Öz H.R.Pakdemirli M.Boyaci H.2024-07-222024-07-22200100207462http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/20434Non-linear vibrations of an axially moving beam are investigated. The non-linearity is introduced by including stretching effect of the beam. The beam is moving with a time-dependent velocity, namely a harmonically varying velocity about a constant mean velocity. Approximate solutions are sought using the method of multiple scales. Depending on the variation of velocity, three distinct cases arise: (i) frequency away from zero or two times the natural frequency, (ii) frequency close to zero, (iii) frequency close to two times the natural frequency. Amplitude-dependent non-linear frequencies are derived. For frequencies close to two times the natural frequency, stability and bifurcations of steady-state solutions are analyzed. For frequencies close to zero, it is shown that the amplitudes are bounded in time.EnglishApproximation theoryBifurcation (mathematics)Natural frequenciesPerturbation techniquesAxially moving materialVibrations (mechanical)Article10.1016/S0020-7462(99)00090-6