Advanced Time-Frequency Analysis for Characterization of Nonlinear Structural Vibrations

Abstract

This paper presents a conjugate-pair decomposition (CPD) method for accurate timefrequency analysis of nonlinear structural response and proposes a method of using perturbation solutions and time-varying frequencies and amplitudes from time-frequency analysis for dynamics characterization and identification of nonlinear structural systems. For a nonlinear nonstationary signal, empirical mode decomposition uses the apparent time scales revealed by the signal's local maxima and minima to sequentially sift intrinsic mode functions (IMFs) of different time-varying scales, starting from high- to low-frequency ones. Results show that IMFs often correspond to a structure’s modal vibrations. Hilbert-Huang transform depends on high-frequency sampling and Hilbert transform (HT) to accurately extract each IMF’s time-varying frequency and amplitude, but its accuracy suffers from the edge effect caused by Gibbs’ phenomenon and HT. On the other hand, CPD uses one or more pairs of windowed adaptive harmonics and function orthogonality to track the timevarying frequency and amplitude of each IMF. Because CPD processes only time-domain data without using HT, it is free from the edge effect and can provide accurate time-varying frequencies and amplitudes for dynamics characterization and non-parametric identification. Moreover, asymptotic analytical solutions from perturbation analysis provide formulas and guidance for parametric identification using each IMF’s time-varying frequency and amplitude to determine the type and order of nonlinearity and system parameters. Furthermore, because CPD is based on circle-fitting, noise filtering is an implicit capability and it can analyze data from low-frequency sampling. Numerical and experimental results show that the proposed methodology is capable of accurate characterization and identification of nonlinear structural systems.