### April 17, 2018

Velichko V.E. (IPME RAS)

Deformation of the reflective surface of the optical mirror under its own weight.

An annular single-layer plate of medium thickness, located on local supports and loaded with gravitational load along the axis of rotation, is considered. The thickness of the plate varies in radius, while one of the surfaces is flat, the material of the plate isotropic. The plate represents the model of the optical mirror of the telescope.

To derive the equations of the stress-strain state of the plate, the theory of shells of average thickness of Palia-Spiro (PS) with a reduction surface (PP) combined with a flat part of the plate is used. This theory takes into account the transverse shear and the change in the thickness of the plate deformation rectilinear element, normal to the PP before the application of loads. The problem is reduced to a system of differential equations of the 10th order, which is solved by an orthogonal run. This solution is compared with the solution
obtained by the finite three-dimensional element method (FEM) in ANSYS software.

**
Velichko Viktor E.
** – Graduate student (extramural studies) Institute
of Problems of Mechanical Engineering Russian Academy of Sciences
(IPME RAS). At the same time structural engineer branch
joint-stock company “Scientific and Production Corporation
“Precision Instrument-Making Systems” in St. Petersburg. Research interests:
solid mechanics, theory of plates and shells,
optimization in mechanics, stability theory.

### April 3, 2018

Smirnov A.S., Smolnikov B.A. (SPbPU)

Energy-time optimization criterion in the Hohmann problem

It’s given a new formulation of the classical problem of astrodynamics –
the Hohmann problem – on the optimization of the two-pulse transition of a
spacecraft between two coplanar circular orbits. The energy-time quality indicator
equal to the product of the total increase in the characteristic velocity for
the duration of the transition is adopted as optimization criterion. The detailed
solution of this problem is given, as a result of which the dependence of the
optimal value of the dimensionless initial velocity on the ratio between the
radii of the initial and final orbits is established. The numerical estimates
of the efficiency of the proposed interorbital transition regime are made based

**
Smirnov Alexey S.
** – Assitant Professor of the
Department «Mechanics and control processes» of Peter the
Great St. Petersburg Polytechnic University. Research interests:
analytical mechanics, theory of oscillations, rigid body dynamics, stability theory,
optimization in mechanics, waves in continua.

**
Smolnikov Boris A.
** – Professor of the department «Mechanics
and control processes», Peter the Great St. Petersburg Polytechnic
University. Research interests: general mechanics, biomechanics,
robotics, motion of cosmic objects, control theory. The author of
four books and numerous articles on the rigid body dynamics, robotics
and the mechanics of controlled space objects.

### March 20, 2018

Dzebisashvili G.T. (SPbSU)

Free vibrations of cylindrical shells with the square and rectangular cross-section.

The free localized vibrations of cylindrical shells with
the square and rectangular cross-section are studied in the work.

By means of numerical calculations using Rayleigh–Ritz method and the finite
element method, the natural frequencies of the shells of different sizes are
analyzed and compared.
The distribution of the natural frequencies depending on the shell material
and the shell size is obtained.

**
Georgii T. Dzebisashvili
** – the 4th year Bachelor student
of Department of Mathematics and Mechanics at St.
Petersburg State University. Scientific area:
shell theory. Supervisor – Prof. S.B.Filippov.

### March 6, 2018

Gruzdev K.S. (SPbSU)

TO THE FLOW OF THE INLET OF THE SUPERSONIC (HYPERSONIC) FLYING APPARATUS PROBLEM.

In flights with supersonic speed, the distribution of pressure
at the supersonic inlet is interesting. One of the cases was
analyzed before. However, in addition to the simplest flow around
the inlet, an interesting case of adding energy directly before the
body is of interest. Depending on the position of the local time and
the local size of the energy adding, it is possible to change the
operating mode of the supersonic engine, that is, to increase the
pressure at the inlet, thereby increasing the engine power, or to
reduce, while creating an air starving situation for the engine,
which in turn can lead to an end work of the latter.

