Summary
Transverse vibrations of a beam moving with time dependent axial velocity have been investigated. Analytical solutions of the problem are found using the systematic approach of Lie group theory. Group classification with respect to the arbitrary velocity function has been performed using a newly developed technique of equivalence transformations. From the symmetries of the partial differential equation, the way of deriving exact solutions for the case of arbitrary velocity is shown. Special cases of interest such as constant velocity, harmonically varying velocity and exponentially decaying velocity are investigated in detail. Finally, for a simply supported beam, approximate solutions are presented for the exponentially decaying and harmonically varying cases.
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Özkaya, E., Pakdemirli, M. Group — theoretic approach to axially accelerating beam problem. Acta Mechanica 155, 111–123 (2002). https://doi.org/10.1007/BF01170843
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DOI: https://doi.org/10.1007/BF01170843