Vibration of the Duffing Oscillator: Effect of Fractional Damping | Zendy

Marek Borowiec | Zendy; Grzegorz Litak | Zendy; Arkadiusz Syta | Zendy

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Vibration of the Duffing Oscillator: Effect of Fractional Damping

Author(s) -

Marek Borowiec,

Grzegorz Litak,

Arkadiusz Syta

Publication year - 2006

Publication title -

shock and vibration

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.418

H-Index - 45

eISSN - 1875-9203

pISSN - 1070-9622

DOI - 10.1155/2007/276515

Subject(s) - homoclinic bifurcation , homoclinic orbit , duffing equation , lyapunov exponent , nonlinear system , mathematics , amplitude , chaotic , perturbation (astronomy) , bifurcation , mathematical analysis , classical mechanics , control theory (sociology) , physics , quantum mechanics , control (management) , management , artificial intelligence , computer science , economics

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

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