Dynamic stability of stepped beams under moving loads

Abstract

The dynamic stability of a stepped beam subjected to a moving mass is investigated in this study. The equations of motion for transverse vibrations of the beam are developed in distributed parameter and finite element forms. The impulsive parametric excitation theory is used to predict the stability of the beam when subjected to periodic parametric excitations. The accuracy of the theory is verified by obtaining the stability boundaries of a simply supported beam and comparing the results with the results reported in the literature. Stability maps are then obtained for clamped-free uniform beams as well as clamped-free stepped beams. It is found that the stability of certain beam modes can be improved by providing the beam with appropriately spaced steps. It is shown that better stability characteristics can be obtained by using piezoelectric actuators. Stability analyses of beams with periodic piezoelectric and/or viscoelastic steps are a natural extension of the present work.