Analysis of Dynamic stability of Beams under Travelling Follower loads

It was found that the perturbation equation of motion of the thin-walled beam subjected to the travelling follower load system becomes the Hill's equation and that parametrically excited unstable coupled vibrations occur. The boundary frequency equations of the simple parametric resonance, form which the instability regions are estimated, are obtained by Bolotin's method. The instability regions of a simply supported beam are illustrated, taking into account the effects of load mass.