RESONANT-OVERLAP PHENOMENA IN STOCHASTIC LAYERS OF NON-LINEAR HAMILTONIAN SYSTEMS WITH PERIODICAL EXCITATIONS

An accurate standard-map approach, instead of the approximate standard-map approach, is developed for the analytical prediction of the onset of a new resonant overlap forming a new resonant-separatrix web in the stochastic layer. This accurate approach applies to the twin-well Duffing oscillator for...

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Veröffentlicht in:Journal of sound and vibration 2001-03, Vol.240 (5), p.821-836
1. Verfasser: LUO, A.C.J.
Format: Artikel
Sprache:eng
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Zusammenfassung:An accurate standard-map approach, instead of the approximate standard-map approach, is developed for the analytical prediction of the onset of a new resonant overlap forming a new resonant-separatrix web in the stochastic layer. This accurate approach applies to the twin-well Duffing oscillator for illustration of the resonant overlap phenomena in stochastic layers. The excitation strengths are obtained analytically for the onset of the specified resonant-separatrix webs in the stochastic layer. This accurate approach gives a very good prediction compared to numerical results for the lower order resonant overlap. When excitation strength is very weak, the accurate and approximate standard-map methods are in good agreement, and the accurate one is applicable to non-linear systems with strong excitations. However, the further improvement should be completed for a more accurate, analytical prediction of the onset of a new resonant overlap in stochastic layers of non-linear Hamiltonian systems with periodical excitations.
ISSN:0022-460X
1095-8568
DOI:10.1006/jsvi.2000.3288