A new approach to analysis of the dynamic behaviour of axially moving orthotropic web is presented. In this paper the numerical method of Unger's transition matrix and Godunov's orthogonalization procedure are used to solve the non-linear problem of axially moving system. The results of numerical investigations show the solutions of the linearized and non-linear problems. Free vibrations of the steel web in subcritical and supercritical regions of transport speed are analyzed.
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