INSTITUTE
OF MECHANICS AND ENGINEERING; KAZAN SCIENCE CENTER; RAS
SCIENTIFIC SEMINAR
(Papers survey, presented at
the Seminar and final scientific Conference for 2003)
D.A.Gubaidullin
Institute of Mechanics and Engineering; Kazan Science Center; RAS
Lobachevsky 2/31, Kazan 420111 RUSSIA
e-mail:
gubajdullin@mail.knc.ru
The Scientific Seminar
"Problems of Continuum Mechanics" works in the Institute of Mechanics and
Engineering, Kazan Science Center RAS. The Chairman of the Seminar is Director
of the Institute Dr. Sc. (Phys. & Math.) D.A.Gubaidullin. Problem reports
and dissertations of researchers of the Institute and scientists from other
organizations are presented and discussed at the Seminar. Main scientific
directions:
ž
non-linear mechanics of thin-walled constructions, hydroaeroelastic and
wave systems;
ž
dynamics of multiphase multicomponent media in porous structures and
technological plants;
ž
non-linear stability theory of control systems with variable structure.
The following reports were presented
at the Seminar in 2003 and at the final scientific Conference'2003.
May
8, 2003
A.A.Aganin, N.A.Khismatullina (IME).
Computation of liquid vorticity in non-spherical bubble dynamics. The purpose of this work is to compare the efficiency of a number of
numerical techniques with respect to their computational time costs. The
techniques based on the finite-difference method (the FDM technique), the
collocation method (the technique with differentiating the integral boundary condition
and the one without it) and the Bubnov-Galerkin method (the BGM technique) have
been considered. The central differences are used as approximations for the
derivatives in FDM. Harmonics are chosen as basic functions in BGM. Problems of
decaying a small distortion of the spherical surface of a bubble and dynamics
of a bubble under harmonic liquid pressure variation are used for comparison.
The FDM technique has been shown to be the most efficient one in all the cases.
April
10, 2003
V.G.Malakhov (IME).
Nonlinear problems of computation and optimization of shells of
revolution. On materials of thesis for Candidate of Science
Degree, speciality: 01.02.04 - Mechanics of deformable solid. Reviewer: D. Sc.
Gribov A.P. The techniques of computation and optimization of a compound shell
of revolution including the thin-walled shell elements connected to one another
with elastic rings have been proposed. Physical and geometrical nonlinearities
are taken into account in the equations of shells. Parameters of optimization
are the shell thickness and dimensions of the cross-sections of the rings.
Problems of weight optimization under bounds on strength and the problems of
optimal material distribution in the compound shell of revolution of maximum
stiffness have been considered. The results of solution of some new problems
are presented.
October
22, 2003
Seminar,
dedicated to U.N.Zakirov on his 70-th Birthday
U.N.Zakirov (IME).
Life, technology, science. I had to communicate
with the astrophisical group of academician Ja.B.Zeldovish. I have understood,
that in theoretical mechanics there is no relativistic mechanics of jet
propulsion; the theory of prompt flights in far space on the basis of
non-chemical power sources. Let's introduce according to Sing - the English mechanical
engineer and physicist three patterns: M1 - pattern of Newton mechanics, M2 -
pattern of Einstein mechanics. The theories of Newton and Einstein are so
closely related, that sometimes it is difficult to make a distinguish between
them. They differ by representation about Newtonian time and terrain clearance
hardness (M1). In conclusion, within 30 years, it is possible to state, that
the relativistic mechanics of jet propulsion (L.I.Sedov, U.N.Zakirov) has been
established. As for the theory of stability, the generalization of the theorems
of Lyapunov in pattern M2 is possible.
Oktober
30, 2003
A.L.Tukmakov (IME).
Nonlinear dynamics of thin-walled elements of the designs cooperating
with gas and diagnostics of nonlinear fluctuations. On
materials of thesis for Doctor of Science Degree, specialities: 01.02.04 -
Mechanics of deformable solid and 01.02.05 - Mechanics of liquid, gas and
plasma. Reviewers: D. Sc. (Phys. & Math.) Aganin A.A., D. Sc. (Phys. &
Math.) Golovanov A.I. The work is devoted to the research of nonlinear dynamics
of aeroelastic systems. The mechanisms of aeroelastic interaction are
investigated by the methods of numerical modelling and the nonlinear effects
accompanying dynamics of environments are analyzed. A new method of diagnostics
of the nonlinear fluctuations allowingš
to identify dynamic processes is presented.
March
25, 2004
I.V.Morenko (IME).
