Determination of the natural frequencies of axially moving beams by the method of multiple scales
The natural frequencies of an axially moving beam were determined by using the method of multiple scales.The method of second-order multiple scales could be directly applied to the governing equation if the axial motion of the beam is assumed to be small.It can be concluded that the natural frequencies affected by the axial motion are proportional to the square of the velocity of the axially moving beam.The results obtained by the perturbation method were compared with those given with a numerical method and the comparison shows the correctness of the multiple-scale method if the velocity is rather small.
the method of multiple scalesnatural frequencyaxially moving beam
杨晓东、陈立群
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Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University,Shanghai 200072,P.R.China
Department of Mechanics,College of Sciences,Shanghai University,Shanghai 200444,P.R.China
the method of multiple scales natural frequency axially moving beam
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