3: 1 Internal Resonance in Multiple Stepped Beam Systems

A. Tekin; E. Özkaya; S. M. BagdatlL

doi:10.3879/j.issn.1000-0887.2009.09.007

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A. Tekin, E. Özkaya, S. M. BagdatlL. 3: 1 Internal Resonance in Multiple Stepped Beam Systems[J]. Applied Mathematics and Mechanics, 2009, 30(9): 1057-1068. doi: 10.3879/j.issn.1000-0887.2009.09.007

Citation:

A. Tekin, E. Özkaya, S. M. BagdatlL. 3: 1 Internal Resonance in Multiple Stepped Beam Systems[J]. Applied Mathematics and Mechanics, 2009, 30(9): 1057-1068. doi: 10.3879/j.issn.1000-0887.2009.09.007

Citation:

A. Tekin, E. Özkaya, S. M. BagdatlL. 3: 1 Internal Resonance in Multiple Stepped Beam Systems[J]. Applied Mathematics and Mechanics, 2009, 30(9): 1057-1068. doi: 10.3879/j.issn.1000-0887.2009.09.007

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3: 1 Internal Resonance in Multiple Stepped Beam Systems

doi: 10.3879/j.issn.1000-0887.2009.09.007

1.
Technical Vocational School of Higher Education, Celal Bayar University, Soma, Manisa, Turkey;

Received Date: 2009-01-20
Rev Recd Date: 2009-06-19
Publish Date: 2009-09-15

Abstract

Abstract

Vibrations of multiple stepped beams with cubic nonlinearities were considered.3:1 internal resonance case was investigated for the system.A general approximate solution of the problem was found using the method of multiple scales,a perturbation technique.The modulation equations of the amplitudes and the phases were derived for two modes.These equations were utilized to determine steady state solutions and their stabilities.It was assumed that external forcing frequency is near to the lower frequency.For numeric part of the study,3:1 ratio in natural frequencies was investigated.These values were observed to be between first and second natural frequencies in cases of clamped-clamped,clamped-pinned support and between second and third natural frequencies in case of pinned-pinned support.Finally,a numeric algorithm was used to solve 3:1 internal resonance.The first mode is externally excited for clamped-clamped,clamped-pinned support and the second mode is externally excited for pinned-pinned support.Then,amplitudes of first and second modes were investigated when the first mode is externally excited.Amplitudes of second and third modes were investigated when the second mode is externally excited.Force-response,damping-response and frequency-response curves were plotted for internal resonance modes of vibrations.Stability analysis was carried out for these plots.
- stepped beam,
- 3: 1 internal resonance,
- stability analysis,
- nonlinear vibration,
- perturbation method

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References(19)

References

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