Amplitude and Frequency Modulation Method for Identification of Nonlinear Structural Vibrations

Abstract

This paper presents an amplitude and frequency modulation method (AFMM) for extracting nonlinear characteristics and intermittent transient responses by processing stationary/transient responses using the empirical mode decomposition, Hilbert -Huang trans form (HHT), and nonlinear dynamic characteristics derived from perturbation analysis. A sliding -window fitting (SWF) method is derived to show the physical implication of the proposed method and other methods for transforming time -domain data into frequenc y-domain data. Similar to the wavelet transform the SWF uses windowed regular harmonics and function orthogonality to extract time -localized regular and/or distorted harmonics. On the other hand the HHT uses the apparent time scales revealed by the signal' s local maxima and minima and cubic splines of the extrema to sequentially sift components of different time scales, starting from high -frequency to low -frequency ones. Because HHT does not use predetermined basis functions and function orthogonality for component extraction, it provides more accurate instant amplitudes and frequencies of extracted components for accurate estimation of system characteristics and nonlinearities. However, the discontinuity -induced Gibbs' effect makes HHT analysis inaccurate a round the two data ends. Numerical results show that the proposed AFMM can provide accurate parametric estimations of softening and hardening effects, different orders of nonlinearity, nonlinear system parameters, and intermittent transient s.