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Reduced-Order Modeling of Strongly Nonlinear Modal Interactions in a Systems with Strongly Nonlinear Attachments through Slow-Fast Partitions of the Dynamics, and Empirical Mode Decompositions

Alexander Vakakis, Lawrence Bergman, Young Sup Lee, D. Michael McFarland, Stylianos Tsakirtzis
We perform nonlinear system identification of strongly nonlinear transient modal interactions occurring in systems possessing essentially nonlinear attachments. The nonparametric identification is performed, (i) by performing slow-fast partitions of the transient dynamics through a complexification - averaging technique, and (ii) by means of Empirical Mode Decomposition (EMD) of the nonlinear time series applied together with Wavelet Transforms. We show that the dominant intrisic mode functions (IMFs) resulting from EMD coincide with the slow-flow responses. Based on this result, we develop a reduced-order modeling approach that can be extended to a broad range of applications involving nonlinear interactions.
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