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Meccanica
Erschienen in: Meccanica 3/2020

12.02.2020

Backbone curves of coupled cubic oscillators in one-to-one internal resonance: bifurcation scenario, measurements and parameter identification

verfasst von: Arthur Givois, Jin-Jack Tan, Cyril Touzé, Olivier Thomas

Erschienen in: Meccanica | Ausgabe 3/2020

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Abstract

A system composed of two cubic nonlinear oscillators with close natural frequencies, and thus displaying a 1:1 internal resonance, is studied both theoretically and experimentally, with a special emphasis on the free oscillations and the backbone curves. The instability regions of uncoupled solutions are derived and the bifurcation scenario as a function of the parameters of the problem is established, showing in an exhaustive manner all possible solutions. The backbone curves are then experimentally measured on a circular plate, where the asymmetric modes are known to display companion configurations with close eigenfrequencies. A control system based on a Phase-Locked Loop (PLL) is used to measure the backbone curves and also the frequency response function in the forced and damped case, including unstable branches. The model is used for a complete identification of the unknown parameters and an excellent comparison is drawn out between theoretical prediction and measurements.
Vorheriger Artikel Non-standard and constitutive boundary conditions in nonlocal strain gradient elasticity
Nächster Artikel Discontinuum analysis of the fracture mechanism in masonry prisms and wallettes via discrete element method

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Fußnoten
1
In practice the current intensity in the coil is measured, and is assumed to be proportional to the actual force with no phase lag.
 
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Metadaten
Titel
Backbone curves of coupled cubic oscillators in one-to-one internal resonance: bifurcation scenario, measurements and parameter identification
verfasst von
Arthur Givois
Jin-Jack Tan
Cyril Touzé
Olivier Thomas
Publikationsdatum
12.02.2020
Verlag
Springer Netherlands
Erschienen in
Meccanica / Ausgabe 3/2020
Print ISSN: 0025-6455
Elektronische ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-020-01132-2

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