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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2007-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2007/276515 |
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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. |
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| ISSN: | 1070-9622 1875-9203 |