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Registration Number

0221U102176, 0116U003101 , R & D reports

Title

Mathematical problems of the dynamics, stabilisation and optimisation of complex mechanical systems

Head

Lukovskyi Ivan O, Доктор фізико-математичних наук

Registration Date

28-01-2021

Organization

Institute of Mathematics of the National Academy of Sciences of Ukraine

Description

The object of research is dynamics and stability of complex mechanical systems "body - liquid with a free surface" and the corresponding non-classical boundary problems, differential and difference systems of equations, mathematical models of control systems. The purpose is to construct mathematical models of mechanical systems that have reservoirs with liquid, elastic elements, are under vibration, inertial, etc. loads; development of analytical and numerical methods for solving non-classical boundary problems; analysis of stability, robust stabilization and optimization of complex control systems. Research methods - variational, asymptotic, spectral linear algebra, Lyapunov functions of stability theory, operator, etc. The main results are: boundary problems with a free surface; it is shown that finding their solutions is equivalent to determining stationary points of special type functionals; an approximate-analytical method for constructing the solution is proposed; methods for reducing the fluid problems to mathematical models in the form of systems of nonlinear ordinary differential equations are constructed (important cases - tanks of nuclear reactors, rocket and space systems, bioreactors for protein cultivation); methods for studying the fluid dynamics in conical cavities are proposed; the established motions of the hydromechanical system are found, their stability is investigated; methods of quality assessment, robust stabilization and optimization of control systems are developed; solved the problem of synthesis of continuous and discrete control systems based on static and dynamic regulators, which reduce and minimize the weighted level of extinguishing external disturbances; based on the Ritz method, spectral boundary value problems with transmission conditions are solved; an algorithm for calculating free oscillations of shells of rotation, partially filled with liquid, when the shell is under the action of a tensile load, is proposed.

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