A scheme for applying an averaging method to the problem of convection in a two-layer system with an interface under the influence of high-frequency vibration is proposed. The derivation of the averaging equations is given, and the stability of the equilibrium of the averaged problem is considered. Long-wavelength asymptotics of steady and oscillatory instability are constructed. The results of numerical calculations for acetonitrile-n-hexane and silicone oil-fluorinert systems are given. The directions in which the investigation of thermovibrational convection in problems with free surfaces and interfaces can be continued, are indicated.
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