TAILIEUCHUNG - Mathematical modelling and control of the evolution of dynamic systems interacting with medium

The article proposes a new method of mathematical modeling evolutional systems interacting with medium. A cutting process or tribo-space formed in the contact area of two conjugate mechanical subsystems is considered as medium. The features of the medium depend not only on state coordinates of systems but also on trajectories. | Vietnam Journal of Mechanics, VAST, Vol. 33, No. 3 (2011), pp. 148 – 161 MATHEMATICAL MODELLING AND CONTROL OF THE EVOLUTION OF DYNAMIC SYSTEMS INTERACTING WITH MEDIUM . Zakovorotny1, Nguyen Dong Anh2 , Pham Dinh Tung1 1 Don State Technical University, Rostov-Don, Russia 2 Institute of Mechanics, Hanoi, Vietnam Abstract. The article proposes a new method of mathematical modeling evolutional systems interacting with medium. A cutting process or tribo-space formed in the contact area of two conjugate mechanical subsystems is considered as medium. The features of the medium depend not only on state coordinates of systems but also on trajectories. It is obtained that the parameters of the medium are performed as integral operators of equations like Volterra equations of 2nd type. The problems of control of evolutional systems are being analyzed. Keywords: Evolutional system, interact, medium. 1. INTRODUCTION Studying evolution of technical systems is traditional and corresponds to the problem of ensuring reliability. In particular, studying evolutional transformations of processes on cutting machines affects the development of wearing of instruments changing cutting products quality indexes [see . 1-5]. All those indexes characterize the external display of evolutional changes. The evolutional changes of dynamic characteristics of cutting process, which influences the parameters of geometrical quality of goods and the state of cutting process, perform a more important meaning. They affect the current characteristics of the irreversible transformations, which are characterized by trajectories of changing the power of irreversible transformations of the function of work being performed. In technical systems with the friction areas the evolutional changing of matrices of dynamic rigidity and dissipation of tribo-space, being formed in the areas of conjugation of the contacted elements, takes place. The article is devoted to studying evolutional changes of the .

• Toán học
• Vietnam Journal of Mechanics
• Mathematical modelling and control of the evolution
• Dynamic systems interacting with medium
• Mathematical modeling evolutional systems interacting
• Two conjugate mechanical subsystems
• Dang Dinh Ang
• Nonlinear analysis and mechanics
• Dynamic problems involving stationary cracks
• The Wiener Hopt technique
• Dual integral equations
• Dual integrals in non linear fracture mechanics
• Non linear fracture mechanics
• Energy release rate
• Discuss the obtained
• The alpha finite element method (αFEM)
• Solid mechanics using triangular and tetrahedral elements
• Suitable computational cost
• NS FEM makes
• The upper bound property
• Non linear constitutive problems in solid mechanics
• Non linear constitutive problems
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• The application FEM
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• H14 31 model to forecast heavy rainfall in Vietnam
• Betts Miller Janjic
• Three rain seasons
• Manufacturing dry mixed cement mortar
• High compressive strength
• High flexural strength
• Low shrinkage and high watertightness for restoration
• Damaged hydraulic structures in Vietnam
• Standard gradient models and crack simulation
• Standard gradient models
• The propagation of cracks
• Damage mechanics and crack simulation
• The interaction between two parametric excitations
• The second and third degrees
• The asymptotic method of nonlinear mechanics
• Dynamic system governed
• Comparison of two hydrological model simulations
• Nam and Xinanjiang for Nong Son catchment
• The Central Vietnam
• The runoff components
• 3 D numerical simulation
• The tidal circulation
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• The kinetic energy distribution
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• The analysis of responses
• The original nonlinear systems
• The study of nonlinear mechanics
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• Theory and experiment
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• The aerodynamic characteristics
• The Institute of Mechanics
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• p refinement
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• Some initial experimental results
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• Water layer formation
• Hanoi Institute of Mechanics
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