Sessions 2016-2017

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Computers make
very fast,
very accurate
mistakes.

April 25, 2017

V.V. Makevnina (SPbSU)
Study of a possibility of the analysis of the lungs mechanics for use in clinical practice.
The report is devoted to research of a possibility and relevance of creating the method to estimate and to visualize the regional distribution of ventilation in lungs. The report contains the short review of the human lungs models and the method to estimate and to visualize influence of ventilation on lungs biomechanics of the specific patient.
Victoria V. Makevnina – the first year master student of the Faculty of Mathematics and Mechanics at the Saint-Petersburg State University. Area of scientific interests - respiratory support, biomechanics of lungs. Scientific supervisor prof. Sergey K. Matveev.

April 18, 2017

A.V. Tarasov (SPbSU)
Infinite plate with elliptic inclusions under uniaxial tension.
The comparative analysis of Hardimans solution and Malkovs solution for this type of problems is considered. These solution were received using different methods in the theory of elasticity. In Malkovs paper it was claimed that Hardimans solution is incorrect, and it has some errors. It should be checked.

In addition, the analysis of stability using the method of virtual displacements and the increment of plate energy is given.
Andrey V. Tarasov – the first year Ph.D. student of the Department of Theoretical and Applied Mechanics at the Mathematics and Mechanics Faculty of the Saint-Petersburg State University. Scientific supervisor Asso. Prof. Galina V. Pavilaynen.

April 4, 2017

O.V. Barinova (SPbSU)
Particular solutions of Chapman-Kolmogorov equation and their connection with equations of mathematical physics.
In this paper we establish the connection of some particular solutions of the bilinear equations of Kolmogorov-Chapman with linear differential and integro-differential equations. Moreover, the examples of random Markov processes with continuous and discontinuous trajectories. The differential diffusion equation, integro-differential equations. It appeared, among integro-differential equations are equations with singular integrals and equations with fractional derivatives, previously in the theory of Markov processes are unknown to us. In the derivation used the asymptotic analysis of non-standard evaluation of integrals Erdelyi and procedures of taking the integral using the principal value of Cauchy and other techniques from mathematical physics.
Olga V. Barinova – the first year master student of the Faculty of Mathematics and Mechanics at the Saint-Petersburg State University. Scientific supervisor – Prof. R.N. Miroshin.

March 28, 2017

V.E. Kondrenkina (SPbSU)
Effect of hygroscopic growth on light scattering by salt aerosols
One of the major uncertainties in the understanding of Earths climate system is the interaction between solar radiation and aerosols in the atmosphere. This is due to the fact that the aerosols are the most variable component of the atmosphere. An aspect of this variability is related to the dependence of the optical properties of hygroscopic aerosols on relative humidity. Therefore, the estimation of the aerosol radiative forcing requires the calculation of the scattering coefficients of wet aerosols. This work is dedicated to that problem in the context of inorganic salt particles, with well-studied hygroscopic properties. Calculation of scattering coefficients of polydisperse aerosols are based on Mie theory. A strong dependence of the scattering coefficient of salt particles upon relative humidity was found that confirms the importance of taking into account the hygroscopic growth of aerosols in the atmospheric optics problems.
Vladlena E. Kondrenkina – the first year master student of the Faculty of Mathematics and Mechanics at the Saint-Petersburg State University. Project scientific supervisor – PhD. S.S. Vlasenko.

March 21, 2017

M.D. Ushakov (SPbSU)
Influence of dissipative processes on regularities of fracture in aging viscoelastic media.
Operating conditions, which may contain plastics, polymer products and structures, are not always favorable to the stable state of the material. Polymer materials are affected by mechanical (voltage varying intensity), physical (heat, light, radiation), chemical (oxygen, water, etc) factors. Internal physical and chemical processes that occur as a result of these effects lead to a change in the characteristics of the polymers. In total, these processes determine the aging of the material.

Due to massive introduction of polymers and polymer-based composites in engineering, agriculture, medicine, aircraft industry it is the question of forecasting performance of these materials with regard to the aging factors.

There are many examples of the destruction of structural elements after a long period of usage. This process is associated with the accumulation of damage, various defects of micropores, cracks. When the damage reaches a dangerous level - material is destroyed. In its simplest form "damage" can be described by some scalar, which can be interpreted as "continuity".

