Abstract
We perform system identification and modelling of the strongly nonlinear modal interactions in a system composed of a linear elastic rod with an essentially nonlinear attachment at its end. Our method is based on slow/fast decomposition of the transient dynamics of the system, combined with empirical mode decomposition (EMD) and Hilbert transforms. The derived reduced order models (ROMs) are in the form of sets of uncoupled linear oscillators (termed intrinsic modal oscillators – IMOs), each corresponding to a basic frequency of the dynamical interaction and forced by transient excitations that represent the nonlinear modal interactions between the rod and the attachment at each of these basic frequencies. A main advantage of our proposed technique is that it is nonparametric and multi-scale, so it is applicable to a broad range of linear as well as nonlinear dynamical systems. Moreover, it is computationally tractable and conceptually meaningful, and it leads to reduced order models of rather simple form that fully capture the basic strongly nonlinear resonant interactions between the subsystems of the problem.
Highlights
The need for system identification and reduced order modeling arises from the fact that, presented with sensor data, the analyst is generally unaware of details of the underlying dynamical system from which they originated
This facilitates the use of the numerical Fourier transform (FT) followed by experimental modal analysis (EMA) [4] to extract natural frequencies, mode shapes and modal damping ratios, from which the parameters of the assumed linear model can be determined once the mass distribution is known
This is due to the fact that the proposed method directly analyzes the actual measured time series which contain full information of the dynamics and do not rely on computed characteristics of the signals
Summary
The need for system identification and reduced order modeling arises from the fact that, presented with sensor data, the analyst is generally unaware of details of the underlying dynamical system from which they originated. The classical FT is not able to properly isolate and extract this information and, may lead the less experienced analyst to mistake phenomena such as internal and combination resonances for natural frequencies, to fail to account for sensitivities of the response to force and voltage magnitudes, initial conditions, and to miss or misinterpret other unique behaviors These observations highlight the importance of developing effective, straightforward, nonparametric system identification and reduced order modeling methods for characterizing strongly nonlinear, complex, multi-component systems that will be as utilitarian as (the well established) EMA is for linear systems.
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