**GENERAL**

**MECHANICS**

**S. GROZDEV**

Institute of Mechanics, Bulg. Ac. Sci. Sofia

On the Appearance of the Fractional Calculus

Some basic facts are analyzed
which have inspired the foundation of the temporary fractional calculus.
The main ideas of the Riemann-Liouville fractional calculus are discussed
in connection with the classical Abel integration equation.

Mechanical Faculty, Skopje, Macedonia

Dynamical Model of a High Speed Linkage Mechanism With Elastic Elements

A dynamic model for a high
speed four bar linkage mechanism is studied in this paper. Except the follower
all other elements are elastic. The theory of continual systems is applied
to create a discrete dynamic model.

The formulation of the problem
is by a nonlinear differential equation with variable coefficients. The
influence of the crank and the coupler vibrations on the accuracy of the
follower motion is discussed in this paper. Especially the influence
of the vibration process on the digressing of the real kinematics function
with respect to the ideal kinematics function of the follower is discussed.
At the end a numerical example is presented.

**V. G. PETROV G.
NIKOLOV I. EDISSONOV**

Institute of Mechanics, Bulg. Ac. Sci., Sofia

Reconstruction of Polynomial right-hand Side of One-dimensional Dynamical System on Given Integral Curve

In this paper is proposed
a method for reconstruction of unknown right-hand side of one-dimensional
dynamical system in terms of Taylor's (Maclaurin) series at given concrete
solution of the system. In the case when the unknown right-hand side is
a polynomial, a theorem giving a method for determination of the polynomial
coefficients is proved. Further, the proposed method is applied on a concrete
one-dimensional system.

**FLUID**

**MECHANICS**

**E. TOSHEV T. PARTALIN
T. PETROVA**

** **Institute of
Mechanics, Bulg. Ac. Sci., Sofia University of Sofia,

Faculty of Mathematics
and Informatics

Numerical Study of Flow-Particle Interaction

By using a numerical simulation
method, based on solving of 2D Navier- Stokes equations, the incompressible
flow past a single particle or a pair of particles are investigated. In
the case of two particles, the spherical particles in tandem are considered.

The flow around the spheres
is inducted by uniform at infinity flow, parallel to their center line.
The velocities distribution and drag coefficients are found for different
values of Reynolds number Re (from 1 to 100), and different distances between
the particles L (from 0.125 to 20 radii). In the case of single particle
two different types of particles are considered. First type is the case
when the particle is in the shape of solid cylinder and the second type
is the case of hollow cylinder. The represented results are for values
of Reynolds number Re from 1 to 100, and particle length F from 0.5 to
8.5 character lengths for hollow cylinder, and from 0.25 to 4.25 character
lengths for solid cylinder. By using the smoke wire visualization technique
the flow around the hollow cylinder particle, or a pair of spherical particles
is shown.

** B. E. DJAKOV**

Institute of Electronics, Bulg. Ac. Sci., Sofia

One-dimensional Calculations for a Transonic Nozzle Flow of a High-Temperature Gas

Steady ID gas flows with
chemical changes, exposed to cross-sectional variation, heat loss, wall
friction or transition from equilibrium to chemical "freezing" are studied
by solving the gas dynamical equations. The nozzle shape and the nature
of gas influence the gas flow parameters. Our results are compared with
calculations by the Shapiro- Hawthorne method.

**MECHANICS**

**B. YANEV**

Columbia University, New York City, USA

Review of Selected Topics in Dynamic Analysis of Structures for Seismic Performance

The topics discussed herein
are selected for their relevance to the subject generally defined as "Earthquake
Engineering" and for the direct involvement of the author in some of the
work on their resolution.

**V. GRINTCHENKO T.TRIFONOV
Y. SIDEROV**

Institute of Hydromechanics,
Ukr.Ac.Sci.,Kiev.

Vassil Levski Military Academy,
Veliko Turnovo

University Of V. Turnovo
"St. St. Cyril and Methodius".

On the Acoustic Field of a Cylindrical Focusing projector

In this paper are presented the analytical and numerical results of a sound field of the cylindrical focusing projector. The structure of the field is determined on the base of the wave equation, boundary conditions and the condition of radiation. The method of the partial regions is used. For simplicity, the numerical examples are studied for symmetric excitation. The results are applicable to the optimum of acoustic and ultrasonic transducers.

**R. BLAGOEVA**

Institute of Mechanics, Bulg. Ac. Sci., Sofia

On a Numerical Scheme for Solving Nonlinear Diffusion and Sorption Problems

A numerical approach for
solving a class of problems for internal diffusion and sorption is considered.
The corresponding general problem is posed under appropriate assumptions
for the known functions ensuring the existence of a bounded solution. The
correctness of the numerical scheme, derived by using the Galerkin semidescrete
method and a time difference method, is investigated in the general case
of nonlinear problems. Some sufficient conditions for the scheme stability
are obtained, as well as the physical correctness condition of the numerical
solution in case of reversible soption.

**MECHANICS**

**G. KOLAROV**

Technical University of Sofia

A Possibility to Extend

the Finite Prism Method

A possibility to extend the
finite prism method, that is a semianalytical method for solving elastic
problems for. 3D prismatic bodies, is presented. The known solutions are
based on separation of variables and on trigonometric functions for the
analytical part of the solution along the body axis. In this paper trigonometric
and hyperbolic functions are proposed for the analytical part of the solution.
They are based on the analogy with the eigenfunctions for beam vibration.
This allows the applications of arbitrary boundary conditions at the ends
of the body. Two examples are presented, too.

**TS. IVANOV R. SAVOVA**

University of Sofia, Faculty
of Mathematics and Informatics

Institute of Mechanics,
Bulg. Ac. Sci., Sofia

Superposed Deformations and Stability

Large deformations and their
approximations of different order superposed on a large deformation and
their connection with stability problems are considered. It is supposed
that after the first large deformation the body is in an equilibrium position
whose stability is under consideration on the basis of the Lyapunov approach
developed by Koiter for mechanics of continua. This approach leads to systems
of linear equations and boundary conditions which are closely connected
with the equations and boundary conditions in the theory of isothermal
static deformations of different order superposed on a finite deformation.
The thermal and Kelvin-Voigt viscous effects do not influence on the consideration
of the stability problem when the body forces and surface tractions are
weakly conservative.

**MECHANICS**

**V. BARANOV G. KALUJNY
P. POLTEV H. HRISTOV**
**Z. CHIWIKOV K. BOYADJIEV**

Tula State University, Tula,
Russia GNPP -Splav, Tula, Russia Military Research Institute, Sofia, Bulgaria

Dunarit-Ltd., Rousse, Bulgaria

Vazov Engineering Plants-Ltd.,
Sopot, Bulgaria

Experimental -Theoretical Determination of Physical Constants Included in a Phenomenologic Model of Destructions

In this paper has been developed
and realized an experimental theoretical method for determination of the
numerical values of the physical constants included in the structure of
the phenomenologic model for destruction of real material which allows
the application of this model for evaluation of strength of structures
in case of

tensile step loading. The
authors present the constant value of altiminum.

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