Stability of two viscous fluid layers separated by a thin elastic plate under a vertical oscillation.

Abstract

The stability of two viscous fluid layers which are separated by a thin elastic plate under a vertical oscillation is investigated theoretically using a linear perturbation theory. Two fluid layers are horizontally bounded by two sinusoidally oscillating walls. The upper fluid is lighter than the lower one. The general stability boundaries for the given wave numbers are found analytically in the form of an infinite band determinant. And the neutral stability curves are composed of these stability boundaries in the plane of the frequency and the amplitude of the imposed vertical oscillation for the cases of first-, second- and fourth-order solution. When the ratio of thickness of the upper fluid layer to the total one is small or near unity, the system considered force of the elastic plate, their increase makes the system more stable, but it makes the system more unstable in the region of a small value of them. When the ratio of density of the upper fluid layer to the lower one increases, the system is stabilized.