Moldenhauer et al. - Characterizing Instantaneous Frequency and Damping of NL Sys - IMAC2021

Extensions to a Method for Characterizing Instantaneous Frequency and Damping of Nonlinear Systems In nonlinear dynamic testing, many different analysis techniques exist for characterizing the instantaneous frequency and damping of a recorded signal. Several of the more popular methods utilize the Hilbert Transform to determine the amplitude envelope and phase of an arbitrary signal. While straightforward and very computationally inexpensive, the Hilbert Transform is prone to significant end-effects and is limited to mono-harmonic signals. To bypass these deficiencies, Goyder and Lancereau proposed a method for directly identifying the instantaneous frequency and damping of a free decay signal via an optimization-based curve fitting scheme. This work builds upon Goyder and Lancereau’s approach by detailing several extensions to their fundamental process, such as higher order approximations to amplitude and phase, fitting to specific frequency bands, characterizing multi-harmonic signals, forming representations of displacement, velocity, and acceleration, and identifying natural frequency and damping ratio during both forced and free response. The new method is applied both to synthesized and measured data from nonlinear dynamic systems with bolted joints and provides new insights into coupling between the underlying linear vibration modes.