Issue 3
JTAM, Sofia, vol. 27 Issue 3 (1997)

On the Appearance of the Fractional Calculus

S. Grozdev
Institute of Mechanics, Bulg. Acad. Sci. Sofia


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.

JTAM, Sofia, vol. 27 Issue 3 pp. 01 (1997)

Dynamical Model of a High Speed Linkage Mechanism with Elastic Elements

K. Andjushev, L. Azievska, Al. Malchevski
Mechanical Faculty, Skopje, Macedonia

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.

JTAM, Sofia, vol. 27 Issue 3 pp. 02 (1997)
Reconstruction of Polynomial right-hand Side of One-dimensional Dynamical System on Given Integral Curve

V. G. Petrov, G. Nikolov, I. Edissonov
Institute of Mechanics, Bulg. Acad. Sci., Sofia

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.

JTAM, Sofia, vol. 27 Issue 3 pp. 03 (1997)
Numerical Study of Flow-Particle Interaction

E. Toshev1, T. Partalin2, T. Petrova2
1 Institute of Mechanics, Bulg. Acad. Sci.
2Sofia University of Sofia, Faculty of Mathematics and Informatics

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.

JTAM, Sofia, vol. 27 Issue 3 pp. 04 (1997)
One-dimensional Calculations for a Transonic Nozzle Flow of a High-Temperature Gas

B. E. Djakov
Institute of Electronics, Bulg. Acad. Sci., Sofia

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.

JTAM, Sofia, vol. 27 Issue 3 pp. 05 (1997)
Review of Selected Topics in Dynamic Analysis of Structures for Seismic Performance

B. Yanev
Columbia University, New York City, USA

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.

JTAM, Sofia, vol. 27 Issue 3 pp. 06 (1997)
On the Acoustic Field of a Cylindrical Focusing Projector

V. Grintchenko1, T. Trifonov2, Y. Siderov3
1Institute of Hydromechanics, Ukr. Acad. Sci., Kiev.
2Vassil Levski Military Academy, Veliko Turnovo
3University of V. Turnovo "St. St. Cyril and Methodius".

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.

JTAM, Sofia, vol. 27 Issue 3 pp. 07 (1997)
On a Numerical Scheme for Solving Nonlinear Diffusion and Sorption Problems

R. Blagoeva

JTAM, Sofia, vol. 27 Issue 3 pp. 08 (1997)
A Possibility to Extend the Finite Prism Method

G. Kolarov
Technical University of Sofia

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.

JTAM, Sofia, vol. 27 Issue 3 pp. 09 (1997)
Superposed Deformations and Stability

Ts. Ivanov1, R. Savova2
1University of Sofia, Faculty of Mathematics and Informatics
2Institute of Mechanics, Bulg. Acad. Sci., Sofia

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.

JTAM, Sofia, vol. 27 Issue 3 pp. 10 (1997)
Experimental -Theoretical Determination of Physical Constants Included in a Phenomenologic Model of Destructions

V. Baranov1, G. Kalujny1, P. Poltev2, H. Hristov3, Z. Chiwikov4, K. Boyadjiev 5
1Tula State University, Tula, Russia
2GNPP -Splav, Tula, Russia
3Military Research Institute, Sofia, Bulgaria
4Dunarit-Ltd., Rousse, Bulgaria
5Vazov Engineering Plants-Ltd., Sopot, Bulgaria

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.

JTAM, Sofia, vol. 27 Issue 3 pp. 11 (1997)