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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 2011, 16(1), 203-215;

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

Department of Mechanical Engineering, Bartin University 74100, Bartin, Turkey
Department of Genetics and Bioengineering, Fatih University 34500, B. Cekmece, Istanbul, Turkey
Department of Mechanical Engineering, Celal Bayar University 45140, Muradiye, Manisa, Turkey
Authors to whom correspondence should be addressed.
Published: 1 April 2011
PDF [377 KB, uploaded 6 April 2016]


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
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Bağdatlı, S.; 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.

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