基于Hilbert-Huang变换的框架结构非线性地震响应分析
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摘要
利用HHT方法分析多自由度框架结构地震作用下的动力响应.分析结果显示:由于多自由度结构地震响应所含频率成分复杂,用HHT方法难以直接得到多自由度结构地震作用下的非线性时变特征.考虑到多自由度结构大多以低阶振型为主,本文以结构一阶振型为例,引入等效单自由度来分析多自由度结构的动力特征.结果表明,利用等效单自由度结构的瞬时卓越频率可以得到多自由度结构刚度的时变动力特征.
The seismic response of MDOF frame was analyzed by Hilbert-Huang Transform.The results showed that the nonlinear time variant characteristics of MDOF frame under seismic load was hard to obtain by HHT,because of the complicated frequencies in the seismic response of MDOF frame.Because the vibration of MDOF frame is based on the low order mode shape,in this paper,considering the first order mode shape,the dynamic characteristic of MDOF system was analyzed by introducing the equivalent single-degree-of-freedom system.The results showed that the time variant dynamic characteristic of MDOF frame could be obtained by the instant excellence frequency of equivalent single-degree-of-freedom.
The seismic response of MDOF frame was analyzed by Hilbert-Huang Transform.The results showed that the nonlinear time variant characteristics of MDOF frame under seismic load was hard to obtain by HHT,because of the complicated frequencies in the seismic response of MDOF frame.Because the vibration of MDOF frame is based on the low order mode shape,in this paper,considering the first order mode shape,the dynamic characteristic of MDOF system was analyzed by introducing the equivalent single-degree-of-freedom system.The results showed that the time variant dynamic characteristic of MDOF frame could be obtained by the instant excellence frequency of equivalent single-degree-of-freedom.
引文
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3陈换过,闫云聚,姜节胜.基于HHT的机翼盒段的健康监控.动力学与控制学报,2006,4(1):93～96Chen Huanguo,Yan Yunju,Jiang Jiesheng.HHT-based health monitoring of wingbox section.Journal of Dynamics and Control,2006,4(1):93～96(in Chinese))
4J.N.Yang,Y.Lei S.Lin N.Huang.Hilbert～Huang based approach for structural damage detection.Journal ofEngi-neering Mechanics,2004130(1):85～95
5J.N.Yang,Y.Lei,S.Pan,N.Huang.System identifi-cation of linear structures based on Hilbert-Huang spectralanalysis.Part1:normal modes.Earthquake Engineering and Structural Dynamics,2003,32:1443～1467
6J.N.Yang,Y.Lei,S.Pan,N.Huang.System identi-fication of linear structures based on Hilbert?Huang spec-tral analysis.Part2:complex modes.Earthquake Engineer-ing and Structural Dynamics,200332:1533～1554
7陈隽,徐幼麟,李杰.Hilbert-Huang变换在密频结构阻尼识别中的应用.地震工程与工程振动,2003,23(4):34～42(Chen Juan,Xu Youlin,Li Jie.Hilbert-Huang transform for damping ratio identification of structures with closely spaced modes of vibration.Earthquake Engineering and En-gineering Vibration,2003,23(4):34～42(in Chinese))
8续秀忠,李中付,华宏星等.非平稳环境激励下线性结构在线模态参数辨识.上海交通大学学报,2003,37(1):119～126(Xu Xiuzhong,Li Zhongfu,Hua Hongxing etc.On-line modal parameters identification of linear structures under non-stationary ambient excitation.Journal ofShanghai Jiao-tong University,2003,37(1):119～126(in Chinese))
9Feldman.Non-linear system vibration analysis using Hilbert transform-I Free vibration analysis method'FREEVIB.'Mechan-ical Systems and Signal Processing,1994,8(2):119～127
10公茂盛,谢礼立.HHT方法在地震工程中的应用之初步探讨.世界地震工程,2003,19(3):39～43(Gong Maosheng,Xie Lili.Discussion on the application of HHT method to earthquake engineering.World Earthquake Engi-neering,2003,19(3):39～43(in Chinese))
