Abstract
Non-linear flexural vibrations of a nearly square plate when excited periodically with forces normal to the mid-plane of the plate are studied when the excitation frequency is near that of one of the antisymmetric modes. It is shown that there are two distinct cases, depending on whether the loading is “antisymmetric” or “symmetric”. The present work is concerned with the former case. The physical phenomena are due to a 1:1 resonance of the modes. The motions can be in one or the other of the antisymmetric modes or in mixed modes and can be in the form of travelling waves of “pseudo-standing” waves, which are travelling waves with jerky motions. The presence of Hopf bifurcations leads to amplitude-modulated travelling waves as well as period-doubling bifurcations to chaos. A global analysis for the undamped case shows global chaotic phenomena similar to those observed in the case of water waves.
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