Smart Materials and Structures. 2004, 13(2): 415-423
35李家伟,云庆华等主编.兰姆波及其在薄板探伤中的应用.锅炉压力容器无损检测技术.天津科学出版社, 1985: 101-119
36应崇福,张守玉,沈建中.超声在固体中的散射.北京:国防工业出版社, 1994: 236-241
37刘镇清,他得安.用二维傅里叶变换识别兰姆波模式的研究.[J].声学技术, 2002, 19(4): 212-219
38郑祥明,顾向华等.超声兰姆波的时频分析.[J].声学学报.2003, 28(4): 386-
39 Shenfang Yuan, Lei Wang, Ge Peng. Neural Network Method Based on a New Damage Signature for Structural Health Monitoring. Thin-Walled Structures. 2005, Vol. 43:553-563
40徐颖娣,袁慎芳,彭鸽.二维结构损伤的主动Lamb波定位技术研究.航空学报. 2004(5): 476-479
41刘镇清.无损检测中的超声兰姆波.无损检测. 1999, 21(9): 409-432.
42蒋福棠,何双起,沈建中.兰姆波探伤中一些问题的探讨.[J].材料工程. 1996, 41(10): 29-31
43 J·Krautkramer著,李靖等译.超声检测技术.广州:广东科技出版社, 1984: 453-469
44 GB2108-80薄钢板兰姆波探伤法
45 GB8651-88金属板材超声波探伤方法
46 QJ1269-87金属薄板兰姆波探伤方法
47徐可北.金属薄板兰姆波检验技术.[J].无损检测.1999, 21(10): 32-36
48张灵研,石立华,李炎新.Matlab与C语言混合编程测试系统.电子测量技术, 2003. (6): 39-40
49 Alna V. Oppenheim, Ronald W. Schafer. Discrete Time Signal Processing. London: Prentice Hall. 2005: 826-870
50 Farrar C. R., K. M. Cone. Vibration Testing of the I-40 Bridge before and after the Introduction of Damage. Proceeding of the 13th lnternational Modal Analysis Conference. 1995, 2460: 203-209
51 West W. M. Single Point Random Model Test Technique Application to Failure Detection. The Shock and Vibration Bulletin. 1982, 52(4): 25-31
52 [美]L.科恩著,白居宪译.时频分析理论与应用西安:西安交通大学出版社, 1998: 23-47
53胡昌华,周涛,夏启兵等.基于MATLAB的系统分析与设计—时频分析.西安:西安电子科技大学出版社, 2002: 5-16
54张贤达,保铮.非平稳信号分析与处理.北京:国防工业出版社, 1998: 52-62
55葛哲学,陈仲生.Matlab时频分析技术及其应用.北京:人民邮电出版社, 2006: 289-301
56李刚.时频分析方法在智能结构损伤在线检测中的应用研究[硕士学位论文]南京:南京航空航天大学, 2005: 4-6
57 William H. Prosser, Michae1 D. Seale And Barry T. Smith. Application of the Pseudoe Wigner-ville Distribution to the Measurement of the Dispersion of Lamb Mode in Graphite Epoxy Plates. The Eighth International Symposium on Nondestructive Characterization of Materials. 1997: 256-269
58 Macr Niethammer, Laurence J. Time-frequency Representations of Lamb Waves. J Acoust Soc Am, 2001. 109: 1841-1847
59 Huang N E, Shen Z and Long S R. The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and No-stationary Time Series Analysis. Pro R Soc Lnod A. 1998, 454: 903-995
60 Achenbach, J.D. Wave Propagation in Elastic Solids. New York: North-Holland, 1984: 459-467
61 Giurgiutiu, V. Zagrai, An Embedded Active Sensors for In-situ Structural Health Monitoring of Thin-wall Structures. ASME [J].Vibr Acoust. 2002: 293-30
62 Alleyne D N, Cawley P. The Interaction of Lamb Waves with Defects IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 1992, 39: 381–397
63 Lowe M J S, Diligent O. Low-frequency Reflection Characteristics of the S0 Lamb Wave from Rectangular Notch in a Plate. [J]. Acoust. Soc. Am. 2002, 111: 64–74
64 Lowe M J S, Cawley P, Kao J Y and Diligent O. The Low Frequency Reflection Characteristics of the Fundamental Antisymmetric Lamb Wave A0 from a Rectangular Notch in Plate. [J]. Acoust. Soc.Am. 2002, 112: 2612–2622
65 Kessler Seth, Spearing S Mark and Soutis Constantions. Smart Materials and Structures. 2002, 11: 269-278
66 Wilcox P.D., Lowe M.J.S., Cawley P. Journal of Intelligent Material Systems and Structures. 2001, 12: 553-565
67 Andrei Nikolaevitch Zagrai. Piezoelectric-wafer Active Sensor Electro-mechanical Impendance Structural Health Monitoring. University of South Carolina. D. S. Thesis. 2002: 61-97
