Nonlinearity identification by time-domain-only signal processing

Abstract

A conjugate-pair decomposition (CPD) method is proposed for signal decomposition, dynamics characterization, and nonlinearity identification all in the time domain only. CPD uses the empirical mode decomposition method with signal conditioning techniques to decompose a compound signal into well separated intrinsic mode functions (IMFs) and then uses a pair of sliding conjugate functions to accurately extract the time-varying frequency and amplitude of each IMF using only three neighboring data points for each time instant. Because the variations of frequencies and amplitudes of IMFs contain system characteristics, they can be used for dynamics characterization and nonlinearity identification of discrete and continuum systems. Several discrete and continuum systems' simulated and experimental responses are used to validate CPD's accuracy and capability for system and nonlinearity identification. Experimental nonlinear free vibration of a horizontally cantilevered steel beam subject to an initial tip displacement is analyzed using CPD, and direct numerical simulations using a fully nonlinear finite-element code are also performed and compared. Both experimental and numerical results show that the first-mode vibration contains a softening cubic nonlinearity, and the shortening-induced longitudinal inertia and nonlinear modal coupling of the first few modes make the effective modal damping of the first mode nonlinear.