Group - Theoretic approach to axially accelerating beam problem

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Date

2002

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Abstract

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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Beams and girders , Boundary conditions , Mathematical models , Mathematical transformations , Partial differential equations , Velocity , Axially accelerating beam problem , Equivalence transformations , Lie group theory , Vibrations (mechanical)

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http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/20310

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