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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832551615832260608 |
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| author | Marek Borowiec Grzegorz Litak Arkadiusz Syta |
| author_facet | Marek Borowiec Grzegorz Litak Arkadiusz Syta |
| author_sort | Marek Borowiec |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-905e5d1f109647da81c0c47eccb3d062 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-905e5d1f109647da81c0c47eccb3d0622025-02-03T06:01:01ZengWileyShock and Vibration1070-96221875-92032007-01-01141293610.1155/2007/276515Vibration of the Duffing Oscillator: Effect of Fractional DampingMarek Borowiec0Grzegorz Litak1Arkadiusz Syta2Department of Applied Mechanics, Technical University of Lublin, Nadbystrzycka 36, PL-20-618 Lublin, PolandDepartment of Applied Mechanics, Technical University of Lublin, Nadbystrzycka 36, PL-20-618 Lublin, PolandDepartment of Applied Mechanics, Technical University of Lublin, Nadbystrzycka 36, PL-20-618 Lublin, PolandWe 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.http://dx.doi.org/10.1155/2007/276515 |
| spellingShingle | Marek Borowiec Grzegorz Litak Arkadiusz Syta Vibration of the Duffing Oscillator: Effect of Fractional Damping Shock and Vibration |
| title | Vibration of the Duffing Oscillator: Effect of Fractional Damping |
| title_full | Vibration of the Duffing Oscillator: Effect of Fractional Damping |
| title_fullStr | Vibration of the Duffing Oscillator: Effect of Fractional Damping |
| title_full_unstemmed | Vibration of the Duffing Oscillator: Effect of Fractional Damping |
| title_short | Vibration of the Duffing Oscillator: Effect of Fractional Damping |
| title_sort | vibration of the duffing oscillator effect of fractional damping |
| url | http://dx.doi.org/10.1155/2007/276515 |
| work_keys_str_mv | AT marekborowiec vibrationoftheduffingoscillatoreffectoffractionaldamping AT grzegorzlitak vibrationoftheduffingoscillatoreffectoffractionaldamping AT arkadiuszsyta vibrationoftheduffingoscillatoreffectoffractionaldamping |