Hydrodynamics ofš the inertial
separators and filters. On materials of thesisš 01.02.05 - Mechanics of liquid, gas and
plasma. Research manager: D. Sc. Fedyaev V.L. Reviwer: PhD Osipov P.P. The
gauze drag of the various cross-section cylinders are investigated. The turn
ability of the circular cylinder gauze is studied at the small and intermediate
Reynolds number. A new forms of the separator profile and filters for water
purification from the carry-over are suggested. The efficiency of the work is
acknowledge of the calculation.
The following report was presented at plenary
Session of the Final Scientific Conference'2003 of the Kazan Science Center
RAS.
February
9, 2004
V.L.Fedyaev (IME).
Modernization of the industrial cooling towers. The objects of these investigations are the industrial cooling towers.
These installations are widespread in energetics, as well as in chemical and metallurgical
works. New systems of the water-supply, fills, traps of the drops, ventilators
are proposed. Robust quality of the suggested constructions has been confirmed
by math modeling.
The following reports were presented at section
Sessions.
February
12, 2004
D.A.Gubaidullin, A.A.Nikiforov (IME).
Peculiarities of acoustics of vapor-gas-liquid media. Linear theory of propagation of the plane, spherical and cylindrical
perturbations in the polydispersed vapor-gas-drops systems and in mix of a
fluid with gas or vapor bubbles is developed. The equations of movement are
presented, the dispersion ratious are obtained, the evolution of pulse waves is
performed, the influence of processes geometry, heat and mass transfer and the
basic parameters of mixtures are analysed. The character of the harmonical
waves propagation in spherical and cylindrical cases is the same as for the
plane waves. The strongest attenuation and change of the form of pulse
spherical perturbations in contrast to the cylindrical and plane cases as well
as the strongest dependence of spherical and cylindrical wave propagation from
the initial radius of perturbations have been estabilished.
D.A.Gubaidullin (IME), R.G.Zaripov (IME),
R.G.Galiullin (Kazan State University), L.A.Tkachenko (IME).
Nonlinear oscillations of aerosol in an open tube nearby a sub-harmonic
resonance. Nonlinear oscillations of a small-dispersible
aerosol in an open tube close to a half of fundamental frequency are
considered. Aerosol oscillations were generated by a plane piston; a tube
included a quartz section with photo-transducer for registration of
light-penetrability of a medium that governs particle concentration. The
concentration of aerosol monotonously decreases in due course and with growth
of frequency of excitation. Dependences of time of an enlightenment of an
aerosol on frequency have non-monotonic character with a minimum at transition
through a resonance. It is revealed, that reduction of length of a tube results
in decrease of an enlightenment time of an aerosol.
S.K.Zaripov (KSU, Institute of
Mathematics and Mechanics), W.Hollander (Fraunhofer Institute
Toxikologie und Experimentelle Medizin, Hannover, Germany).
Hydrodynamically interacting droplets at small finite Reynolds numbers. Droplets moving at close distances interact hydrodynamically. Here we
present the experimental and theoretical results of the study with monodisperse
73 Þm diameter droplets with initial velocities between 1.5 and 2.5 m/s and
variable generation rate (ranging from 125 to 1000 s-1 emitted horizontally and
vertically). The hydrodynamic interactions depend on the spatial distance, and
we observed a considerable increase of the stopping distance with increasing
generation rate. Reviewing the various approaches for the description of
hydrodynamic interactions, we adapted a theory for stationary Stokes flow past
a linear array of spheres to our situation and found a surprisingly good
agreement between our experiments and the above model. Even better agreement
was obtained by additionally taking the Basset force into account. This work
was supported by the German Academic Exchange Service DAAD (N 325-2002) and
partially by Russian Foundation for Basic Research under grant number
02-01-00836 as well as by German Space Agency DLR under grant 50WM0037.
A.A.Aganin, L.A.Kosolapova, V.G.Malakhov (IME).
Nonlinear dynamics of a bubble in a liquid at axisymmetric distortion of
its spherical shape. Nonlinear axisymmetric
oscillations of a gas bubble in a liquid are considered. Distortion of the
spherical shape of the bubble is presented in the form of spherical harmonic
power series. Mathematical model equations include nonlinear terms of second
order of smallness with respect to the amplitudes of the harmonics.
Nonlinearity influence on the bubble oscillations under periodic variation of
the liquid pressure is investigated under various values of the initial
distortion and the number of harmonics used to present the distortion of the
spherical shape of the bubble.
A.A.Aganin, T.S.Guseva (IME).
Spherical shape stability of a gas bubble in a liquid during its strong
enlargement-compression. Spherical shape stability
of a gas bubble in a liquid during its strong single enlargement-compression
has been studied with allowing for its shape oscillations before beginning the
expansion. Distortions of the bubble spherical shape are assumed small
axisymmetric in the form of single spherical harmonics. The liquid near the
bubble is considered to be viscous incompressible, the pressure inside the
bubble being the same everywhere. Strong dependence of distortion value during
the bubble enlargement-compression on the bubble shape oscillation phase at the
moment of the expansion beginning (initial phase) has been found. Spherical
shape stability was analyzed by using the worst scenario defined by distortions
maximal with respect to the initial phase.
