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Supercritical Frequencies of Planar Vibration of Axially Moving Beams with Fixed Boundaries
LUO Yi;DING Hu
2011, 31 (6):
29-32.
DOI: 10.3969/j.issn.1006-1355-2011.06.007
The natural frequencies of nonlinear planar vibration of axially moving beams are numerically investigated in the supercritical speed range. The finite difference schemes are presented for the static equilibrium equation in the coupled plane of the beam in the supercritical range, and the non-trivial solutions are obtained. Based on the non-trivial statically equilibrium configuration, a typical governing equation of continuous gyroscopic systems is established in the supercritical range via introducing a coordinate transform. The natural frequencies are investigated for the planar vibration via the 8-term Galerkin method to truncate the corresponding governing equations of the beam in the supercritical state without nonlinear parts under the fixed boundary conditions. The effect of number of the terms of the Galerkin truncation method on the solution of the natural frequencies is also studied by analyzing the numerical results.
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