The lecture is devoted to the deriving of the averaged equations of motion for an inviscid incompressible inhomogeneous in density fluid in the presence of high-frequency vibrations. The fluid entirely fills a given rigid domain; vibrations are caused by the vibrations (the periodical displacements) of the domain as a whole. The used averaging procedure represents the two-timing method with the averaging over the ‘fast’ time scale. The derived equations are presented as the set of the ‘fast’ equations of motion (which must be solved first) and the ‘slow’ equations. Two interesting examples related to the waves and stability will be considered if time permitted.
