线性SDOF体系共振动力响应的Hilbert谱分析  

Hilbert spectral analysis of resonant dynamic response of linear SDOF system

作　　者：张郁山[1] 梁建文[2] 胡聿贤[1] 

机构地区：[1]中国地震局地球物理研究所,北京100081 [2]天津大学土木工程系,天津300072

出　　处：《地震工程与工程振动》2006年第5期32-40,共9页Earthquake Engineering and Engineering Dynamics

基　　金：国家自然科学基金项目(50278090)

摘　　要：利用HHT方法分析了线性SDOF体系在共振状态下的强迫动力响应,系统地研究了线性SDOF体系在简谐波、线性调频波与正弦调频波输入下处于共振状态时结构动力响应的H ilbert谱与本征模态函数的特征,并且将H ilbert谱、Morlet小波谱及Fourier幅值谱所蕴含的物理意义及分辨率特性进行了比较。研究结果表明,与Fourier幅值谱相比,H ilbert谱在刻画非平稳时程的某些时变特征方面更加直观,其物理意义更加明确,而与Morlet小波谱相比H ilbert谱则具有较高的分辨率。By Hilbert-Huang Transform （HHT）, the forced dynamic response of a linear SDOF system in the resonant state is analyzed, and the characteristics of the Hilbert spectra and the intrinsic mode functions of the structural dynamic responses under the inputs of harmonic, linearly-frequency-modulated, and sinusoidally-frequency-mod- ulated waves are systematically studied. The physical significances embedded in as well as the resolution characteristics of the Hilbert spectrum, the Fourier amplitude spectrum, and the Morlet wavelet spectrum are compared. It is demonstrated that, as compared with Fourier amplitude spectrum, Hilbert spectrum is more direct in describing some time-dependent characteristics of non-stationary time history, with its physical＇ significance being clearer; while as compared with the Morlet wavelet spectrum, the Hilbert spectrum has higher resolution.

关 键 词：线性 单自由度体系 希尔伯特-黄变换(HHT) Hilbert谱 本征模态函数(IMF) 

分 类 号：P315.915[天文地球—地震学]