Long transient phenomenon in nonlinear structural vibration

Abstract

The long transient phenomenon in nonlinear structural vibrations is examined in detail by using a signal decomposition and processing method based on the empirical mode decomposition, Hilbert–Huang transform (HHT), and nonlinear dynamic characteristics derived from perturbation analysis. A sliding-window fitting (SWF) technique is derived to show the physical implication of Hilbert–Huang transform and other time–frequency decomposition methods. The SWF uses windowed regular harmonics and function orthogonality to simultaneously extract time-localized regular and/or distorted harmonics. Because of the use of pre-determined basis functions, function orthogonality, and windowed curve fitting for component extraction, it cannot extract accurate time-varying frequencies and amplitudes of harmonics distorted by nonlinearities. On the other hand, the HHT uses the apparent time scales revealed by the signal's local maxima and minima to sequentially sift distorted harmonics of different time scales, starting from high-frequency to low-frequency ones. Because Hilbert–Huang transform does not use predetermined basis functions and function orthogonality for component extraction, it provides more accurate signal decomposition and instant amplitudes and frequencies of extracted distorted harmonics. Numerical results show that the proposed HHT-based signal decomposition and processing method can accurately decompose nonlinear nonstationary signals and extract accurate intrawave amplitude and phase modulations, distorted harmonic response under a single-frequency harmonic excitation, and different types and orders of nonlinearities. Using this signal processing method, the long transient phenomenon in nonlinear vibrations is found to be caused by nonlinearities, coupling of transient and forced vibrations, and/or modal coupling of multiple modes.