### April 23, 2019

D.V. Franus (SPbSU)

Features of finite-element modeling of eye biomechanic's problems in COMSOL

The features of finite-element modeling of the corneoscleral shell of human eye under the pressure of applied vacuum compression ring on the example of the
COMSOL software package are considered. The aspects of building the geometry of an elastic multilayer thin-walled shell consisting of two spherical parts: 1) the corneal and 2) the scleral shell are considered in detail.
The features of the use of a curvilinear coordinate system, parameters and variables, contact pair settings are described.

As a result of modeling, the nonlinear relation between modulus of elasticity of the sclera and both displacement and stress of the scleral shell under the load of a vacuum compression ring is revealed.

**
Dmitry V. Franus
** – PhD

### April 9, 2019

I.A. Zakharov (SPbSU)

Ñollision integrals of charged particles

In the modern molecular-kinetic theory of gases, the calculation of transport c
oefficients (such as thermal conductivity, viscosity, diffusion coefficients)
requires the calculation of Ω-integrals. The coefficients of the systems of
equations are expressed with Ω-integrals, with the help of which the
above-mentioned transfer coefficients are calculated. The aim of the
work was to write a software module within the framework of the Kappa
chair project, which calculates collision integrals (Ω-integrals) for
collisions of charged and neutral particles. The main field of application
of the developed module is the calculation
of heat fluxes near the surface of high-speed aircraft.

**
Ilya A. Zakharov
** – the 1st Master student of Department of Hydroaeromechanics
of the Faculty of Mathematics and Mechanics at St. Petersburg State University.
Scientific area: molecular-kinetic theory of gases, calculation
of heat fluxes.
Scientific supervisor – Prof. E.V. Kustova.

### March 12, 2019

A.V. Dementyev (SPbSU)

Specific features of the reflection by the radiation
of a compact highly focused rotating source

The location is based on the fact that the analysis of the properties of the reflected signal provides opportunity to get information about the surface of the studied or revealed object. In the case of the location of farther objects and in larger solid angle two methods can be used: 1) to send the high energetic flux of the radiant energy (electromagnetic, acoustic etc.) at once on all possible directions by the short impulses; 2) to concentrate this flux in the narrow ray and scan different directions by it. Given the finite value of the speed of propagation of the signals the irradiation of one and the same object by these two methods may result in the appearance of the reflected impulses with different parameters.

In this research the reflection by the screen of the spherical and ellipsoidal form of the electromagnetic radiation of the compact source uniformly rotating about its axis and radiating in the limited solid angle is considered. The profiles of the reflected impulses are calculated, as well as the moments of their arrival at the remote observer. The conditions are determined under which the above methods of the irradiation of the screen give the reflected impulses with substantially different parameters.

**
Dementyev Andrei Viktorovich
** – Associate Professor of the
Department of Astrophysics, Faculty of Mathematics and Mechanics,
SPbSU. Research interests: Theory of Radiative Transfer, Physical Kinetics.

### February 26, 2019

V.V. Komarov (SPbSU)

INVESTIGATION OF THE HYDROACOUSTIC IN A PIPE WITH A RING-SHAPED
OBSTACLE WITH THE WATER FLOW

When fluid flows in various channels and valves, hydrodynamic noise, vibration and noise near the device may occur. The process of hydrodynamic noise in the liquid itself is complex and is associated with the presence of vorticity. When the flow is detached from the wall, vortices and an uneven pressure field are formed, but this field is not a sound as the disturbances propagate with the flow velocity. The existing vortices hit the elastic walls of the channel, causing their oscillations, which will be the source of the sound and propagate with the speed of sound in the liquid. In this regard, the complex problem of determining hydrodynamic noise and vibration-noise characteristics can be considered separately.

In this work, a non-stationary hydrodynamic field is investigated when water
flows in a circular pipe with a spacer. As a result of the hydrodynamic calculation,
nonstationary pressure distributions along the pipe walls and nonstationary flow patterns of the beam are determined. The Fourier transform of the unsteady pressure field on the walls is performed and these data are sources for the calculation of the vibro-acoustic problem.

**
Vladislav V. Komarov
** – the 1st Master student of Department of Hydroaeromechanics
of the Faculty of Mathematics and Mechanics at St. Petersburg State University.
Scientific area: computational hydrodynamics, hydroacoustics.
Scientific supervisor – Asso.Prof. A.G. Karpenko.

### February 12, 2019

A.A. Morshchinina, D.A. Morshchinina (Radioavionica Ñorporation)

Analysis of reliability and safety of the Control Ñomputer System produced by Radioavionica Corporation

The structure of the Control Ñomputer System produced by Radioavionica Corporation is considered. The mathematical models of its functioning are developed. The parameters of reliability and safety of the system and its elements are determined. The analysis of reservation influence on their values is carried out. On the basis of the obtained results the reliability and safety of the Control Ñomputer System of various configurations are estimated.

**
Diana A. Morshchinina
** –
PhD, head of the Department of technological and mathematical
support of scientific and technical center of perspective development
of Radioavionica Corporation. Scientific interests: theory of elasticity,
theory of reliability.

**
Alina A. Morshchinina
** –
PhD, leading specialist of scientific and technical center of
perspective development of Radioavionica Corporation.
Scientific interests: theory of elasticity, theory of reliability.

### December 4, 2018

Fazlyeva K.M. (SPbSU)

Control of vibration damping of a three-mass system in horizontal motion.

