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The problem of hydroelasticity of the plate forming at wall of the slot-hole channel with a pulsing layer of viscous incompressible liquid at the set harmonious law of a pulsation of pressure at its end face in flat statement is put and analytically solved. The set regional task represents nonlinear related system of the equations of Navier-Stokes for a layer of viscous incompressible liquid and the equation of dynamics of a plate (beam strip). Conditions of sticking of liquid act as regional conditions to impenetrable walls of the channel, a condition of the free expiration of liquid at end faces of the channel and a condition of a hinged supporting of a plate wall of the channel. The complex of dimensionless variables of a considered task is created and small parameters of a task are allocated. As small parameters we have chosen the relative thickness of a layer of liquid and relative amplitude of a deflection of a plate. Considering asymptotic decomposition in the allocated small parameters of a task we have carried out its linearization by a method of indignations. The solution of the linearized task is obtained by a method of the set forms for a mode of the established harmonic oscillations. Thus, proceeding from boundary conditions for a channel plate wall, the form of its deflection is set in the form of ranks on trigonometrical functions from longitudinal coordinate. The law of a deflection of an elastic wall of the channel and distribution of hydrodynamic parameters are found in liquid. We have obtained frequency dependent functions of distribution of amplitudes of a deflection and dynamic pressure along the channel and frequency dependent functions of distribution of phase shift of a deflection of a wall and pressure in the channel of rather initial indignation at an end face. On the basis of calculations it is shown that resonant fluctuations of an elastic wall of the channel, pressure excited by insignificant pulsations at its end face, can cause essential changes of dynamic pressure and be the main reason of vibration cavitation in liquid.

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The problem of dynamic interaction of elastically fixed channel wall with pulsating viscous incompressible liquid layer is set up and analytically solved. The problem in a flat setting for the regime of a stationary pulsating liquid movement in the cannel under the suggested harmonic law of pressure pulsating at its butt end is considered. The formulated bound problem represents non-linear connected Navier-Stocks equations system for viscous incompressible liquid layer and the equation of elastically fixed channel wall dynamics. The conditions of liquid adhesion to impenetrable channel walls and the condition of free leakage of liquid at channel butt ends are presented in the paper as the bound ones. The complex of dimensionless variables of the problem under consideration and its small parameters are singled out well. The relative thickness of liquid layer and relative amplitude of channel wall fluctuations are taken as small parameters. The linearization of the problem by means of perturbation method is made in the course 7900 R. R. V. Ageev et al. of asymptotic expansions, according to the small parameters, singed out above. The solution of the linearized problem is made by means of the assigned forms method for adjusted harmonic fluctuations. The law of elastically fixed channel wall shift and hydrodynamic parameters distribution in liquid are defined. Frequency dependent function of dynamic pressure distribution along the channel, frequency dependent function of phase shift pressure in the channel, amplitude frequency characteristics and phase frequency characteristics of elastically fixed channel wall in relation to the initial perturbation in the butt end are received.