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.