Vibration of the Duffing oscillator: Effect of fractional damping

Article type: Research Article

Authors: Borowiec, Marek | Litak, Grzegorz | Syta, Arkadiusz

Affiliations: Department of Applied Mechanics, Technical University of Lublin, Nadbystrzycka 36, PL-20-618 Lublin, Poland | Department of Applied Mathematics, Technical University of Lublin, Nadbystrzycka 36, PL-20-618 Lublin, Poland

Note: [] Corresponding author. E-mails: m.borowiec@pollub.pl,g.litak@pollub.pl

Abstract: 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.

Keywords: Duffing oscillator, Melnikov criterion, chaotic vibration

Journal: Shock and Vibration, vol. 14, no. 1, pp. 29-36, 2007