BIFURCATION AND AMPLITUDE MODULATED MOTIONS IN A PARAMETRICALLY EXCITED TWO-DEGREE-OF-FREEDOM NON-LINEAR SYSTEM

✍ Scribed by J.-C. JI; L. YU; Y.-S. CHEN

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 278 KB
• Volume: 228
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1999.2473

✦ Synopsis

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 "rst 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.