In this study, nonlinear transverse vibrations of an Euler–Bernoulli beam with multiple supports are considered. The beam is supported with immovable ends. The immovable end conditions cause stretching of neutral axis and introduce cubic nonlinear terms to the equations of motion. Forcing and damping effects are included in the problem. The general arbitrary number of support case is considered at first, and then 3-, 4-, and 5-support cases are investigated. The method of multiple scales is directly applied to the partial differential equations. Natural frequencies and mode shapes for the linear problem are found. The correction terms are obtained from the last order of expansion. Nonlinear frequencies are calculated and then amplitude and phase modulation figures are presented for different forcing and damping cases. The 3:1 internal resonances are investigated. External excitation frequency is applied to the first mode and responses are calculated for the first or second mode. Frequency-response and force-response curves are drawn.
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e-mail: erdogan.ozkaya@bayar.edu.tr
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April 2008
Research Papers
Nonlinear Transverse Vibrations and 3:1 Internal Resonances of a Beam With Multiple Supports
E. Özkaya,
E. Özkaya
Department of Mechanical Engineering,
e-mail: erdogan.ozkaya@bayar.edu.tr
Celal Bayar University
, 45140, Muradiye, Manisa, Turkey
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S. M. Bağdatlı,
S. M. Bağdatlı
Department of Mechanical Engineering,
Celal Bayar University
, 45140, Muradiye, Manisa, Turkey
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H. R. Öz
H. R. Öz
Department of Genetic and Bioengineering,
Fatih University
, 34500, B. Çekmece, İstanbul, Turkey
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E. Özkaya
Department of Mechanical Engineering,
Celal Bayar University
, 45140, Muradiye, Manisa, Turkeye-mail: erdogan.ozkaya@bayar.edu.tr
S. M. Bağdatlı
Department of Mechanical Engineering,
Celal Bayar University
, 45140, Muradiye, Manisa, Turkey
H. R. Öz
Department of Genetic and Bioengineering,
Fatih University
, 34500, B. Çekmece, İstanbul, TurkeyJ. Vib. Acoust. Apr 2008, 130(2): 021013 (11 pages)
Published Online: March 21, 2008
Article history
Received:
April 10, 2007
Revised:
June 14, 2007
Published:
March 21, 2008
Citation
Özkaya, E., Bağdatlı, S. M., and Öz, H. R. (March 21, 2008). "Nonlinear Transverse Vibrations and 3:1 Internal Resonances of a Beam With Multiple Supports." ASME. J. Vib. Acoust. April 2008; 130(2): 021013. https://doi.org/10.1115/1.2775508
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