In this research we consider the damage parameters (continuity) of visco-elastic Maxwell model recorded on the scale of the effective time. Effective time parameter allows us to describe the interrelated deformation and physicochemical processes, which gives a better description of the damage in the aging process. Based on the solutions of the system of Maxwell's interrelated equations and the parameter of damage, the appropriate creep and damage parameter curves are constructed. It is shown that these relations describe qualitatively, and in case of creep - quantitatively, the corresponding experimental curves.
Maxim D. Ushakov – the first year master student of the Faculty of Mathematics and Mechanics at the Saint-Petersburg State University. Scientific interests area – long time strength and age hardening of polymers. Scientific supervisor – Prof. R. A. Arutyunyan.

March 14, 2017

V.G. Druzhinin (SPbSU)
Semi-automatic system for cargo damping.
The aim of this work is to create a semi-automatic system for damping of cargo, suitable for all obsolete load-lifting systems. The damping system is based on the work principle of experienced crane operators. It is required that when the system is stopped, the oscillations are damped within 10-15 seconds, until the residual amplitude of 1-2 degrees.

The control object model was developed to create a damping system based on this model. A damping system was developed to control the crane carriage. Simulation of the work of the synthesized regulator was conducted and its work was evaluated.
Vasily G. Druzhinin – the first year master student of the Faculty of Mathematics and Mechanics at the Saint-Petersburg State University. Scientific interests area physical mechanics, theory of automatic control. Scientific supervisor Prof. V.A. Morozov.

February 28, 2017

Ya.V. Cherneikina (SPbSU)
Microstructures and mechanical properties of magnesium alloy processed with high-pressure torsion.
The aim of this study is to increase the mechanical and corrosion properties of magnesium alloy Mg-1%Ca, subjected to high-pressure torsion (HPT). As the result of the study, an ultrafine-grained (UFG) structure with an average grain size of 210 9 nm was obtained by HPT. The UFG samples were annealed at different temperatures. The optimal combination of high strength (245 12 MPa) and ductility (4,0 0,3%) was observed in the samples after HPT and heat treatment of 250o. Coatings were applied to the samples with different average grain size by the method of plasma electrolytic oxidation (PEO) to improve the corrosion resistance. As a result, it was found that the samples without coating are highly susceptible to corrosive wear. PEO coating is beneficial to the corrosion resistance of the material.
Yana A. Cherneikina – the first year master student of the Faculty of Mathematics and Mechanics at the Saint-Petersburg State University. Scientific interests area – materials science and metal processing. Scientific supervisor – PhD O.B. Kulyasova.

February 21, 2017

F.A. Gadzhiev (SPbSU)
Influence of high-pressure torsion on mechanical and fatigue properties of VT6 alloy.
The object of this study is to investigate the effect of sample size on the fatigue and mechanical properties of alloy VT6. Comparison of the stress-strain diagrams shows a satisfactory mechanical properties accordance. Analysis of the obtained Woehler diagrams reveals a coincidence during low-cycle tests. Nevertheless a discrepancy in the high-cycle test was observed. So the endurance limit of the alloy presented by small-size specimens is lower than the standard one. Mechanical test of the Ti-6Al-4V alloy subjected to HPT processing and subsequent annealing is also presented.
Farid A. Gadzhiev – the first year master student of the Faculty of Mathematics and Mechanics at the Saint-Petersburg State University. Scientific interests area – materials science and metal processing. Scientific supervisor – Prof. R.Z. Valiev.

February 14, 2017

A.V. Zeninskaya (SPbSU)
Free vibrations of the cylindrical elliptical shell near the generatrix by Timoshenko-Reissner model.
Free vibrations localized in a neighbourhood of the weakest generatrix of the cylindrical elliptical shell are considered. The edges of shell are articulately supported. The equations of free vibration of an isotropic shell can be obtain on the basis of the classical Kirchhoff-Love model. The accuracy of the Kirchhoff-Love equations for a transversely isotropic shell is not enough. The Timoshenko-Reissner model taking into account a transversal shear are used in this study.
Anna V. Zelinskaya – the first year PhD student at the Department of Theoretical and Applied Mechanics of St. Petersburg State University. Research interests - mechanics thin structures. Scientific supervisor – Prof. P.E. Tovstik.

February 7, 2017

D.V. Franus (SPbSU)
FEM in Mechanics of Solids with applicationts to Ophthalmology.
Dmitry V. Franus – a graduate of the postgraduate education of the Department of Theoretical and Applied Mechanics at Saint-Petersburg State University (2015). Scientific interests area – the theory of plates and shells, biomechanics. Scientific supervisor – Prof. S. M. Bauer.

