The Onset of Oscillation of an Elastic Plate Lying Spread out on a Liquid Layer under a Vertical Periodic Motion

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A thin elastic plate lies spread out on a horizontally viscous liquid layer with a finite depth. The liquid layer is excited from its bottom by a vertical periodic force. In this paper, whether or not the elastic plate is excited parametrically is investigated theoretically and experimentally. The boundaries of the region of instability in the space of the amplitude and frequency of the imposed oscillation are found for the subharmonic response by a linear theory. They are dependent on the wave number of the disturbance. The critical amplitudes of the imposed oscillation, below which the plate is stable, have a minimum value with respect to the wave number of the disturbance. The critical condition for the onset of instability is determined by this minimum critical amplitude. These theoretical results are found to be in fairly good agreement with the experimental ones obtained by using a thin rubber plate.