68 Yuan Shenfang, Wang Lei, Shi LiHua. On-line Damage Monitoring in Composite Structures. Journal of Vibration and Acoustics. 2003, Vol.125, April: 178-186
69王磊,袁慎芳,朱安华.基于主动监测技术的蜂窝夹心结构损伤监测研究.仪器仪表学报. 2002, 23(4): 422-425
2 Sohn H, Farrar C R, Hemez F. A Review of Structural Health Monitoring Literature: 1996-2001, Los Alamos National Laboratory Report, LA-13976-MS, 2003
3 Aktan A E, Tsikos C J, Catbas F N. Challenges and Opportunities in Bridge Health Monitoring 2000, Stanford University, Palo Alto, Califonia, 1999: 461-473
4 Matsuzaki Yuji. Smart Structures Research in Japan, Review Article. Smart Materials and Structures. 1997, 6(4): 1-10
5 Ko J,Chan T. Dynamics Monitoring of Structural Health in Cable Supported Bridge. Smart Structures and Materials 1999: Smart Systems for Bridges, Structures, and Highways. Proceedings of SPIE. 1999, 3(671): 161-172
6欧进萍,肖仪清,黄虎杰.海洋平台结构实时安全监测系统.海洋工程. 2001, 19(2): 1-6
7 H..Lamb. On the Waves in an Elastic Plate. Proceedings of the Royal Society of London. 1917: 293-312
8 [美]阿肯巴赫著.徐植信,洪锦如译.弹性固体中波的传播.上海:同济大学出版社. 1994: 125-130
9 D.E.Chienti, R.W.Martin. Nondestructive Evaluation of Composite Lamin-ates by Leaky Lamb Waves. Ultrasonics. 1991, 29(5): 13-21
10 Igor Aleksandrovich Viktorov.Rayleigh and Lamb Waves. [M]. New York: Plenum Press. 1967: 67-77
11 T Kundu, T Ghosh, K Maslov. Detection of Kissing Bonds Lamb Waves. [J]. Ultrasonics. 1998, 35 (8): 573-580
12 Zhongqing Su, LinYe, Xiongzhu Bu. A Damage Technique for CF/EP Composite Laminates Using Distributed Piezoelectric Transducers. [J]. Composite Structures. 2002, 57(14): 465~471
13 Ivan Bartoli, Mahmood Fateh, Erasmo Viola. Modeling Guided Wave Propagation with Appilcation to the Longrang Defection in Rail Road Tracks.[J]. NDT&E International. 2005, 38 (5):325~334
14 D.C.Worlton. Experimental Confirmation of Lamb Waves at Megacycle Frequencies. Journal of Applied Physics. 1961, 32(6): 967-971
15李申.超声兰姆波探伤研究与应用.机械设计与制造. 2001, 42(6): 85-87
16 Victory I V. Rayleigh and Lamb Waves Physical Theory and Applications. Plenum Press. New Yrok. 1967: 336-341
17 W.Sachse, Y.H.Pao. On the Determination of Phase and Group Velocities of Dispersive Waves in Solids. [J]. Appl. Phys. 1978, 49(8): 4320-4327
18 Saravanos D.A.,P.R. Heyliger. Coupled Layerwise Analysis of Composite Beams with Embedded Piezoelectric Sensors and Actuators. Journal of Intelligent Material Systems and Structures. 1995, (6): 350-362
19 Saravanos D.A., Birman V., D.A.Hopkins. Detection of Delaminations in Composite Beams Using Piezoelectric Sensors. Proceedings of the 35th Structure, Structural Dyamics and Materials Conference of the AIAA. 1994: 181-191
20 Percival W.J., E.A.Birt. Insight: Non-Destructive Testing and Condition Monitoring. 1997vol. 39: 728-735
21 Kercel, Klein. Separation of Lamb Waves in Laser Ultrasonics. In Applications and Science of Computation Intelligence. III Proceedings of SPIE. 2000. Vol. 4055: 350-361
22 Quan Wang, Xiaomin Deng. Damage Detection with Spatial Wave1ets. International Journal of Solids and Structures. 1999: 3443-3468
23 K.Worden,G.Manson, D.Allman. Experimental Validation of a Structural Health Monitroing Methodology: Part I. Novelty Detection on a Laboratory Structure. Journal of Sound and Vibration. 2003, Volume.259 Issue 2, 323-343
