Dynamic modelling and stability analysis of axially oscillating cantileverbeams

Dynamic stability of an axially oscillating cantilever beam is investigated in this paper. Equations of motion for the axially oscillating beam are de rived and transformed into dimensionless forms. The equations include harmo nically oscillating parameters which are related to the motion-induced stif fness variation. Stability diagrams of the first and the second order appro ximate solutions are obtained by using the multiple scale perturbation meth od. The stability diagrams show that there exist significant difference bet ween the first and the second order approximate solutions. It is also found that relatively large unstable regions exist around the first bending natu ral frequency, twice the first bending natural frequency, and twice the sec ond being natural frequency. The validity of the stability diagram is verif ied by direct numerical integrations of the equations of motion of the syst em. (C) 1999 Academic Press.