Pakdemirli M.Öz H.R.2024-07-222024-07-2220080022460Xhttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/19029The transverse vibrations of simply supported axially moving Euler-Bernoulli beams are investigated. The beam has a time-varying axial velocity with viscous damping. Traveling beam eigenfunctions with infinite number of modes are considered. Approximate analytical solutions are sought using the method of Multiple Scales, a perturbation technique. A detailed analysis of the resonances in which upto four modes of vibration involved are performed. Stability analysis is treated for each type of resonance. Approximate stability borders are given for the resonances involving only two modes. For higher number of modes involved in a resonance, sample numerical examples are presented for stabilities. © 2007 Elsevier Ltd. All rights reserved.EnglishApproximation theoryEigenvalues and eigenfunctionsEuler equationsLinear stability analysisProblem solvingBeam vibrationsEuler-Bernoulli beamsInfinite mode analysisVibration controlArticle10.1016/j.jsv.2007.10.003