December 20, 2016

S.V. Kashtanova (SPbSU)
Studies of the mechanical properties of nano-sized objects.
The present work consists of three chapters. The applications of classical and non-classical theories of multi-layered shells for determination of the Young's modulus of asbestos nanotubes and a qualitative comparison between these theories are discussed in the first chapter.

The second chapter examines two cases of the surface tensions effects on the stability of a stretched infinite plate with a hole (on the boundary of the hole and along the plate), a qualitative comparison of these cases and comparison with the experiment.

The third chapter is devoted to the study of the stability loss of an infinite plate with a circular inclusion of another elastic material, the influence of the elastic moduli on the stability loss and the qualitative comparison of the results with the ANSYS data.
Stanislava V. Kashtanova – a graduate of the postgraduate education of the Elasticity Department of the Faculty of Mathematics and Mechanics at Saint-Petersburg State University (2016). Scientific interests area – shells and membranes, stability loss, nanomechanics. Scientific supervisor – academician of Russian Academy of Sciences, prof. N.F. Morozov, scientific consultant – prof. S.M. Bauer.

December 13, 2016

A.S. Smirnov and B.A. Smolnikov (SPbSU)
Resonance oscillations control in the non-linear mechanical systems
The existence and location of controlled resonance modes which are of practical interest are studied in the work. The subject of research is the simplest mechanical system with two degrees of freedom a double mathematical pendulum. So-called collinear control is formed. It is kinetic, i. e. taking into account the dynamic structural features. The evolution process of oscillation forms is analyzed during the transition from linear to non-linear field on the basis of this control. Asymptotic formulas are constructed for the analytical description of non-linear oscillations. They adequately reflect the behavior of the system and correlate well with the numerical results.
Alexey S. Smirnov – the second year master student, Department of Mechanics and Control Processes, Institute of Applied Mathematics and Mechanics, Peter the Great SPbPU. Research interests: analytical mechanics, rigid body dynamics, optimization in mechanics. Scientific supervisor Prof. B.A. Smolnikov
Boris A. Smolnikov – Professor, Department of Mechanics and Control Processes, Institute of Applied Mathematics and Mechanics, Peter the Great SPbPU. Research interests: general mechanics, biomechanics, robotics, motion of cosmic objects, control theory

December 6, 2016

I.A. Melemchuk (SPbSU)
Investigation of the structure and mechanical properties of titanium alloy VT8M-1 subjected to severe plastic deformation.
The objective of this work is to analyze the formation of ultrafine-grained (UFG) structure and enhancement of the mechanical characteristics of VT8M-1 alloy by severe plastic deformation (SPD).

Microstructural studies have shown that in the course of SPD of the alloy VT8M-1 processed by equal channel angular pressing (ECAP), the fragmentation and globularization of lamellae occur. After 6 ECAP passes a bimodal structure is formed, consisting of globules of the primary α-phase and a fine disperse globular mixture of (α+ β)-phases, with an average particle size of 0.67 microns.

The strength properties of the alloy are significantly increased due to formation of the UFG structure, with a slight decrease of plasticity.
Melemchuk Ilya A. – the first year master student of the Faculty of Mathematics and Mechanics Saint-Petersburg State University. Scientific interests area material science and metal processing. Scientific supervisor PhD G.S. Dyakonov.

November 22, 2016

D.G. Korytnikov (SPbSU)
To the question of electrodynamic control of rotational motion of the screened spacecraft around the center of mass on the regressing orbit.
In this work the rotational motion of the spacecraft (SC) around the center of mass, moving on the Earth orbit, is studied. The SC is equipped with the charged screen of electrostatic protection with the controlled charge distribution, as well as with its own controlled magnetic moment. The perturbing influence of the gravitational moment is considered. The secular perturbations of the orbit caused by the second zonal harmonic of the geopotential are taken into account. The octupole approximation of the geomagnetic field is used. The problem of electrodynamic stabilization of rotational motion of the SC in the orbital coordinate system in case of the regressing orbit is solved by means of the Lorentz moment and the moment of magnetic interaction. For the solution of the problem the system of electrodynamic stabilization of the SC is used. Due to noncentrality of the gravitational field, the terms not depending on the orientation of the SC appear in the expression of the gravitational moment. The method of electrodynamic compensation of the permanent perturbing moment is developed and applied to the problem. The efficiency of the proposed technique is shown in a number of numerical experiments.
Dmitry G. Korytnikov – the first year master student of the Faculty of Mathematics and Mechanics at the Saint-Petersburg State University. Scientific interests area: electrodynamic control of rotational motion of the spacecraft around the center of mass. Scientific supervisor Prof. A.A. Tikhonov.

