N. I. Lobachevsky State University of Nizhni Novgorod


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RESEARCH INTO DYNAMICS OF DISCRETE AND DISTRIBUTED CONTROLLED MECHANICAL SYSTEMS:

 

- Construction and analysis of mathematical models of mechanical systems with the purpose of detection of new physical effects and determining the conditions for stability and occurrence of self-oscillations, solution of problems of stabilization of mechanical systems' motion by means of control;
 
- Analysis of rapidly rotating bodies' stability in fields of force of various physical nature; solution of important  problems of stabilization of unstable rotating objects by means of gyroscopic and dissipative forces and problems of calculation and design of contactless suspensions;
 
- Research of mathematical models of complex self-oscillatory systems in machine-tool construction;

 

- Mathematical modelling of systems  in vacuum engineering.

 

Main results:
Leading experts:
Main technological and research equipment:
Main partners and customers:
Key projects (sources of financing):
Main publications:
  

 

Main  results:
- The theory, analytical and numerical methods and algorithms for the synthesis of control laws for stabilization and oscillation suppression in mechanical and electromechanical systems have been developed. Mathematical models have been built, optimum parameters for objects of mechanical and power engineering have been determined. Laws of optimum control of injury-safe systems on motor transport have been obtained;
- A number of applied problems of optimal suppression of oscillations in high-rise structures caused by wind and seismic factors have been solved;
- A generalization of Kelvin's theorem on achieving rotating bodies' stability by means of gyroscopic forces has been given. Conditions for stability of rotating bodies in a contactless suspension have been obtained. A mathematical model for explaining the observed long-term changes in the speed of rotation of the Earth has been developed;
- Scientific principles for  construction of mathematical models of complex self-oscillatory systems in machine-tool industry have been developed. Methods for stability analysis and research of the global structure of the phase space in quasilinear distributed systems with a lag have been developed. Sensitivity theory in application to the analysis and synthesis of free and forced oscillations in multidimensional distributed systems has been developed. A technique of search for sensitive connections and the most significant mechanisms of self-excitation of oscillations for self-oscillatory objects in mechanical engineering has been devised;
- Mathematical models and methods of optimal design of self-oscillatory systems with a lag have been developed. Conditions of stability and occurrence of self-oscillations in distributed electromechanical systems and systems with a lag have been obtained. Recommendations on improvement of pre-production models of equipment have been provided, algorithms and program systems which have been used in the industrial enterprises of mechanical engineering (Nizhni Novgorod and Dmitrov factories of milling machines, Chepetsk mechanical factory, Gorky Automobile Plant, Research Institute of Measuring Systems, etc.) have been created;
- Analytical and numerical analysis of possible types of motions and their bifurcations in four-dimensional singularly perturbed model of a mechanical system with Painlevé paradox has been performed;
- Phase and bifurcation portraits of dynamics of a gravitational controlled rotator have been obtained. Optimally stable algorithms for controlling active magnetic bearings have been developed along with a technique for balancing a rigid rotor;
- A mathematical model of the vacuum pump/compressor has been developed. It shows promise for creating an automatic system for deep vacuum measurement in  space research.

The obtained results have no analogues, they have been recognized among experts in the field of oscillation theory and nonlinear dynamics, mechanics, control theory and machine dynamics, methods of data array processing, problems of dynamics in mechanical engineering and machine-tool building, problems of controlling dynamic objects under the conditions of uncertainty, mathematical modelling.

The obtained results can be used in:
- Design of effective means for providing vehicle safety;
- Solution of vibration problems at metal cutting;
- Solution of problems of the analysis and synthesis of complex mechanical systems in automotive and mechanical engineering.

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Leading experts:
- Yuri Isaakovich Neimark, D.Sc. (Engineering), Professor;
- Dmitry   Vladimirovich Balandin, D.Sc. (Physics and Mathematics) , Professor;
- Gennady Grigorevich Denisov , D.Sc. (Physics and Mathematics), Professor;
- Valery Vyacheslavovich Novikov, D.Sc. (Physics and Mathematics);
- Victor Sergeevich Voronkov, D.Sc. (Physics and Mathematics);
- Vadim Pavlovich Ivanov, Cand.Sc.(Physics and Mathematics);
- Sergey Nikolaevich Strebulyaev , Cand.Sc.(Engineering).

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Main technological and research equipment:
- Standard personal computers with the system of  automated research of technical devices "MATLAB";
- Installation for suspending magnetic bodies.

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Main partners:
- Institute of problems of mechanics of the Russian Academy of Sciences,
- Institute of problems of mechanical engineering of the Russian Academy of Sciences,
- Research institute of mechanics of the Moscow State University,
- Moscow and St.-Petersburg State Universities,
- University of Virginia, USA (Laboratory of automobile safety).

Main customers:
- Joint-Stock Company "OKB-Nizhni Novgorod " of the Federal Agency for Atomic Energy,
- Nizhni Novgorod and Dmitrov factories of milling machines.

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Key projects (sources of financing):
- Projects of the Russian Foundation for Basic Research 01-01-00591 à , 01-01-00169 à , 02-01-00921, 04-01-81009 à , 06-01-00368 à , 06-01-03010 à;
- The analytical departmental target program of the Federal Agency for Education «Development of the scientific potential of  higher education institutions», Project 1.52.06.

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Main publications:
- Balandin D.V., Kogan M.M. Synthesis of control laws  on the basis of linear matrix inequalities. Ì.: Fizmatlit. 2007. 280 Pp.
- Balandin D.V., Bolotnik N.N., Pilkey W.D., Purtsezov S.V., Shaw C.G. Concept of a platform-based impact isolation system for protection of wheelchair occupants from injuries in vehicle crashes // Medical Engineering and Physics. 2008. V. 30. P. 258-267.
- Balandin D.V., Bolotnik N.N., Belozerov A.S. Analysis of limits for protecting human head from the injuries caused by impacts, in view of the duration of a shock impulse // Izvestiya Rossiiskoi Akademii Nauk. Control theory and systems. 2008. 1. Pp. 67-77.
- Denisov G.G., Novikov V.V., Fedorov A.E. Gravitational interaction of Earth's mantle and its hard core and variations in the length of day // Astronomical journal. 2008. V . 52. No.12. Pp.  1027-1034.
- Denisov G.G., Novikov V.V., Fedorov A.E. Dynamics of a body with an electric charge in the field of a point charge // Izvestiya Rossiiskoi Akademii Nauk. Mechanics of solids. 2007. No.6. Pp. 4-13.
- Voronkov V.S., Denisov G.G. A technique for the balancing of a rigid rotor in two radial elastic bearings // Problems of mechanical engineering and reliability of machines. 2006. No.4. Pp.  32-30.
- Gorodetsky Yu.I. Sensitivity functions and dynamics of complex mechanical systems. A manual. Nizhni Novgorod. NNSU. 2006. 256 Pp.

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