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
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摘要
系统地研究了双线性单自由度体系在简谐波输入下表现出非线性力学行为时,输入简谐波频率对体系动力响应的H ilbert谱、H ilbert边缘谱及Fourier幅值谱的影响。研究结果表明,如果体系输入简谐波频率为f,那么体系动力响应H ilbert边缘谱的能量分布在f附近一个较宽的频带上,该频带的产生是体系动力响应H ilbert谱中所蕴含的波内调制的必然结果,它源自于体系某个本征振动模态瞬时频率的波动,而这种瞬时频率的波动描述了体系屈服与卸载的非线性力学行为;体系动力响应的Fourier幅值谱自3f起,每隔2f就会出现一个幅值明显高出周围其它分量的Fourier“伪”谐波分量,这也是体系非线性力学行为所造成的结果。
The influence of input harmonic frequency on the Hilbert spectrum, Hilbert marginal spectrum, and the Fourier spectrum of dynamic response of the bilinear SDOF system, which exhibited non-linear behavior under the harmonic input, was systematically studied. It is demonstrated that, with the input harmonic frequency being f: (1) the energy of Hilbert marginal spectrum is distributed in a relatively wide frequency band that is the result of the intra-wave modulation embedded in the Hilbert spectrum of dynamic response, which comes from the undulation of instantaneous frequency of some intrinsic oscillation mode of system, and such instantaneous frequency undulation describes the yielding-unloading non-linear mechanical behavior of the system; (2) in the Fourier amplitude spectrum of dynamic response, there appear some spurious harmonics, whose amplitudes are much higher than the other adjacent components and whose frequencies start from 3fand increase by 2f, and such phenomenon is also the result of non-linear mechanical behavior of the system.
The influence of input harmonic frequency on the Hilbert spectrum, Hilbert marginal spectrum, and the Fourier spectrum of dynamic response of the bilinear SDOF system, which exhibited non-linear behavior under the harmonic input, was systematically studied. It is demonstrated that, with the input harmonic frequency being f: (1) the energy of Hilbert marginal spectrum is distributed in a relatively wide frequency band that is the result of the intra-wave modulation embedded in the Hilbert spectrum of dynamic response, which comes from the undulation of instantaneous frequency of some intrinsic oscillation mode of system, and such instantaneous frequency undulation describes the yielding-unloading non-linear mechanical behavior of the system; (2) in the Fourier amplitude spectrum of dynamic response, there appear some spurious harmonics, whose amplitudes are much higher than the other adjacent components and whose frequencies start from 3fand increase by 2f, and such phenomenon is also the result of non-linear mechanical behavior of the system.
引文
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[2]Huang N E,Shen Z,Long R S.A new view of non linear water wavesH ilbert spectrum[J].Ann.Rev.Flu id M ech.1999,31:417~457.
[3]Loh C H,W u T C,Huang N E.Application of the emp iricalmode decomposition H ilbert spectrum m ethod to identify near-fau lt ground-motioncharacteristics and structural responses[J].Bu lletin of the Seismological Society ofAm erica,2001,91(5):1339~1357.
[4]P ines D,Salvino L W.Health mon itoring of structures using emp irical mode decomposition and phase dereverberation[A].Proceed ings of the2001 M echan ics and Materials Summ er Conference[C].UCSD:San D iego,CA,2001.228~229.
[5]Yang J N,Lei Y,Pan SW,et a.l System identification of linear structures based on H ilbert-huang spectral analysis[J].Part 1:Normalmodes.Earthquake Engineering and Structural Dynam ics,2003,32:1443~1467.
[6]Yang J N,Lei Y,Pan SW,et al.System identification of linear structures based on h ilbert-huang spectral analysis[J].Part 2:ComplexModes.Earthquake Engineering and Structural Dynam ics,2003,32:1533~1554.
[7]张郁山.希尔伯特-黄变换(HHT)与地震动时程的希尔伯特谱———方法与应用研究[D].北京:中国地震局地球物理研究所,2003.
[8]Zhang Y,L iang J,Hu Y.H ilbert spectrum and intrinsic oscillation mode of dynam ic response of a b ilinear SDOF system:influence of harmon icex-citation amplitude[J].Earthquake Engineering and Engineering V ibration,2005,4(1):17~26.
[9]Pan T C,Lee C L.Application ofwavelet theory to identify yield ing in seism ic response of B i-linear structures[J].Earthquake Engineering andStructural Dynam ics.2002,31:379~398.
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