Application Of Hilbert-Huang Transform In Dynamic Response Characteristic Analysis Of 2-DOF System

This dissertation was devoted to the application of the Hilbert-Huang transform in the field of dynamic response.Aiming at the sifting range problem in EMD, it was proposed that not all the data can be well sifted and there was range of sifting. An improved method named EMD based on Fourier transform can sift the mode-mixing signal into good mode, which was proposed by Yang. The IMF components and Hilbert spectrum of the excited dynamic responses of linear time-invariant 2-DOF system and two types of linear time-variant 2-DOF systems were studied, such as the 2-DOF system with gradually changing stiffness and the 2-DOF system with suddenly broken stiffness. When the linear 2-DOF system was excited by regular inputs, HHT described the linear mechanical behavior of system by the inter-wave combination mechanism among different intrinsic oscillatory modes of dynamic response of system. By the aide of the IMF components representing the steady-state response and the transient response, the information about the input and the system can be obtained, respectively; and thus the vibration properties of system can be identified. When the system was excited by earthquake ground motion, the aforementioned steady-state response and transient response of vibration cannot be distinguished. However, the study manifested that the Hilbert spectrum can still represent precisely the energy distribution of the dynamic response of system in the time-frequency plane.The second part was dedicated to the study of the physical meanings embedded in the HHT spectrum of dynamic response of bilinear 2-DOF system, and the study of the influences of different factors, such as the amplitude and the frequency of single-component harmonic input, the damping of system, on the characteristics of these two spectra. The yielding time history of the bilinear 2-DOF system during its vibration gives out the physical meaning of undulation of instantaneous frequency of the corresponding IMF component. This part also studied the characteristics of Fourier spectrum, Morlet wavelet spectrum and its marginal spectrum, and Hilbert spectrum and its marginal spectrum of the dynamic response of system under the inputs of earthquake ground motion.At last, the physical meanings embedded in the HHT spectrum and Fourier spectrum of dynamic response of different equivalent linear SDOF systems is studied. And the influences of different factors, such as the amplitude of input single-component harmonic, on these two spectra were discussed. The similarities and differences of equivalent linear system were studied. In addition, this part also studied frequency spectrum of the dynamic response of system under the inputs of earthquake ground motion.