Vibration of the Duffing Oscillator: Effect of Fractional Damping

We have applied the Melnikov criterion to examine a global homoclinic bifurcation and transition to chaos in a case of the Duffing system with nonlinear fractional damping and external excitation. Using perturbation methods we have found a critical forcing amplitude above which the system may behave...

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Bibliographic Details
Published inShock and vibration Vol. 14; no. 1; pp. 29 - 36
Main Authors Borowiec, Marek, Litak, Grzegorz, Syta, Arkadiusz
Format Journal Article
LanguageEnglish
Published Hindawi Limited 01.01.2007
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Summary:We have applied the Melnikov criterion to examine a global homoclinic bifurcation and transition to chaos in a case of the Duffing system with nonlinear fractional damping and external excitation. Using perturbation methods we have found a critical forcing amplitude above which the system may behave chaotically. The results have been verified by numerical simulations using standard nonlinear tools as Poincare maps and a Lyapunov exponent. Above the critical Melnikov amplitude μ_c, which a sufficient condition of a global homoclinic bifurcation, we have observed the region with a transient chaotic motion.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:1070-9622
1875-9203
DOI:10.1155/2007/276515