Exploring localization in nonlinear oscillator systems through network-based predictions

Localized vibrations, arising from nonlinearities or symmetry breaking, pose a challenge in engineering, as the resulting high-amplitude vibrations may result in component failure due to fatigue. During operation, the emergence of localization is difficult to predict, partly because of changing parameters over the life cycle of a system. This work proposes a novel, network-based approach to detect an imminent localized vibration. Synthetic measurement data are used to generate a functional network, which captures the dynamic interplay of the machine parts, complementary to their geometric coupling. Analysis of these functional networks reveals an impending localized vibration and its location. The method is demonstrated using a model system for a bladed disk, a ring composed of coupled nonlinear Duffing oscillators. Results indicate that the proposed method is robust against small parameter uncertainties, added measurement noise, and the length of the measurement data samples. The source code for this work is available at C. Geier [(2024). “Code for paper Exploring localization in nonlinear oscillator systems through network-based predictions,” Zenodo. https://doi.org/10.5281/zenodo.12611988].

Subjects

Nonlinear dynamics modeling and theories

Localized states

Oscillators

Data science

Signal processing

Numerical methods

Network theory

Complex systems theory

Time series analysis

DDC Class

620: Engineering

Funding(s)

Komplexe Netzwerkanalyse als alternative Perspektive auf die nichtlineare Dynamik großer mechanischer Mehrkomponenten-Strukturen: Entwicklung von neuen Ansätzen für ein besseres Verständnis von technischer Strukturdynamik

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Exploring localization in nonlinear oscillator systems through network-based predictions