Stability of two-mode internal resonance in a nonlinear oscillator

Damián H. Zanette ()
Additional contact information
Damián H. Zanette: Centro Atómico Bariloche (Comisión Nacional de Energía Atómica) and Instituto Balseiro (Universidad Nacional de Cuyo), Consejo Nacional de Investigaciones Científicas y Técnicas

The European Physical Journal B: Condensed Matter and Complex Systems, 2018, vol. 91, issue 5, 1-7

Abstract: Abstract We analyze the stability of synchronized periodic motion for two coupled oscillators, representing two interacting oscillation modes in a nonlinear vibrating beam. The main oscillation mode is governed by the forced Duffing equation, while the other mode is linear. By means of the multiple-scale approach, the system is studied in two situations: an open-loop configuration, where the excitation is an external force, and a closed-loop configuration, where the system is fed back with an excitation obtained from the oscillation itself. The latter is relevant to the functioning of time-keeping micromechanical devices. While the accessible amplitudes and frequencies of stationary oscillations are identical in the two situations, their stability properties are substantially different. Emphasis is put on resonant oscillations, where energy transfer between the two coupled modes is maximized and, consequently, the strong interdependence between frequency and amplitude caused by nonlinearity is largely suppressed.

Keywords: Statistical; and; Nonlinear; Physics (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1140/epjb/e2018-90030-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:eurphb:v:91:y:2018:i:5:d:10.1140_epjb_e2018-90030-0

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/10051

DOI: 10.1140/epjb/e2018-90030-0

Access Statistics for this article

The European Physical Journal B: Condensed Matter and Complex Systems is currently edited by P. Hänggi and Angel Rubio

More articles in The European Physical Journal B: Condensed Matter and Complex Systems from Springer, EDP Sciences
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().