Bifurcation and Amplitude Modulated Motions in a Parametrically Excited Two-Degree-Of-Freedom Non-Linear System

Author： Yu L.

ISSN： 0022-460X

Source： Journal of Sound and Vibration, Vol.228, Iss.5, 1999-12, pp. : 1125-1144

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Abstract

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.