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Article

Non-Linear Transverse Vibrations and 3:1 Internal Resonances of a Tensioned Beam on Multiple Supports

by
S.Murat Bağdatlı
1,*,
H. Rıdvanz Öz
2,* and
Erdoğan Özkaya
3,*
1
Department of Mechanical Engineering, Bartin University 74100, Bartin, Turkey
2
Department of Genetics and Bioengineering, Fatih University 34500, B. Cekmece, Istanbul, Turkey
3
Department of Mechanical Engineering, Celal Bayar University 45140, Muradiye, Manisa, Turkey
*
Authors to whom correspondence should be addressed.
Math. Comput. Appl. 2011, 16(1), 203-215; https://doi.org/10.3390/mca16010203
Published: 1 April 2011
Versions Notes

Abstract

In this study, nonlinear transverse vibrations of a tensioned Euler-Bernoulli beam resting on multiple supports are investigated. The immovable end conditions due to simple supports cause stretching of neutral axis and introduce cubic nonlinearity to the equations of motion. Forcing and damping effects are included in the analysis. The general arbitrary number of support case is investigated and 3, 4, and 5 support cases analyzed in detail. A perturbation technique (the method of multiple scales) is applied to the equations of motion to obtain approximate analytical solutions. 3:1 internal resonance case is also considered. Natural frequencies and mode shapes for the linear problem are found for the tensioned beam. Nonlinear frequencies are calculated; amplitude and phase modulation figures are presented for different forcing and damping cases. Frequency-response and force-response curves are drawn. Different internal resonance cases between modes are investigated.
Keywords: vibration; multiply supported beam; axial tension; perturbation method vibration; multiply supported beam; axial tension; perturbation method

Share and Cite

MDPI and ACS Style

Bağdatlı, S.M.; Öz, H.R.; Özkaya, E. Non-Linear Transverse Vibrations and 3:1 Internal Resonances of a Tensioned Beam on Multiple Supports. Math. Comput. Appl. 2011, 16, 203-215. https://doi.org/10.3390/mca16010203

AMA Style

Bağdatlı SM, Öz HR, Özkaya E. Non-Linear Transverse Vibrations and 3:1 Internal Resonances of a Tensioned Beam on Multiple Supports. Mathematical and Computational Applications. 2011; 16(1):203-215. https://doi.org/10.3390/mca16010203

Chicago/Turabian Style

Bağdatlı, S.Murat, H. Rıdvanz Öz, and Erdoğan Özkaya. 2011. "Non-Linear Transverse Vibrations and 3:1 Internal Resonances of a Tensioned Beam on Multiple Supports" Mathematical and Computational Applications 16, no. 1: 203-215. https://doi.org/10.3390/mca16010203

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