A mathematical model for studying the nonlinear response of the endwall of a narrow channel filled with a viscous fluid to the vibration of the channel’s upper wall was formulated. The channel, formed by two parallel, rigid walls, was investigated. The right end-channel wall was supported by a nonlinear spring. At the end of the left channel, the fluid flowed into a cavity with constant pressure. The upper channel wall oscillated according to a given law. As a result of the interaction between the endwall and the upper wall via a viscous fluid, the forced, nonlinear oscillations of the channel endwall arose. The fluid motion was considered in terms of the hydrodynamic lubrication theory. The endwall was studied as a spring-mass system with a nonlinear cubic restoring force. The coupled hydroelasticity problem was formulated, and it was shown that the problem under consideration was reduced to a single equation in the form of the Duffing equation. The nonlinear hydroelastic response of the end wall was determined by means of the harmonic balance method. The results of numerical experiments on nonlinear hydroelastic response behavior and a comparison with the case when the support spring is linear were presented. The obtained results are of a fundamental nature and can be used in modeling various devices and systems that have narrow channels filled with viscous fluid and are subjected to vibrations on one side of the channel. For example, coolant pipes are subjected to vibrations from the engine. Of particular interest is the application of the presented solution to the mathematical modeling of nano- and micro-spacecraft systems with fluids since the proposed decision allows for the consideration of some boundary effects, which is important for nano- and micro-spacecraft due to their small size.

The article considers dynamic processes mathematical modeling in a mechanical system, consisting of an elastic hollow cylinder, surrounded by an elastic medium and containing viscous liquid and vibrating coaxial rigid cylinder. The amplitude frequency characteristic for investigating bending cylinder oscillations as one-mass system is defined. It is shown, that the constructed amplitude characteristic makes it possible to define the considered system resonance frequencies oscillations. The calculations demonstrated the significance of taking into account viscous liquid inertia and the surrounding elastic medium.

The coupled elastohydrodynamic problem based on the dynamic equations for a viscous incompressible fluid and for two closed finite-length cylindrical elastic shells, inner and outer, described using...

The influence of elastic compliance of the float housing on the vibration perturbing moment in gyros with cylindrical floating suspension in the case of symmetric fluid outflow was studied in [1, 2]....