Abstract
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.
Highlights
The problems of mathematical modeling of elastic construction elements interaction with liquid are of theoretical and practical interest [1]
References [22, 23] are devoted to the plate oscillation investigation, the plate standing on the elastic foundation and interacting with viscous liquid layer
In accordance with the approach, suggested in [18], we study the deflection of a hollow cylinder, surrounded by an elastic medium, by means of one-mass system
Summary
The problems of mathematical modeling of elastic construction elements interaction with liquid are of theoretical and practical interest [1]. [2,3,4,5,6,7,8] deal with hydroelasticity problems of homogeneous plates, interacting with viscous liquid layer in various settings. References [10,11,12] investigate the hydroelastic oscillations of three-layered plates, interacting with viscous pulsating liquid, as well as under inertial excitation. The non-linear longitudinal deformation wave propagation in cylinder shells, filled with viscous liquid and in axis-symmetric setting is presented in [19, 20]. Mathematical modeling of hydroelastic oscillations of a hollow cylinder, surrounded by an elastic medium and containing a viscous liquid and an oscillator, remained beyond the framework of the sources, mentioned above. The problem under consideration is of undoubted interest for the research
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