In this paper we plan:

1. To simulate numerically the flow around the air intake without an energy supply to the fixed Mach number (M = 5);

2. To simulate numericallythe flow around the inlet for the same Mach number, but with a local energy supply in different parts of the computational domain

3. To compare the results and draw conclusions.

**
Kirill S. Gruzdev
** –
the 1st year Master student of Department of Mathematics
and Mechanics at St. Petersburg State University.
Scientific area: supersonic and hypersonic flows. Supervisor – Supervisor: Asso. Prof. A.G. Karpenko

### February 20, 2018

Kaufman D.V. (SPbSU)

Experimental evaluation of rotational
derivatives of a body of revolution
with different noses

Based on experiments on the decay of rotational oscillations
of an axisymmetric body in the airflow, rotational derivatives
of the pitching moment coefficients are determined. It turns out
that the more elongated noses are characterized by larger absolute
magnitude of rotational derivatives. The presence of a coaxial disk
in front of the cylindrical part of the body instead of the streamlined
nose also leads to an increase in rotational derivatives in absolute
magnitude.

**
Daniil V. Kaufman
** –
the 1st year Master student of Department of Mathematics
and Mechanics at St. Petersburg State University.
Scientific area: ideal fluid dynamics, viscous fluid dynamics,
gas dynamics. Supervisor – Dr.Sc. A. N. Ryabinin.

### December 5, 2017

Saifutdinov A.I. (SPbSU)

NUMERICAL ANALYSIS OF THE INFLUENCE OF THE SIGNAL VOLTAGE FORM ON SPATIO-TEMPORAL PARAMETERS OF BARRIER MICRO-DISCHARGE IN ARGON

In work on the basis of a hybrid model, numerical experiments were conducted to study the parameters of the dielectric barrier microdischarge at atmospheric pressure in argon in a wide range of input conditions. A comparative analysis of the results obtained with a voltage signal applied to the electrodes in the form of a sinusoidal and rectangular shape is presented. In particular, for both cases, the spatio-temporal dependences of the densities of charged and excited particles, the electric field, the time dependences of the discharge current density and the voltage drop between the electrodes, and the time dependences of the accumulation of charges on the right and left dielectrics are presented. The results of numerical experiments demonstrate the principal dependence of the spatial and temporal characteristics of the barrier microdischarge at atmospheric pressure in argon on the shape of the applied voltage. Thus, in the case of a rectangular-shaped supply voltage applied to the electrodes, two current pulses are always observed for a half-period (regardless of the amplitude of the supply voltage). In the case of a sinusoidal signal, the number of current pulses depends on the amplitude of the applied voltage.

**
Almaz I. Saifutdinov
** –
the 1st year Master student of Department of Mathematics and
Mechanics at St. Petersburg State University. Scientific area:
low-temperature plasma, plasma chemistry, gas discharges, mathematical
modeling, probe plasma diagnostics. Supervisor - Prof E.V. Kustova.

### November 28, 2017

Saveleva A.Yu. (SPbSU)

Shape memory effects in TiNi alloy with various grain sizes

This work is devoted to the study of the transformation plasticity and
shape memory effects in the Ti - 50,2 at.% Ni alloy with various grain sizes.
The obtained results show that strain variation during cooling occurs in some
stages depending on the grain size and stress. In grains with the size of less
than 80 nm, strain variation is observed only in the case when the stress acting
in cooling and heating overcomes the critical value. An increase in stress leads
to the increase in the transformation plasticity and shape memory effects as well
as in the temperatures of the martensitic transformations. A decrease in grain size
results in the decrease in the transformation plasticity effect and the martensitic
transformations temperatures, while the shape memory effect value depends on the
grain size in a non-monotonic way. The maximum recoverable strain
of 15% is observed in a sample with the grain size of 130 nm.

**
Anastasia Yu. Saveleva
** –
the 1st year Master student of Department of Mathematics
and Mechanics at St. Petersburg State University. Scientific area:
shape memory effect, materials science.
Supervisor – Doctor of Physics and Mathematics N.N. Resnina

### November 21, 2017

Alfiya Ya. Nigmatullina (SPbSU)

Influence of thermal treatment conditions on physical and mechanical properties of Cu-2Be alloy processed by high-pressure torsion.