The research concerns one of the central problems of
the control theory. An incompletely controlled mechanical
system with a finite number of degrees of freedom is considered.
The system motion may be affected by the control force acting
on one of its generalized coordinates. The problem of vibration damping,
i.e. finding the control force that moves the system at the specified distance
from the initial resting state to the final resting state for a finite time period.
To solve this problem we apply the methods of nonholonomic mechanics
with higher-order constraints. It was also shown how the
generalization of Gauss's principle of least constraint allows to
construct the control function that is
significantly different from solutions obtained by classical methods.

**
Camilla M. Fazlyeva
** –
the 2nd year Master student of the
Department of Theoretical and Applied Mechanics of the Faculty
of Mathematics and Mechanics at St. Petersburg State University.
Scientific area: nonholonomic mechanics, control theory.
Scientific supervisor – Prof. M.P. Yushkov.

### November 27, 2018

V.S. Federyaeva (SPbSU, JSC«NIIEFA»),
I.V. Vitkovsky, M.M. Golovanov, I.R. Kirillov, K.A. Komov,
S.A. Krizhanovsky, D.M. Obukhov,G.V. Preslitsky (JSC«NIIEFA»).

New methods and approaches to development of electromagnetic pumps for
liquid metal fast breeder reactors

New methods and approaches to development of electromagnetic pumps for
liquid metal fast breeder reactors are considered based on the design of
immersed EMP of BN-1200 cold trap. Results of complex research of novel
high temperature resistant electrical engineering materials to meet service
life requirements at high temperature are shown. Main issues on improvement
of manufacturing technology of those materials are stated. Computational
results aimed to optimize EMP design, fulfill
stated above requirements and confirm specified parameters are presented

**
Valeriya S. Federyaeva
** –
the 1st year Master student of
Department of Hydroaeromechanics of the Faculty
of Mathematics and Mechanics at St. Petersburg State University.
Scientific area: computational fluid dynamics, high temperature resistant
inorganic materials.

### October 30, 2018

Yu. M. Dahl (SPbSU), A. A. Morshchinina (Radioavionica Ñorporation), D. A. Morshchinina (Radioavionica Ñorporation)

SOME OF THE PROBLEMS OF BENDING AND STABILITY OF ELASTIC BEAMS AND PLATES

The problem of the stress-strain state of a curved beam loaded with an arbitrary transverse load was considered. The integration of the differential bending equation was made by using the operating method. The connection of this method with the method of initial parameters was determined.

The stability of prismatic bars was investigated by the operational method. The physical meaning of the "completely indefinite" numerical factor in the theoretical works of the authors describing the forms of stability loss of bars was determined. The local loss of stability of thin-walled elements of engineering structures was analyzed. The results of some theoretical and experimental studies of this problem were presented.

The features of deformation of thick plates and thin plates with elliptical cut were presented. It was noted that the stress concentration coefficient is a function which depends on the deformed cut configuration.

The results of laboratory experiments on stretched polymer films with a system of rectilinear cuts were presented. The solution of the plane problem of the theory of elasticity about the stretching of a plane with a lattice of rectilinear cuts was presented.

**
Yuriy M. Dahl
** – Doctor of Science (Physics&Math),
professor. Scientific area: theory of elasticity.

**
Alina A. Morshchinina ** – PhD,
lead engineer of scientific and technical center
of perspective development of Radioavionica Ñorporation.
Scientific area: theory of elasticity.

**
Diana A. Morshchinina ** –
PhD, lead specialist of scientific and technical center of perspective
development of Radioavionica Ñorporation. Scientific area: theory of elasticity.

### October 23, 2018

L.A. Igusheva (SPbSU)

Rod dynamic fracture in the Klein-Gordon field

The interaction model of a constant cross-section rod with an elastic environment is considered. The
directly proportional to the displacement resistance forces impacted on the rod.
The equation of longitudinal vibrations of the rod interacting with the elastic medium is obtained. This
equation is well-known Klein-Gordon equation. The solution of this equation is found. Displacements and
stresses arising in the rod under dynamic loading are calculated.
The wave propagation and reflection from the free boundary of a finite-length rod are considered. The
possibility of the effect of spall fracture is shown. Fracture phenomenon is predicted by the incubation time
criterion. In several special cases, the dependence of the threshold value of the load amplitude on the critical
time of the rod fracture and on the duration of the load is found. With a small coefficient of environment
resistance, a range of optimal frequencies load for rod fracture is found.
With an increase in the resistance coefficient of the environment, it is noted that the rod fracture
occurred with the direct propagation of the wave along the rod. It is shown that there are optimal frequencies of
load when the rod fracture occurred.

**
Liudmila A. Igusheva
** – the 1st year Master student of Department of Theory of Elasticity of the Faculty
of Mathematics and Mechanics at St. Petersburg State University. Scientific area: fracture dynamics. Scientific
supervisor - Corresponding Member of the Russian Academy of Science, Professor, Dr. of Science Y.V. Petrov.

V.N. Kylev (SPbSU)

Prediction of some types of failure in the main parts and nodes of special heat engines.

Reliable design, ensuring operability (performance of specified functions)
at the whole stage of the product life cycle, is a complex technical task.
During operation, parametric and functional failures may occur.

Parametric failure - change of the specified
operating parameters in unacceptable limits.
This failure leads to an emergency mode of operation,
in which it is important to ensure that the machine is not destroyed.

Functional failure is equivalent to fatigue failure. It can be
associated with the preservation of the overall cyclic strength,
or with its loss during the onset of high load dynamics. In addition,
fatigue failure can lead to the formation and development of fatigue cracks,
leading to the complete destruction of metal structures. Therefore, the main task
of predicting the failure of products is the analysis of metal fatigue.