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 theoretically and experimentally for the case of one-to-two internal resonance and principal parametric resonance of the lower mode. The method of multiple scales is used to determine four first order amplitude- and phase-modulation equations. The non-trivial steady state solutions are obtained from trivial solutions through pitchfork bifurcation. The Melnikov's method is used to predict the critical parameter at which the dynamical system possesses a Smale horseshoe type of chaos. To verify the analytical results, experiments were performed on the T-shaped beam-mass structure. The periodically amplitude-modulated motions and chaotically amplitude-modulated motions were observed during experiments. The results of the experiment showed good qualitative agreement with the theoretical predictions. (C) 1999 Academic Press.