November 15, 2016

A.G. Stotskiy (SPbSU)
Study of the microstructure and mechanical properties of titanium Grade 4 after ECAP-Conform.
The aim of this work is to improve the mechanical properties of titanium Grade 4 by forming ultrafine-grained (UFG) structure by the method of ECAP-Conform and generating plasma electrolytic oxide (PEO) coating on its surface.
As a result of severe plastic deformation in ECAP-Conform performed at 200 C, the significant increase in the tensile strength and microhardness is observed at the initial stages of the deformation. With further deformation, the tensile s trength increases gradually. After 4 ECAP-C passes, the microhardness reaches the saturation that may be associated with the dynamic return. Titanium PEO results show that depending on the conditions of the electrolytic-plasma processing it is possible to obtain coatings with required characteristics.
Oxide layers synthesized on titanium in the calcium acetate electrolyte are used as coatings on metal implants, which in turn is of great interest for the modern medicine.
Andrey G. Stotskiy – the first year master student of the Faculty of Mathematics and Mechanics at the Saint-Petersburg State University. Scientific interests area: materials science and metal processing. Scientific supervisor – PhD.(Eng.) G.S. Dyakonov

November 1, 2016

O. V. Kornienko (SPbSU)
The influence of variable diameter of vibrationally excited molecules on the shear viscosity coefficient
The influence of variable diameter of vibrationally excited molecules on the shear viscosity coefficient in the state-to-state approach is studied. Three models for molecular diameters are considered: Kang--Kunc, Morse, and Tietz--Hua. On the basis of these models, diameters of H2, N2, O2, NO, Cl2, HF, I2 molecules for different vibrational--rotational states are calculated. The Kang and Kunc model yields exponential increasing of the molecular diameter for vibrational levels higher than 10, and therefore its use is reasonable only at low temperatures. Tietz--Hua and Morse models provide similar values for diameters. It is shown that contribution of rotational excitation to the diameters of considered molecules can be neglected. For various potentials, temperatures, and both equilibrium and non-equilibrium vibrational distributions the ratio of state-to-state shear viscosity coefficient to that for the molecule in the ground state is calculated. For all cases considered, rising of molecular size with the vibrational state does not affect the viscosity coefficient; the deviation does not exceed 13%. Thus we prove the validity of the assumption that dependence of elastic collision cross section on the vibrational state can be neglected while calculating state-to-state transport coefficients. This gives justification for applying simplified algorithms for simulation of state-specific transport coefficients which reduce considerably computational resources required for the solution of modern non-equilibrium fluid dynamic problems.
Olga V. Kornienko – the first year master student of the Faculty of Mathematics and Mechanics at the Saint-Petersburg State University. Scientific interests area: kinetic theory of fluids and gases Scientific supervisor – Prof. E.V. Kustova

October 18, 2016

D.Y. Nikitin (SPbSU)
Electromagnetic aspects in attitude dynamics of a shielded Earth artificial satellite with respect to the center of masses
We consider a satellite system with three screens of electrostatic protection, made in the form of charged toroidal shells with the outer radii about 100m. As a result of the interaction of the electric charge of screens with Earth's magnetic field (EMF) the moment of Lorentz forces occurs, influencing the rotational motion of the satellite. In view of the large sizes of design of the electrostatic protection, calculation of the moment of Lorentz forces takes into account the difficult form of screens and the heterogeneity of the earth's magnetic field in the volume of screens. It is assumed that the center of charge satellite coincides with its center of mass. As a computational EMF model, direct magnetic dipole is adopted. In this paper we investigate the possibility of using the moment of Lorentz forces for passive and semi-passive stabilization satellite equipped with of the electrostatic protection, moving in a circular low Earth equatorial orbit. In this paper the mathematical model was made, describing the dynamics of rotational motion of the satellite, equipped with electrostatic protection system in EMF and built its first integral. Direct equilibrium position (DEP) of the satellite in the orbital coordinate system was found. Sufficient conditions for the stability of the DEP by using the first integral were received. The stability area of DEP was analyzed, depending on the system parameters. For dynamically and electrostatically symmetric satellites stationary regimes of rotation in the orbital coordinate system and sufficient conditions for the stability of these rotations are found.
Danil Y. Nikitin – the first year master student of the Faculty of Mathematics and Mechanics at the Saint-Petersburg State University. Scientific interests area: mathematical modeling, movement stability. Scientific supervisor – Prof. A.A. Tikhonov.