An influence of thermal treatment and high-pressure torsion (HPT) processing on secondary phase particles formation and mechanical properties of Cu-2Be alloy was studied. An alloy treated with the homogenized solid solution was subjected to three main thermomechanical treatment regimes: a coarse-grained alloy HPT with subsequent aging, coarse-grained alloy aging with subsequent HPT and aging during HPT at the temperature range from 150°C to 250°C.

The results of X-Ray diffraction (XRD) for the obtained materials showed that the thermomechanical treatment regime affects the grain size, internal stress values and the location of secondary phase CuBe particles in the parent matrix material. According to XRD, a secondary phase particle in the HPT-processed alloy can be located at both, the grains boundaries and in grains interiors.

Studies of the mechanical properties by means of uniaxial tensile tests showed that good combination of strength and plasticity was achieved in the alloy subjected to aging at the temperature 325°C for 10 hours with subsequent HPT processing. Fractography analysis via scanning electron microscopy (SEM) revealed a ductile-brittle fracture behavior of nanostructured Cu-2Be alloy.

Results of this work show that the selection of thermomechanical
treatment regime can be used as a driving factor for desirable phase
formation kinetics with following mechanical properties.

**
Alfiya Ya. Nigmatullina
** –
the 1st year Master student of Department of Mathematics and Mechanics
at St. Petersburg State University. Scientific area: materials science,
nanostructured materials, binary alloys, secondary phase particles.
Supervisor - Ph.D. I.V. Lomakin.

### October 31, 2017

Anton S. Maksimov (SPbSU)

Dynamics of a rotor with a multiball autobalancer

The problem of self-balancing of a statically unbalanced rotor by means of a passive ball auto-balancing device (ABD) is considered. The use of such devices is especially important for rotors with variable unbalance, such as centrifuges for washing or drying machines. A mathematical model was created for a statically unbalanced rotor with a weightless elastic shaft fixed in vertical supports and equipped with a multi-row, multi-ballistic control unit. An algorithm for numerical integration of the system has been developed, taking into account the collision of the balancing balls with each other. The program is written in Mathematica software to calculate the motion of a system containing an ABD with an arbitrary number of concentric circular cavities and an arbitrary number of balls in each cavity. The results of calculations are presented in the form of graphs and computer animation, clearly
demonstrating the processes of movement and interaction of balancing balls.

**
Anton S. Maksimov
** –
the 1st year Master student of Department of Mathematics and Mechanics at
St. Petersburg State University.
Scientific area: mathematical modeling, rotor dynamics, mechatronics.
Supervisor - PhD (Math) A.S. Kovachev.

### October 24, 2017

Shininov T.N. (SPbSU)

Granulation of powdered materials in a drum-type high-speed granulator

Granulation of powdered materials in a drum-type high-speed granulator was studied. A mathematical model was constructed for describing the granulation in a high-speed granulator in which two processes, coagulation and disintegration, are combined. The constants of the integral transform kernel for coagulation and disintegration were determined from the experimental data. It is shown, that the suggested mathematical model adequately represents the real process of granulation
of a hydrophobic additive in the asphalt concrete mix.

**
Timur N. Shininov
** –
the 1st year Master student of Department of Mathematics and Mechanics at St. Petersburg State University. Scientific area: mathematical modeling, dispersed systems, biomechanics.
Supervisor - Prof E.A. Nagnibeda.

### October 17, 2017

Barova A.N. (SPbSU)

Thermocyclic creep of a cylindrical sample

In this work we describe the problem of
the influence of inhomogeneous field of temperatures
on the creep and thermal deformation in the thermocyclic
creep simulation. The equilibrium equation and the theory
of Zhurkov and Kachanov are used to describe the change of
deformation and stress fields. The created algorithm allows
us to computerize the given process.

**
Barova Alina N.
** –
the 1st year Master student of Department
of Mathematics and Mechanics at St. Petersburg
State University. Scientific interests area:
mathematical modeling, creep of metals.
Scientific supervisor - Prof. A.E. Volkov.

