Non-linear transverse vibrations and 3:1 internal resonances of a tensioned beam on multiple supports
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2011
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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. © Association for Scientific Research.
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Control nonlinearities , Damping , Equations of motion , Frequency response , Phase modulation , Resonance , Structural panels , Amplitude and phase modulations , Approximate analytical solutions , Arbitrary number , Axial tensions , Cubic nonlinearities , Damping effect , End conditions , Euler Bernoulli beams , Internal resonance , Linear problems , Method of multiple scale , Mode shapes , Neutral axis , Non-linear , Nonlinear frequency , Nonlinear transverse vibration , Perturbation method , Response curves , Simple support , Supported beams , Tensioned beam , Vibration , Perturbation techniques