A.A.Aganin, D.Yu.Toporkov (IME).
Liquid viscosity effect in nonspherical gas bubble oscillations. The liquid viscosity effect on variation of a small distortion of the
spherical bubble shape is studied during bubble oscillations under periodically
varying liquid pressure. The model with exact account of viscosity effect is
used along with approximate ways. All the approximate ways do not take into
account unsteady diffusion effects of vortex motion of the liquid. Parametric
areas of the problem have been outlined in which these effects do (and do not)
introduce qualitative changes in the shape oscillations. Features of influence
of complex vortex motion of the liquid on variation of the distortion of the
bubble shape have been studied.
V.F.Sharafutdinov (KSU), V.I.Malov (IME).
The peculiarities of rheological models of non-newtonian fluids
constructed on the basis of the experimental s-shaped curves. IT is known that for many newtonian fluids the experimental flow curves
have the S-shaped form. In transition from the experimental S-shaped curve to
the rheological one in variables: stress and velocity of shift, it is suggested
to introduce two rheological dependences. In this case two-phase medium behaves
as non-newtonian fluid until the velocity of shift on the tube wall reaches
some critical value; after reaching this critical value it behaves as newtonian
fluid.
A.B.Mazo (IME).
On boundary conditions in Navier-Stokes stream function-vorticityšš problem for the set of bodies flow
modelling. The method for calculation of stream function
value as well as vorticity on the surface of bodies is developed.
I.V.Morenko, A.B.Mazo (IME).
A numerical simulation of the drag and turn ability of the gauze at the
small and intermediate Reynolds number. The
gauze drag of the various cross-section cylinders are investigated. The turn
ability of the circular cylinder gauze is studied at the small and intermediate
Reynolds number.
M.Kh.Khairullin, R.A.Soultanov, M.N.Shamsiev, R.V.Sadovnikov,
L.A.Tulupov, P.E.Morozov (IME).
Interpretation of hydrodynamic investigations of horizontal wells. The problems of estimation of flow parameters of oil reservoir are
considered on the basis of the regularization methods. The results of the
hydrodynamic investigations of horizontal wells are used as the initial data.
Fluid inflow to horizontal well with horizontal and wave profile is simulated
using the finite-difference and finite element methods.
A.V.Elesin, P.A. Mazurov (IME).
The quasi-gradient minimization method for solution of the inverse
problems. The identification problem of the hydraulic
conductivity in the three-dimensional anisotropic confined aquifer in case of
one-phase filtration according to the head values in observation locations is
solved. A new quasi-gradient algorithm for minimization of a residual function
has been proposed. The sensitivity storage distribution for constructing this
algorithm is used. The properties of a residual function in minimum point have
been analysed. These properties are the basis of a new stopping criterion. In
this criterion the knowledge of errors in head data is not required.
P.A.Mazurov, A.V.Tsepaev (IME).
The solution of three-dimensional flow equation in confined aquifer with
a large number of wells on multiprocessoring systems. A new algorithm has been proposed to solve the flow equation in confined
aquifer on the coarse grid with concentration of grid near the wells. The
algorithm is based on the method of division of domain on subdomains. The
results of solution on multiprocessering systems MVS 1000/16 have been
presented.
I.E.Timoshenko (IME).
On the change of pore and particles sizes distribution functions during
waterflooding of the oil reservoir "polymer-disperse" systems (PDS). The results of modeling of change of pore and particles sizes
distribution functions for waterflooding of oil reservoir
"polymer-disperse" systems are presented. The comparison of numerical
results with the available experimental data is carried out. Their qualitative
concurrence is shown.
I.T.Usmanov (KSU, Institute of
Mathematics and Mechanics).
3D-Modification of the multigrid method for numerical calculation of a
pressure field in the multilayered oilfilds.
3D-modification of the multigrid method for numerical calculation of a pressure
field in the multilayered petroleum layer model is developed within the
framework of two-phase filtration. The iterative process was constructed with
taking into account that thickness of a petroleum layer many times less than
its sizes on spread. All calculations were made for vertical vectors. The grid
is coarsed only in the plan. The operators of restriction and prolongation
remain the same, as in a two-dimensional case. The way of coefficients
modernization for multigrid technology used in case of a given bottom-hole
pressure is elaborated. On the large grids the convergence speed of this
algorithm is shown to be much more than the earlier known ones.
February
13, 2004
U.N.Zakirov (IME).
