Hamiltonian Approach to Multiple Coupled Nonlinear Oscillators

• Authors: S. Durmaz , S. Altay Demirbag , M. Kaya
• Languages of publication: EN

Abstracts

EN

In this paper, Hamiltonian approach is extended to investigate coupled nonlinear multi-degree-of-freedom oscillatory systems. At the beginning of the study, basic principles of Hamiltonian approach are provided for multiple coupled oscillators. In the next section, the amplitude-frequency relation for the two-degree-of-freedom nonlinear mechanical systems is obtained via Hamiltonian approach. The natural frequency expression is compared to show the agreement between the present and published results. Additionally, the approximate and numerical periodic solutions are plotted.

Keywords

EN

05.45.-a; 46.40.-f

Discipline

• 05.45.-a: Nonlinear dynamics and chaos(see also section 45 Classical mechanics of discrete systems; for chaos in fluid dynamics, see 47.52.+j; for chaos in superconductivity, see 74.40.De)
• 46.40.-f: Vibrations and mechanical waves(see also 43.40.+s Structural acoustics and vibration; 62.30.+d Mechanical and elastic waves; vibrations in mechanical properties of solids)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2012
• Volume: 121
• Issue: 1
• Pages: 47-49

Dates

published

2012-01

Contributors

author

S. Durmaz

• Faculty of Aeronautics and Astronautics, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey

author

S. Altay Demirbag

• Faculty of Science and Letts, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey

author

M. Kaya

• Faculty of Aeronautics and Astronautics, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey

References

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• 4. J.H. He, Mech. Res. Commun. 29, 107 (2002)
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• 6. S.H.A. Hashemi Kachapi, R.V. Dukkipati, S.Gh. Hashemi Kachapi, S. Mey Hashemi Kachapi, S. Meh Hashemi Kachapi, S.K. Hashemi Kachapi, Nonlinear Anal., RWA 11, 1431 (2010)
• 7. M. Feldman, J. Sound Vib. 303, 357 (2007)
• 8. M.O. Kaya, S. Durmaz, S. Altay Demirbag, Int. J. Nonlin Sci. Num. Sim. 11, 859 (2010)
• 9. J.H. He, Phys. Lett. A. 374, 2312 (2010)

Identifiers

DOI

10.12693/APhysPolA.121.47