Data-driven system identification of strongly nonlinear modal interactions and model updating of nonlinear dynamical systems

Experimental measurements are fundamental for the calibration and validation of computational models. When a model fails to reproduce measurements, engineers must identify and incorporate the unmodeled and/or uncertain dynamics to reconcile theoretical prediction and experimental observation. While linear identification tools are well-established, practicing engineers face significant barriers when identifying and constructing reduced-order models of the dynamics of nonlinear dynamical systems; the reason is that, typically, nonlinearities introduce new dynamical phenomena that have no counterparts in linear settings. This dissertation focuses on a recently developed, data-driven nonlinear system identification and reduced-order modeling methodology that enables one to detect, characterize and model system nonlinearity using existing computational models and experimental data. This task necessitates the synergistic implementation of diverse theoretical, computational and experimental techniques such as multiple-scale and averaging approximations, resonance capture analyses, empirical mode decomposition, wavelet and Hilbert transforms, and experimental modal analysis. The first portion of this dissertation concerns the development of an advanced signal decomposition procedure, termed wavelet-bounded empirical mode decomposition, and considers applications to the detection of strongly nonlinear modal interactions that populate the dynamics of a cantilever beam with local stiffness nonlinearity and that of a linear oscillator coupled to a vibro-impact nonlinear energy sink (i.e., a strongly nonlinear broadband absorber). The second portion examines the physical underpinnings of the proposed methodology for detecting (even strongly) nonlinear interactions in the form of internal resonances in the measured time series caused by nonlinear modal energy exchanges. Using as an example the dynamics of a cantilever beam supported by a local smooth nonlinearity, the theoretical predictions are validated by experimental measurements and post-processing analysis. The third portion focuses on the identification of a nonlinear energy sink connected to a model airplane wing; the respective theoretical and computational models are updated to accurately capture the nonlinear effects, as indicated by comparison with the measured data. The final portion considers the global effects induced by local lightweight nonlinear attachments by examining the dynamics of a model airplane with a nonlinear stores installed on each wing. The stores are found to induce significant changes in the global dynamics of the plane even though they are local attachments, including strongly nonlinear energy exchanges facilitated by internal resonances between the modes of the plane.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mechanical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2019

Author dc:creator

• Moore, Keegan James

Contributors dc:contributor

• Vakakis, Alexander F.
• Bergman, Lawrence A.
• McFarland, Donald M.
• Tawfick, Sameh H
• Matlack, Kathryn H

• Nonlinear System Identification
• Modal Analysis
• Nonlinear Normal Modes
• Data-driven Identification
• Experimental Vibrations

Statement dc:rights

• Copyright 2018 Keegan James Moore

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/102385

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/102385