Estimating the degree of nonlinearity in transient responses with zeroed early-time fast Fourier transforms

Abstract

Abstract:This work presents a class of time-frequency methods for detecting and characterizing nonlinearity in transient response measurements. The methods are intended for systems whose response becomes increasingly linear as the response amplitude decays. The discrete Fourier Transform of the response data is found with various sections of the initial response set to zero. These frequency responses, dubbed Zeroed Early-time Fast Fourier Transforms (ZEFFTs), acquire the usual shape of linear Frequency Response Functions (FRFs) as more of the initial nonlinear response is nullified. Hence, nonlinearity is evidenced by a qualitative change in the shape of the ZEFFT as the length of the initial nullified section is varied. These spectra are shown to be sensitive to nonlinearity, revealing its presence even if it is active in only the first few cycles of a response, as may be the case with macro-slip in mechanical joints. They also give insight into the character of the nonlinearity, potentially revealing nonlinear energy transfer between modes or the modal amplitudes below which a system behaves linearly. In some cases one can identify a linear model from the late time, linear response, and use it to reconstruct the response that the system would have executed at previous times if it had been linear. This gives an indication of the severity of the nonlinearity and its effect on the measured response. The methods are demonstrated on both analytical and experimental data from systems with slip or impact nonlinearities.

Application of Viscous and Iwan Modal Damping Models to Experimental Measurements From Bolted Structures

“…The responses were first compared in the frequency domain where it was easy to ignore the effect of the rigid body modes. In addition, a zeroed early-time fast Fourier transform (ZEFFT) [3] was used to show how the nonlinearity of both the model and the measured data progressed over time. The ZEFFTs show that the first three modes dominate the response in this frequency range and that the frequencies do not shift very much over time.…”

“…The 4-Parameter Iwan model developed by Segalman [2] captures these effects and has been shown to reproduce the behavior of real lap joints as observed in an extensive testing and modeling campaign [1], including the power law energy dissipation seen in the micro-slip region. In the past decade, the 4-Parameter Iwan model has been implemented to predict the vibration of structures with a few discrete joints [3,4]. However, when modeling individual joints, each joint may require a unique set of parameters, which means that one must deduce hundreds or even thousands of joint parameters to describe a system of interest.…”

Quantifying Epistemic and Aleatoric Uncertainty in the Ampair 600 Wind Turbine

“…This corresponds to exciting the actual hub with a 45 lbf hammer hit. This assumption is justified by the significant frequency shift of the third mode and by the nonlinearity shown by the Zeroed Early FFT method [14] (see Fig. 12.6).…”

Experimental modal substructuring to estimate fixed-base modes from tests on a flexible fixture

“…The beam is attached to the plate with two hex screws. Some initial measurements were processed with the zeroed-fast Fourier transform nonlinearity detection method described in [24], which revealed that the natural frequencies of the system did decrease significantly with increasing excitation amplitude. To remedy this, the system was disassembled and reassembled with adhesive between the beam and plate and with the bolts very tight.…”

“…To remedy this, the system was disassembled and reassembled with adhesive between the beam and plate and with the bolts very tight. After doing this, the method in [24] no longer revealed significant nonlinearity and testing proceeded.…”