October 4, 2016

V.A.Maltsev (GUMRF)
Mathematical modeling of stress-strain state of the ship decking elements.
This work demonstrates modern methods and means of deflection mode calculations occurring to the ship deck elements, used for container loading. It contains the analysis of the modern methods for deflection mode calculation at ship bars on the phase of projecting and exploitation of the ship. The main software complexes, allowing to carry out such calculations, their advantages and disadvantages are reviewed in the work. In order to achieve the target, a software was worked out. The software is based on the method of the final differences, shown in Carmans nonlinear differential equation system, the excellence of which is in the simultaneous deflections and tensions identification, appearing in the object. The results of the formed software functioning are pointed in the work. In addition, this results can be presented in graphical form, which is convenient for visual presentation, and in the form of tables with values. Using this method allows to find the values of the stresses and strains at any grid point of the mesh, which makes it not only versatile, but also faster compared to conventional.
Valery A. Maltsev – the 4th year post-graduate student of the Faculty of Information Technology at Admiral Makarov State University of Maritime and Inland Shipping. Scientific interests area – elasticity theory, stress-strain state of plates, CAD systems. Supervisor – Asso.Prof. S. Sokolov.

September 27, 2016

S.I. Rerikh (SPbSU)
Influence of various plastic deformation processes on the properties of bulk metallic glasses
In the last several years, the influence of various plastic deformation processes on the properties of bulk metallic glasses (BMG) has been investigated. The present work is intended to analyze changes in the microhardness of Zr62Cu22Al10Fe5Dy1 BMG after processing by high-pressure torsion (HPT), one of the severe plastic deformation techniques. The deformation was carried out at room temperature and temperature of 150C using a pressure of 6 GPa and 5 anvil turns. Vickers indentation was used to evaluate the microhardness of the samples in initial state and after HPT-processing. The Vickers microhardness values of the material subjected to HPT technique at room temperature were significantly lower than those of non-deformed material. Nevertheless, HPT processing at 150C resulted in recovery of microhardness values to the initial values and appearance of shear bands. Observable changes can be explained by the redistribution and evolution of free volume. More detailed studies of internal structure will be conducted to reveal the nature of the observed changes.
Stepan I. Rerikh – the first year master student of the Faculty of Mathematics and Mechanics at the Saint-Petersburg State University. Scientific interests area – materials science, plasticity theory. Scientific supervisor – Prof. R.Z. Valiev.

September 13, 2016

D.I. Zhuravleva (SPbSU)
Sensitivity analysis of biomechanics of human eye
Four methods of global sensitivity analysis are described in the work: elementary effects method, Sobol' method, polynomial chaos method and PAWN method. Analysis and validation of three models of intraocular pressure changing while intravitreal injection are performed: in the first two models human eye is considered a sphere of isotropic, in the first one, and of transversally-isotropic, in the second model, material filled with uncompressible liquid, in the third model human eye is believed to be a transversally-isotropic shell filled with uncompressible liquid.
Darya I. Zhuravleva – the first year master student of the Faculty of Applied Mathematics and Control Processes at the Saint-Petersburg State University. Scientific interests area – sensitivity analysis and mathematical modelling in biomechanics. Scientific supervisor – Asso. Prof. Eva B. Frumen.

September 6, 2016

V.A. Shelkovina (SPbSU)
Mathematical models of a rotor equipped with a ball self-balancing system
A static unbalanced Jeffcott rotor equipped with a ball self-balancing system is studied. The rotor rotates with constant angular velocity. Supposing the desired rotor and the balancing balls dynamics variables being "slowly" in a coordinate system, which rotates synchronous with the rotor. The two approximate systems of reduced equations are deduced. The numerical computation of the transient modes and the investigation of balanced/unbalanced static modes stability are made. They result in the fact, that using of the reduced equations does not loss the serious computational accuracy by the defined parameter limitations.
Veronika A. Shelkovina – the second year PhD student of the Department of Theoretical and Applied Mechanics at Mathematics and Mechanics Faculty of the Saint-Petersburg State University. Scientific interests area – rotor dynamics and autobalancing. Scientific supervisors – Asso. Prof. Vladimir G. Bykov