From internal resonance to kinking and stacking in the response of nonlinear oscillators
Citation Link: https://doi.org/10.15480/882.17470
Publikationstyp
Journal Article
Date Issued
2026-06-23
Sprache
English
TORE-DOI
Volume
642
Article Number
119967
Citation
Journal of Sound and Vibration 642: 119967 (2026)
Publisher DOI
Scopus ID
Publisher
Elsevier
In nonlinear dynamical systems, internal resonance is a well known phenomenon. Natural frequencies may change with vibration amplitude, becoming commensurable or close at certain energy levels. Nonlinear modes then interact based on their participating oscillators. Here, we
investigate effects on the response curve of a system as neighboring oscillators are modified. This provides new insights into the relation of internal resonance and the frequency response of coupled nonlinear systems. We use methods of Harmonic Balance and a continuation algorithm to
compute nonlinear frequency response curves and nonlinear normal modes for a model system. It is arranged as a chain of Duffing oscillators with separated natural frequencies. We demonstrate a kinking effect in the response curve once internal resonance emerges in the system’s forced
response. The kink is observed as a shift to higher response levels, stretching the response curve. We also show how this kinking effect is modified by adapting the nonlinearities of neighboring oscillators. The system’s response branches kink vertically as an oscillator in the chain is made
linear, stacking on top of each other. Multiple stable solutions at a certain frequency may then be observed. We show that these solutions correspond to varying degrees of vibration localization in the system. We expect our results to be valuable in system design. It should be possible to exploit
the observed kinking effect, shaping the response curve by adding suitable oscillators of various characteristics. The engineer may thus be able to reach a target system response level at a certain frequency.
investigate effects on the response curve of a system as neighboring oscillators are modified. This provides new insights into the relation of internal resonance and the frequency response of coupled nonlinear systems. We use methods of Harmonic Balance and a continuation algorithm to
compute nonlinear frequency response curves and nonlinear normal modes for a model system. It is arranged as a chain of Duffing oscillators with separated natural frequencies. We demonstrate a kinking effect in the response curve once internal resonance emerges in the system’s forced
response. The kink is observed as a shift to higher response levels, stretching the response curve. We also show how this kinking effect is modified by adapting the nonlinearities of neighboring oscillators. The system’s response branches kink vertically as an oscillator in the chain is made
linear, stacking on top of each other. Multiple stable solutions at a certain frequency may then be observed. We show that these solutions correspond to varying degrees of vibration localization in the system. We expect our results to be valuable in system design. It should be possible to exploit
the observed kinking effect, shaping the response curve by adding suitable oscillators of various characteristics. The engineer may thus be able to reach a target system response level at a certain frequency.
Subjects
Kinking
Stacking
Nonlinear dynamics
Duffing oscillators
Frequency spacing
Internal resonance
Resonance overlap
DDC Class
621: Applied Physics
Publication version
publishedVersion