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Processes of Supersonic Flows Retardation in Channels

Authors: Lipatov I. I.

Investigated are unsteady laminar boundary layer interaction and separation processes in supersonic flow. Deduced are equations describing such flow and obtained are numerical solutions of linearysed and nonlinear system of equations. It is supposed that these results will allow explain effects accompanying supersonic flow retardation in channels. For the full description it is needed to investigate flow in the reattachment region where selfoscillating processes arise.

Recovering Differential Operators on a Graph with a Cycle and with Generalized Matching Conditions

Authors: Yurko V. A.

The solution of the inverse spectral problem is obtained for second-order differential operators on a graph with a cycle and with generalized matching conditions in the internal vertex.

On Convergence of Fourier – Vilenkin Series in L p [0, 1), 0 < p ≤ 1

Authors: Volosivets S. S.

In this paper we study convergence a.e. and L p -convergence (0 < p ≤ 1) of Fourier –Vilenkin series under some tauberian conditions on Fourier coefficients of a function. In the case of Fourier – Walsh series these results are obtained by F. Moricz.

On the Non-Classic Models of Beams, Plates and Shells

Authors: Tovstik P. E.

For the problems of statics, of free vibrations, and of buckling of beams, plates and shells the Timoshenko – Reissner’s model with shear is compared with the classic Kirchhoff – Love model and with the 3D theory of elasticity. By using some test examples the formal asymptotic character of 1D and 2D models is established and their field of application is found. The asymptotic expansions based on the small shell or plate thickness compared with the length of wave are used. The special attention is paid to the buckling or vibration modes localized near the free surface.

Experiments with Non-Stationary Bilinear Discrete Systems

Authors: Speranskii D. V.

The existence conditions of synchronizing, homing and diagnostic sequences for the non-stationary bilinear systems are found. Methods for synthesis of mentioned sequences are suggested.

Duality Theory and Optimization of Sophisticated Engineering Systems

Authors: Пашин В. М.

The design of sophisticated engineering systems (like the ship, airborne vehicle, production complex, etc.) is usually a multilevel process when the object under design is split up into separate sub-systems. At the same time, the quest for the best solutions for separate sub-systems should comply with requirements for optimality of the designed object as a whole. It is suggested to meet this condition with the help of local criteria developed using dual assessments (Lagrangian coefficients) of the duality theory in the non-linear mathematic programming.

Non-Linear Viscoelastic Behavior of Filled Elastomers

Authors: Lomakin E. V., Beliakova T. A., Zezin Y. P.

The analysis of the results of experimental studies of relaxation properties of rubber at room temperature under the conditions of tension and compression at different strain levels is carried out. For the description of viscohyperelastic deformation of filled elastomers, the constitutive relations are used that are the generalization of non-linear elasticity and linear viscoelasticity Boltzmann – Volterra. The method for the determination of interrelated hyperelastic and reological characteristics of deformation is proposed.

Actual Problems of Aerodynamics (Prospect of Shear Flows Control)

Authors: Kozlov V. V., Sherbokov V. A.

The lecture focuses on control of the near-wall and free shear layers emphasizing the control goals and approaches to modification of the flow characteristics. The control methods, both implemented in practice and prospective ones, employing effects of hydrodynamic instability are under the consideration. In some cases, their application makes it possible to modify local and global flow characteristics at a rather small level of the external forcing generating the controlled shear-layer perturbations.

Mathematical Model of the Closed Molecules of DNA

Authors: Ilyukhin A. A., Timoshenko D. V.

Within the limits of rod model the method of definition of parameters of a spatial configuration ofmolecules of nucleinic acids is developed. By means of the developed method necessary and sufficient conditions of existence of family of the closed molecules of DNA are received. The found conditions can be used at synthesis of the closed molecules with the set parameters.

 

Mechanical Problems in Nanotechnology

Authors: Eremeev V. A., Ivanova E. A., Morozov N. F.

During the last decade, production and adoption of nano-aggregations and nano-inclusions have become actual in electronics, medicine, space engineering and many other branches of production. In this connection, the necessity of studying the nano-subject resistance, stiffness, defectology, durability has emerged. Which of the techniques are best applicable? Feasibility of applying the traditional methods of Newtonian Mechanics, which have been developed and tested for centuries, is widely discussed.

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