The problem of dynamic interaction of the plate on the elastic foundation 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 difference of pressure at its butt end is considered. Deflections of plate are modeled as one-mass system elastic displacements. Parameters of one-mass system were found by using method of equivalent mass. The formulated boundary problem represents non-linear Navier-Stocks equations system for viscous incompressible liquid layer and the equation of one-mass system. 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 boundary ones. The linearization of the problem by means of perturbation method is made. The solution of the linearized problem is made by means of the assigned forms method for adjusted harmonic fluctuations.
The mechanical model of the system representing a ribbed pipe of ring like profile, formed by two surfaces of the coaxial cylindrical shells interacting with viscous incompressible liquid, the outer of which is geometrically irregular, and inner one is an absolutely rigid cylinder under the effect of the harmonic pressure 3526 D. V. Kondratov et al. pulsation at pipe ends is considered. The mathematical model of this system, consisting of differential equations in partial derivatives presenting dynamics of viscous incompressible liquid and an elastic ribbed shell together with boundary conditions is constructed. Expressions for amplitude frequency characteristics of outer geometrically irregular shell are discovered.
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