The well-known vibration model of axially moving beam is considered. Both axial moving speed and axial force are assumed to vary harmonically. The Method of Multiple Time Scales (a perturbation method) is used. The natural vibrations of beam are considered for different values of beam parameters. Resonances are obtained for seven different conditions. Solvability conditions for each resonance case are found analytically. Effects of transport velocity, axial force, rigidity and damping are discussed. Stability analysis are obtained for principal parametric resonances. Stable and unstable regions are obtained regarding velocity and force effects separately and together.
Linear models of axially moving viscoelastic beams and viscoelastic pipes conveying fluid are considered. The natural frequencies of the models are calculated. For both models, viscoelasticity terms are assumed to be of order one. Natural frequencies corresponding to various beam and pipe parameters are presented. Effects of viscoelasticity on the natural frequencies are discussed.
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