Bending oscillations of a cylinder, surrounded by an elastic medium and containing a viscous liquid and an oscillator

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

Mathematical modeling of hydroelastic walls oscillations of the channel on Winkler foundation under vibrations

The bending oscillations of a narrow slit channel walls with highly viscous liquid inside and put on a vibrating Winkler foundation are investigated. The channel walls bending oscillations laws are discovered on the basis of hydroelasticity problem solution, as well as pressure in the liquid ones. The deflections amplitudes distribution and liquid pressure along the channel functions are constructed. The obtained results allow investigating dynamic processes, conditioned by constructions elastic elements and viscous liquid interaction in lubrication system, damping and various devices and units

Hydroelasticity of three elastic coaxial shells interacting with viscous incompressible fluids between them under vibration

Elastic cylindrical shells interacting with a viscous incompressible fluid are widely used in various branches of science and technology, such as engineering and aviation engineering. They provide the possibility for solving a lot of problems, such as: reducing constructing weight and dimensions, equalizing dynamic influences and vibration level, as well as reducing friction and wearing, cooling. Mathematical model of the system, representing three coaxial cylindrical shells, freely supported at the ends, and interacting with viscous incompressible fluid between them under mechanical system harmonic vibration is constructed. This mathematical model represents a coupled system consisting of the Navier-Stokes, continuity for each fluid and equations and the ones of elastic coaxial cylindrical shells dynamics which are based on the Kirchhoff-Love hypotheses and the corresponding boundary conditions, namely: for the fluid non-flow and for free attaching for the shells. The constructed mathematical model allows to investigate the oscillations of a mechanical system consisting of coaxial elastic cylindrical shells interacting with viscous incompressible liquids in order to identify dangerous operating modes

Mathematical model of elastic ribbed shell dynamics interaction with viscous liquid under vibration

The mechanical model of the system, formed by two surfaces of the coaxial cylindrical shells interacting with viscous incompressible liquid between them under vibration, is considered. The outer shell is geometrically irregular, and inner one is an absolutely rigid cylinder. The mathematical model of this system, consisting of differential equations in partial derivatives for describing dynamics of viscous incompressible liquid and an elastic ribbed shell together with boundary conditions is constructed. The expressions for amplitude frequency characteristics of outer geometrically irregular shell are discovered

Axisymmetric Longitudinal-Bending Waves in a Cylindrical Shell Interacting with a Nonlinear Elastic Medium

A nonlinear differential equation is derived which describes the propagation of axisymmetric stationary longitudinal-bending waves in infinite cylindrical shell of Timoshenko type, interacting with the external nonlinear elastic medium. A modified perturbation method based on the use of diagonal Pade approximants was applied to build exact solitary-wave solutions of the derived equation in the form of traveling front and the traveling pulse. Numerical solutions of the equation, obtained by means of finite difference method, are in good agreement with the corresponding exact analytical ones

Axisymmetric Longitudinal-Bending Waves in a Cylindrical Shell Interacting with a Nonlinear Elastic Medium

A nonlinear differential equation is derived which describes the propagation of axisymmetric stationary longitudinal-bending waves in infinite cylindrical shell of Timoshenko type, interacting with the external nonlinear elastic medium. A modified perturbation method based on the use of diagonal Pade approximants was applied to build exact solitary-wave solutions of the derived equation in the form of traveling front and the traveling pulse. Numerical solutions of the equation, obtained by means of finite difference method, are in good agreement with the corresponding exact analytical ones