24 M.J.Sundaresan, P.F.Pai, A.Ghoshal. Methods of Distributed Sensing for Health Monitoring of Composite Material Structures Composites. 2001: 1357-1374
25 Demma, A. Cawley, P. Lowe. The Reflection of Guided Waves from Notches in Pipes: A Guide for lnterpreting Corrosion Measurements. NDT&E Internatinoal. 2004, Vol.37.pp:167-180
26 Monkhouse R S C., Wilcox P W. The Rapid Monitoring of Structures UsingInterdigital Llamb Wave Transducers. Smart Materials and Structures. 2000, 9: 304-309
27 Valdez S H D, Soutis C. Structural Intergrity Monitoring of CFRP Laminates Using Piezoelectric Devices. Proceedings of the European Conference on Composite Materials. Brighton, UK. 2000: 1560-1577
28 Andrein.Zagral and Victor Giurgiutiu. Electro-Mechanical Impedance Method for Crack Detection in Thin Wall Structures. In Proc.of the 3rd Inter.Work Shop on Structural Health Monitoring. Stanford: CRC Press. 2001: 176~186
29 V Giurgiutiu, Andrei Zagrai, Jingjing Bao. Embedded Active Sensors for In-situ Structural Health Monitoring of Thin-wall Structures. ASME. 2002, Vol. 124: 293-302
30 Tua P S, Quek S T and Wang Q. Detection of Cracks in Plates Using Piezo-actuated Lamb waves. Smart Mater. Struct. 2004, 13: 643-660
31 Tua P S, Quek S T and Wang Q, Detection of Crack in Cylindrical Pipes and Plates Using Piezo-actuated Lamb Waves. Smart Mater.Struct. 2005, 14: 1325-1342
32 Tua P S, Quek S T and Wang Q. Detection of Crack in Thin Cylindrical Pipes and Plates Using Piezo-actuated Lamb Waves. [J]. Smart Mater. Struct. 2005: 820-831
33 Wang L, Yuan F G.. Damage Identification in a Composite Plate Using Prestack Reverse-time Migration Technique. [J]. Structural Health Monitoring. 2005, 4 (3): 195-211
34 Wang CH, Rose JT, Chang F K. A Synthetic Time-reversal Imaging Method for Structural Health Monitoring. [J]. Smart Materials and Structures. 2004, 13(2): 415-423
35李家伟,云庆华等主编.兰姆波及其在薄板探伤中的应用.锅炉压力容器无损检测技术.天津科学出版社, 1985: 101-119
36应崇福,张守玉,沈建中.超声在固体中的散射.北京:国防工业出版社, 1994: 236-241
37刘镇清,他得安.用二维傅里叶变换识别兰姆波模式的研究.[J].声学技术, 2002, 19(4): 212-219
38郑祥明,顾向华等.超声兰姆波的时频分析.[J].声学学报.2003, 28(4): 386-
39 Shenfang Yuan, Lei Wang, Ge Peng. Neural Network Method Based on a New Damage Signature for Structural Health Monitoring. Thin-Walled Structures. 2005, Vol. 43:553-563
40徐颖娣,袁慎芳,彭鸽.二维结构损伤的主动Lamb波定位技术研究.航空学报. 2004(5): 476-479
41刘镇清.无损检测中的超声兰姆波.无损检测. 1999, 21(9): 409-432.
42蒋福棠,何双起,沈建中.兰姆波探伤中一些问题的探讨.[J].材料工程. 1996, 41(10): 29-31
43 J·Krautkramer著,李靖等译.超声检测技术.广州:广东科技出版社, 1984: 453-469
44 GB2108-80薄钢板兰姆波探伤法
45 GB8651-88金属板材超声波探伤方法
46 QJ1269-87金属薄板兰姆波探伤方法
47徐可北.金属薄板兰姆波检验技术.[J].无损检测.1999, 21(10): 32-36
48张灵研,石立华,李炎新.Matlab与C语言混合编程测试系统.电子测量技术, 2003. (6): 39-40
49 Alna V. Oppenheim, Ronald W. Schafer. Discrete Time Signal Processing. London: Prentice Hall. 2005: 826-870
50 Farrar C. R., K. M. Cone. Vibration Testing of the I-40 Bridge before and after the Introduction of Damage. Proceeding of the 13th lnternational Modal Analysis Conference. 1995, 2460: 203-209
51 West W. M. Single Point Random Model Test Technique Application to Failure Detection. The Shock and Vibration Bulletin. 1982, 52(4): 25-31
52 [美]L.科恩著,白居宪译.时频分析理论与应用西安:西安交通大学出版社, 1998: 23-47
53胡昌华,周涛,夏启兵等.基于MATLAB的系统分析与设计—时频分析.西安:西安电子科技大学出版社, 2002: 5-16
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