### October 3, 2017

Vedenchuk E. A. (SPbSU)

Molecular dynamics simulations of reverse microemulsions

Reverse micelles (basic structural elements of the “water-in-oil” microemulsions) have
been considered in the work. Microemulsion is a thermodynamically stable transparent mixture
of three or more components: surfactants and two non-miscible liquids. Molecular dynamics
simulations of reserve micelles, that contain water and surfactants Span80 and Tween80,
have been investigated in a non-polar liquid n-decane. Spherical micelles, which shape can
be approximated by an ellipsoid with an axial ratio close to one, have been also obtained. The
obtained data on sizes and diffusion coefficients of reverse micelles and water nanodrops are
quantitatively close to the corresponding experimental data of dynamic light scattering and
NMR.

**
Vedenchuk Ekaterina A.
** –
the 1st year Master student of Department of
Mathematics and Mechanics at St. Petersburg State University. Scientific interests area:
hydroaeromechanics, molecular dynamics simulations, biomechanics.

### September 26, 2017

Smirnov A.S., Smolnikov B.A. (SPbPU)

Optimal placement of the hinge support in beam structures

The report discusses methods for locating additional hinge
support in beams. The purpose of the support installation is to fulfill
some optimization requirements. The main object of investigation is the
cantilever beam which experiences the action of various external loads:
concentrated and distributed, longitudinal and transverse. It is shown
that it is possible to achieve a significant reduction in the maximum
deflection and maximum bending moment or critical force, at which
structural stability
loss occurs, by optimal installation of an additional support.

**
Smirnov Alexey S.
** –
assistant of the department «Mechanics and
control processes» of Peter the Great St. Petersburg Polytechnic
University. Research interests: analytical mechanics, theory of oscillations,
rigid body dynamics, stability
theory, optimization in mechanics, waves in continua.

**
Smolnikov Boris A.
** –
candidate of Physical and Mathematical Sciences,
professor of the department «Mechanics and control processes», Peter
the Great St. Petersburg Polytechnic University. Research interests:
general mechanics, biomechanics, robotics, motion of cosmic objects,
control theory. The author of four books and numerous articles on
the rigid body dynamics,
robotics and the mechanics of controlled space objects.

### September 19, 2017

T.S. Shugailo (SPbSU)

Oscillations suppression of cargo carried by the gantry crane KKS10.

Suppression of cargo swings carried by a KKS10 crane for a given
time by a specified distance is considered in the report. The control
force is sought in two ways - by applying the Pontryagin maximum
principle and using the generalized Gauss principle. Solutions obtained
by both methods are compared. The problem is solved under the assumption
of small swinging motions using the
nominal characteristics of a particular gantry crane.

**
Timothey S. Shugailo
** –
the 1st year Master student of the Department
of Theoretical and Applied Mechanics at Saint-Petersburg State
University. Scientific interests area – nonholonomic
mechanics, theory of control, mathematical modelling.
Scientific supervisor – Prof. M.P. Yushkov.

### September 5, 2017

D.V. Franus (SPbSU)

Applications of finite element models of solids in ophthalmology.

Multilayer corneoscleral shell under various mechanical loads is studied
by the finite-element modeling in ANSYS program package. The first part of
the dissertation is devoted to a calculation of intraocular pressure (IOP)
under a load of the flat base stamp with different weighs depending on a
variety of biomechanical characteristics of the corneal multi layered shell.
Next part is concerned with studying changes in IOP after intravitreal injection
of a standard volume into a multilayer corneoscleral shell of variable thickness
and an ellipsoidal shape. In the third part, changes in IOP after refractive
correction of hyperopia are considered and also the stress-strain state of the
corneal shell with
different options for the location of the zone of ablation is analyzed.

**
Dmitry V. Franus
** –
a graduate of the postgraduate education of the Department
of Theoretical and Applied Mechanics at Saint-Petersburg State
University. Scientific interests area – biomechanics, mechanics of
thin-walled structures. Scientific supervisor – Prof. S. M. Bauer.