Bifurcation and amplitude modulated motions in a parametrically excited two-degree-of-freedom non-linear system

The non-linear response of a T-shaped beam-mass structure is investigated t heoretically and experimentally for the case of one-to-two internal resonan ce and principal parametric resonance of the lower mode. The method of mult iple scales is used to determine four first order amplitude- and phase-modu lation equations. The non-trivial steady state solutions are obtained from trivial solutions through pitchfork bifurcation. The Melnikov's method is u sed to predict the critical parameter at which the dynamical system possess es a Smale horseshoe type of chaos. To verify the analytical results, exper iments were performed on the T-shaped beam-mass structure. The periodically amplitude-modulated motions and chaotically amplitude-modulated motions we re observed during experiments. The results of the experiment showed good q ualitative agreement with the theoretical predictions. (C) 1999 Academic Pr ess.