基于Hilbert谱的结构动力响应非线性特征分析
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摘要
介绍了Hilbert-Huang变换的原理和波内调制的概念,对比了地震动作用下单自由度和多自由度结构的线性体系与三线性刚度退化体系绝对加速度响应的Hilbert幅值谱、能量谱,分析系统进入非线性力学状态的重要标志。结果表明:"频带展宽"和"优势频率漂移"是体系动力响应非线性力学行为的两个重要标志。线性体系加速度响应的能量集中在自振频率附近的窄小频带内;而三线性刚度退化体系由于波内调制的原因使Hilbert能量谱频带展宽。并且,能量谱的优势频率受体系屈服频率和开裂频率的影响向低频漂移。在短周期结构中,频带展宽和优势频率漂移较显著,而在长周期结构中表现不明显。
Hilbert spectrum and intra-wave modulation were introduced here.For a SDOF system and a MDOF system,Hilbert amplitude spectra and energy spectra of the absolute acceleration responses under earthquake for both their tri-linear stiffness retrograde systems and their linear systems were compared.The symbols of the non-linear mechanical behavior were analyzed.It was shown that band broadening and dominant frequency drift are two important symbols of the nonlinear mechanical behavior of the dynamic response of a system;the acceleration energy of a linear system is concentrated in a narrow frequency band near its natural frequency and intra-wave modulation causes band broadening in Hilbert energy spectrum of a tri-linear stiffness degradation system;due to influence of yield frequency and cracking frequency,the dominant frequency of the energy spectrum drifts to lower frequency;in short period structures,band broadening and dominant frequency drift are obvious,but in long period structures,they are not significant.
Hilbert spectrum and intra-wave modulation were introduced here.For a SDOF system and a MDOF system,Hilbert amplitude spectra and energy spectra of the absolute acceleration responses under earthquake for both their tri-linear stiffness retrograde systems and their linear systems were compared.The symbols of the non-linear mechanical behavior were analyzed.It was shown that band broadening and dominant frequency drift are two important symbols of the nonlinear mechanical behavior of the dynamic response of a system;the acceleration energy of a linear system is concentrated in a narrow frequency band near its natural frequency and intra-wave modulation causes band broadening in Hilbert energy spectrum of a tri-linear stiffness degradation system;due to influence of yield frequency and cracking frequency,the dominant frequency of the energy spectrum drifts to lower frequency;in short period structures,band broadening and dominant frequency drift are obvious,but in long period structures,they are not significant.
引文
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[2]Huang N E,Shen Z,Long S R,et al.The empirical mode decomposition and Hilbert spectrum for nonlinear and non-stationary time series analysis[J].Proc.R.Soc.Lond.,1998,A454:903～995.
[3]屈文忠,王广,曾又林,等.多自由度振动系统非线性动力特性的HHT辨识方法研究[J].机械科学与技术,2007,26(12):1616-1620.QU Wen-zhong,WANG Guang,ZENG You-lin et al.Identifying the dynamic characteristics of multi-DOF vibration systems using the hilbert-huang transform[J].Mechanical Science and Technology for Aerospace Engineering,2007,26(12):1616-1620.
[4]黄天立,楼梦麟.基于HHT的非线性结构系统识别研究[J].地震工程与工程振动,2006,26(3):80-83.HUANG Tian-li,LOU Meng-lin.System identification of nonlinear structures based on HHT[J].Earthquakeengineering and engineering vibration,2006,26(3):80-83.
[5]易伟建,段素萍.基于Hilbert-Huang变换的框架结构非线性地震响应分析[J].动力学与控制学报,2007,5(3):249-254.YI Wei-jian,DUAN Su-ping.The nonlinear analyses of frame seismic response based on Hilbert-Huang transform[J].Journal of Dynamics and Control,2007,5(3):249-254.
[6]张郁山,梁建文,胡聿贤.双线性单自由度体系强迫动力反应的Hilbert谱与本征振动模态:输入简谐波频率的影响[J].地震工程与工程振动,2005,25(4):1-10.ZHANG Yu-shan,LIANG Jian-wen,HU Yu-xian.Hilbert spectrum and intrinsic oscillation mode of dynamic response ofa bilinear SDOF system:influence of input harmonic frequency[J].Earthquake engineering and engineering vibration,2005.8,25(4):1-10.
[7]Huang N E,Shen Z,Steven R L.A new view of nonlinear water waves:the Hilbert spectrum[J].Annu.Rev.Fluid Mech.,1999,31(1):417-457.
[8]克拉夫R W,彭津J.王光远等译.结构动力学[M].北京:高等教育出版社,2006.
[9]张新培.钢筋混凝土抗震结构非线性分析[M].北京:科学出版社,2003.
[10]徐赵东,郭迎庆.MATLAB语言在建筑抗震工程中的应用[M].北京:科学出版社,2004.
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