Title of article
NON-LINEAR TRANSVERSE VIBRATIONS and 3:1 INTERNAL RESONANCES OF A TENSIONED BEAM ON MULTIPLE SUPPORTS
Author/Authors
Bağdatlı, S.Murat Bartin University - Department of Mechanical Engineering, TURKEY , Öz, H. Rıdvan Fatih University - Department of Genetics and Bioengineering, TURKEY , Özkaya, Erdoğan Celal Bayar University - Department of Mechanical Engineering, TURKEY
From page
203
To page
215
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
Journal title
mathematical and computational applications
Journal title
mathematical and computational applications
Record number
2569142
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