Vibrations of a textile machine rotor

In this paper the vibrations of a textile machine rotor, whose angular velocity is constant, are analyzed. The function of the rotor is to wind up a band of textile material into a roll. The elastic force in the shaft is assumed to be non-linear. First the free vibrations of this rotor are analyzed analytically and numerically. The results are compared. After that the vibrations in the non-resonant case are analyzed. The solution is found by use of the analytical method of multiple scales. The results for free vibrations and for the non-resonant case are compared.