We consider the impact of periodical finite-amplitude perturbations induced by oscillations of the supporting plane on the natural instability of a falling film. The oscillations change the basic state of the flow from steady to periodical; for non-Newtonian liquids, the mean parameters of the basic state depend on the plane’s oscillations. We solve the eigenvalue problem for linearized generalized Navier-Stokes equations using long-waves expansion and Floquet theory. We provide results of calculations for shear-thinning and shear-thickening Carreau liquids. The plane oscillations stabilize or destabilize the flow depending on their frequency; the effect does not qualitatively depend on the amplitude. For Newtonian liquid, diapasons of stabilizing and destabilizing frequency alternate up to infinity. For shear-thinning liquids, low-frequency oscillations destabilize the flow, while high-frequency ones stabilize it increasing the critical Reynolds number; shear-thickening liquids show the opposite behavior.

我们考虑了由支撑平面的振动引起的周期性有限振幅微扰对降膜的自然不稳定性的影响。振荡将流动的基本状态从稳定状态更改为周期性状态。对于非牛顿液体，基本状态的平均参数取决于平面的振荡。我们使用长波展开和Floquet理论解决线性化广义Navier-Stokes方程的特征值问题。我们提供了剪切稀化和剪切增稠的Carreau液体的计算结果。平面振荡根据其频率来稳定或破坏流量。该效果不定性地取决于幅度。对于牛顿液体，稳定和不稳定频率的间隔交替增大到无穷大。对于剪切稀薄的液体，低频振荡使流动不稳定，而高频振荡则稳定流动，从而增加了临界雷诺数。剪切增稠液体表现出相反的行为。