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Registration Number

0214U007982, 0112U001313 , R & D reports

Title

Combinative resonances, bifurcations and parametric stabilization of mechanical systems

Head

Patsegon Mikola,

Registration Date

19-01-2015

Organization

Kharkov National University named after V.N. Karazin

Description

Object of the research - mechanical systems with distributed parameters: magnetic fluids, systems of aggregating particles, tanks with perforated baffles, elastic and viscoelastic tubes filled with Newtonian and non-Newtonian liquids. Aim of the research - creation of new mathematical models of parametric resonance in the finite volumes of the magnetic fluid, the study of resonance phenomena in alternating magnetic and gravitational fields, the study of stability and bifurcations of fluid flows in systems of viscoelastic tubes. Methods of the research - analytical and numerical methods of continuum mechanics and computational mathematics. Boundary value problems for parametric stability of capillary magnetic fluids in an alternating magnetic field with an arbitrary isotropic magnetization are formulated and investigated. Numerical methods for stability studying of equilibrium states of magnetic fluid are developed. Equilibrium shapes of capillary magnetic fluid in a steady azimuthal magnetic field are found and their stability are investigated. Stability of striped dissipative structures in the films of magnetic fluid and the possibility of periodic motions of magnetized media at their parametric instability are investigated. The flow of Newtonian and non-Newtonian fluids in the systems of deformable tubes is studied. The parameters of the wall material of the tube, which provide flow stabilization are found. The resonance phenomena in multilayered viscoelastic waveguides are investigated.

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Борисов І.
Кізілова Н.
Пацегон М.
Попова Л.
Поцелуєв С.
Руднєв Ю.