Effect of vertical quasiperiodic vibrations on the stability of the free surface of an inviscid liquid layer

The aim of the present paper is to examine the effect of the vertical quasiperiodic oscillations on the stability of the free surface of an ideal horizontal liquid layer. The quasiperiodic motion considered here is characterized by two incommensurate frequencies ω1 and ω2. The governing system of equations is reduced to a quasiperiodic Mathieu equation. In this situation, using the harmonic balance method developed by Rand et al. [10, 11] and Hill’s determinants, we determine the marginal stability curves. We show that the quasiperiodic excitation produces a stabilizing or a estabilizing effect and is strongly depending on the ratio of the frequencies.