Abstract
Nonlinear vibrations of the multiple beams which are fixed at their both ends to elastic structures under harmonic excitation are investigated. Van der Pol's method is used to determine the frequency resonance curves. The shape of response curves are hard spring types. Although there exist stable branches near the right hand side in the response curves for the system with a single beam, the corresponding branches become unstable for the system with multiple beams. In addition, additional branches appear, because the multiple beams are coupled with the structure. As the number of the beams increases, the number of these additional branches also increases. The beams vibrate at different amplitudes at the excitation frequency range where a sort of the autoparametric resonance occurs. The system may encounter fold bifurcations, pitchfork bifurcations and Hopf bifurcations depending on the values of the system parameters. Amplitude modulated motions, including chaotic vibrations, are observed in the numerical simulation. Corresponding to the unstable branches, each beam vibrates at different amplitudes; this means "localization phenomena."
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