11邹经湘,于开平.时变结构的参数识别方法.力学进展,2000,30(3):370～377(Zou Jingxiang,Yu Haiping.Meth-ods of time-varying structural parameter identification.Ad-vances in Mechanics,2000,30(3):370～377(in Chinese))
12李桂青,李秋胜.工程结构时变可靠度理论及应用.北京:科学出版社,2001(Li Guiqing,Li Qiusheng.The time varying reliability theories and applications of structur-al engineering.Beijing:Science Press,2001(in Chinese))
13Helmut Krawinkler,G.D.P.K.Seneviratna.Pros and cons of a pushover analysis of seismic performance evalua-tion.Engineering Structures,1998,20(4-6):452～464
14张郁山.HHT与地震动时程的Hilbert谱方法与应用研究.北京:中国地震局地球物理研究所,2003(Zhang Yushan.The study of method of HHTand the Hilbert spectrumof ground mo-tion time history and their applications.Beijing:Institute of geo-physics,China earthquake administration,2003(in Chinese))
2Huang N E,Shen Z,Steven R L.A new view of nonlinear water waves:The Hilbert spectrum.Ann Rev Fluid Mech,1999,31:417～457
3陈换过,闫云聚,姜节胜.基于HHT的机翼盒段的健康监控.动力学与控制学报,2006,4(1):93～96Chen Huanguo,Yan Yunju,Jiang Jiesheng.HHT-based health monitoring of wingbox section.Journal of Dynamics and Control,2006,4(1):93～96(in Chinese))
4J.N.Yang,Y.Lei S.Lin N.Huang.Hilbert～Huang based approach for structural damage detection.Journal ofEngi-neering Mechanics,2004130(1):85～95
5J.N.Yang,Y.Lei,S.Pan,N.Huang.System identifi-cation of linear structures based on Hilbert-Huang spectralanalysis.Part1:normal modes.Earthquake Engineering and Structural Dynamics,2003,32:1443～1467
6J.N.Yang,Y.Lei,S.Pan,N.Huang.System identi-fication of linear structures based on Hilbert?Huang spec-tral analysis.Part2:complex modes.Earthquake Engineer-ing and Structural Dynamics,200332:1533～1554
7陈隽,徐幼麟,李杰.Hilbert-Huang变换在密频结构阻尼识别中的应用.地震工程与工程振动,2003,23(4):34～42(Chen Juan,Xu Youlin,Li Jie.Hilbert-Huang transform for damping ratio identification of structures with closely spaced modes of vibration.Earthquake Engineering and En-gineering Vibration,2003,23(4):34～42(in Chinese))
8续秀忠,李中付,华宏星等.非平稳环境激励下线性结构在线模态参数辨识.上海交通大学学报,2003,37(1):119～126(Xu Xiuzhong,Li Zhongfu,Hua Hongxing etc.On-line modal parameters identification of linear structures under non-stationary ambient excitation.Journal ofShanghai Jiao-tong University,2003,37(1):119～126(in Chinese))
9Feldman.Non-linear system vibration analysis using Hilbert transform-I Free vibration analysis method'FREEVIB.'Mechan-ical Systems and Signal Processing,1994,8(2):119～127
10公茂盛,谢礼立.HHT方法在地震工程中的应用之初步探讨.世界地震工程,2003,19(3):39～43(Gong Maosheng,Xie Lili.Discussion on the application of HHT method to earthquake engineering.World Earthquake Engi-neering,2003,19(3):39～43(in Chinese))
11邹经湘,于开平.时变结构的参数识别方法.力学进展,2000,30(3):370～377(Zou Jingxiang,Yu Haiping.Meth-ods of time-varying structural parameter identification.Ad-vances in Mechanics,2000,30(3):370～377(in Chinese))
12李桂青,李秋胜.工程结构时变可靠度理论及应用.北京:科学出版社,2001(Li Guiqing,Li Qiusheng.The time varying reliability theories and applications of structur-al engineering.Beijing:Science Press,2001(in Chinese))
13Helmut Krawinkler,G.D.P.K.Seneviratna.Pros and cons of a pushover analysis of seismic performance evalua-tion.Engineering Structures,1998,20(4-6):452～464
14张郁山.HHT与地震动时程的Hilbert谱方法与应用研究.北京:中国地震局地球物理研究所,2003(Zhang Yushan.The study of method of HHTand the Hilbert spectrumof ground mo-tion time history and their applications.Beijing:Institute of geo-physics,China earthquake administration,2003(in Chinese))
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