Motion and stability of the concentrated variable rest mass point in
gravitational field of a charged radiative body. The
equations of motion of the concentrated variable mass point in gravitational
field of the massive electrified body (solution of Vaidya-Bonner ) in the
context of the five-dimensional theory of Kaluza-Klein are studied at an
assumption of proportionality of the five-dimensional and four-dimensional
intervals. In studied system the change of the rest mass (energy) of particles
is compensated by the change of radiation energy of the gravitating body; it is
demonstrated that in the equation deviation of the nonlinear terms depend on
the factor, bound with parameters of the change of the rest mass and change of
a specific charge. The generalized criterion of orbital stability of particle
according to L.Kaplan is analysed.
M.S.Ganeeva, V.E.Moiseeva (IME).
The carrying capacity of a reservoir for cryogenic liquid under the
nonaxisymmetric loading. We numerically investigate
the behaviour of the construction in the form of shells of revolution with the
branching meridian under the nonaxisymmetric thermo-force loading. As a rule,
the carrying capacity of the construction is estimated on the basis of the
achieved level of stresses. In the present work we study the carrying capacity
of a tank for cryogenic liquid, which is subjected to windlike loading, on the
basis of achieving the material yield strength and (or) the critical level of
compressive stress resultants. We have considered means of improving the
carrying capacity of the construction. The problem is solved with regard to the
geometric and material nonlinearities.
E.A.Shirokova (KSU).
Particular solution of the 3d analog of the second basic problem of the
theory of elasticity for cylindrical elastic solids. The method of construction of the particular solution of the following
problem is found: given the displacements at n+1 level of the cylindrical
surface of a cylindrical solid, the stresses in the solid should be found. The
solution has the form of a polynomial over the corresponding coordinate and can
be obtained via solution of the boundary value problems. One can find the exact
solution for the case when the cross section of the cylindrical solid is the
image of the unite disk under the rational function. For the case of circular
hollow cylinder together with the displacements at n+1 level of the external
cylindrical surface the constant pressure and the sliding condition on the
internal surface are given. The examples are constructed.
L.R.Sekaeva, D.V.Berezhnoi, Yu.G.Konoplev (KSU).
Three-dimensional problem of interaction of the dry and water-saturated
continua. The technique of the stress-strained station
analysis of the dry and water-saturated grounds, interacting with deformable
constructions, based on the finite element method is presented. Static and
dynamic interaction of the underground industrial constructions with a ground
is considered.
A.I.Golovanov, A.F.Chigaboutdinov (KSU).
Natural and forced shell vibrations. FEM technique. The article is devoted to realization of the numerical investigation
and simulation of dynamic process for the complex shell constructions.
Numerical results based on the finite element method are presented.
N.M.Yakupov, R.G.Nurullin, A.R.Nurgaliev (IME).
Films and membranes: application and methods of computation. In films and membranes there can be various defects. A small review of
the used methods of computation is presented. It is noted, that the works
devoted to construction of curves of deformation with the use of
two-dimensional approach, as well as theš
experimental works on the research of durability of films are few. The
work is devoted to development of the effective experimental - theoretical method
of research of the strength and deformation characteristics of films and
membranes with defects. The results of computation for samples with corrosion
deterioration are given.
F.H.Akhmetzyanov (Kazan State
Architectural-Building Academy), N.M.Yakupov (IME).
An estimation of parameters damages of microstructure of cements stone. The analysis of experimental works is carried out in the area of
microstructure of cements stone. From fraktogramm of destruction of cements
stone both the length and width of disclosing of the microcrack as well as the
distance between them are established. The applicability of the concept of the
destructionš mechanics of for the
description of microcracking of cements stone is shown.
R.A.Kayumov (Kazan State
Architectural-Building Academy), Yu.G.Konoplev (KSU), B.F.Tazioukov (KSU).
Identification of mechanical data of an elastic composite on the basis
of results of a solution of problems of constructions stability. The procedure of definition stiffness coefficients of a composite
fillet is proposed, of which beforehand curved thin elastic plate or
cylindrical panel is made. The problem is reduced to a problem of nonlinear
programming about minimization of a discrepancy between values of the
calculated and experimental values of a critical loading. The approach permitting
to gain good coordination of the calculated and experimental data by
introduction of expansion of function of the purpose is proposed.
N.K.Galimov, R.G.Nurullin, A.A.Leontiev (IME).
On elastic balance of round membranes and flat spherical shells under
the action of uniform pressure. The solution of a
task in three approximations and their comparison with the exact solution is
given. It is noted, that the solution of a task within the limits of elasticity
of a material in the second approximation gives quite acceptable result.
Potential
participants are kindly invited for the presentation of their results at the
Seminar.
Contact
address - gubajdullin@mail.knc.ru
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