Issue 3

JTAM, Sofia, vol. 15 Issue 3 (1984)

Prof. Dr. G. Bradistilov, Corresponding Member of the Bulgarian Academy of Sciences – 80 Years Since the Day He Was Born

Editorial Board

JTAM, Sofia, vol. 15 Issue 3 pp. 013-014 (1984)

Kinematical Theory of the Infinitely Close Positions of a Solid Body with a Single Fixed Point. II

S. Buchvarov
High. Inst. Electr. Eng., Dârvenitsa

The paper presents a solution of the problem, considering 4 infinitely close positions of a sphere, moving on the surface of its eigen sphere of motion. However, results are valid for the motion of a solid body, fixed to the moving sphere, as well. The circle point cones and those of the centres, as well as Ball's straight lines, are determined kinematically.

JTAM, Sofia, vol. 15 Issue 3 pp. 015-023 (1984)

Steady Motion of Lagrange's Gyroscope Systems with a Tree-Like Structure

L. Lilov, N. Vassileva
Inst. Mech., Biomech., Bl. 8 Geo Milev

The authors derive the necessary and sufficient conditions of the steady motion of a system of n Lagrange's gyroscopes. The gyroscope axes are fixed in the three dimensional space, which rotates with a constant angular velocity with respect to the inertial space. The system is of a tree-like structure and the gyroscopes are fixed by means of spherical joints which occupy the ends of the axes of symmetry. One of the gyroscopes, however, possesses a fixed point. The paper generalizes results, presented in [1] and referred to the special case of a monocontour system of bodies.

JTAM, Sofia, vol. 15 Issue 3 pp. 024-034 (1984)

Investigation of the Vibro Characteristics of Electro- and Motocars

L. Goranova, Vl. Ovcharov

The paper has been presented at the 4th National Congress of Theoretical and Applied Mechanics, Varna 1981.

JTAM, Sofia, vol. 15 Issue 3 pp. 035-038 (1984)

On the Uniqueness of the Structural Formula of an Elastic Body

Jan Rychlewski

The author has presented in his previous papers a structural formula [1.9], revealing entirely the mathematical character of the basic law of the linear theory of elasticity, i.e. the Hooke's law. In his recent paper he proves that this formula is unique and therefore is of an objective physical character.

JTAM, Sofia, vol. 15 Issue 3 pp. 039-044 (1984)

Propagation of Harmonic Waves in an Oblique Elastic Plate

S. Kislyakov
High. Inst. Arch. Civ. Eng., 1 Hr. Smirnenski Blvd.

The propagation of harmonic waves in a thin elastic plate with slanted edges is investigated, especially with respect to reflection effects. It is established that some values of the plate obliquity angle exist, for which the incident P-wave is reflected into an SV-wave only, while for other values it is just the opposite. It is possible that at the first reflection the incident SV-wave may be reflected into an SV-wave only, but it may also happen that the first reflection cannot be explained in terms of the ray theory. As for the reflections that follow, it has been proved that for some values of the plate obliquity angle, waves with periodically repeating reflections may occur, where the P- and SV-waves are continuously transformed into each other and carry in turn the whole energy of the process. For numberless obliquities of the plate it is also possible that the incident wave, after many reflections (whose number is exactly known), may turn back as a wave of the same type.

JTAM, Sofia, vol. 15 Issue 3 pp. 045-052 (1984), [Full Article]

Investigation of Stresses and Strains in the Transversal Direction of Underground Facilites Undergoing Seismic Impacts

Ts. Ivanov, T. Angelov
Inst. Mech. Biomech., Bl. 8 Geo Milev

The paper presents an investigation of the stressed and strained state of a soil – tunnel system under seismic impacts. It is assumed that the properties of the engineering facilities are viscoelastic and the soil is layered, whereas layers possess various viscoelastic characteristics. The soil-facility contact is assumed to be ideal. However, the effects of damping, thickness and the tunnel shape are investigated as well.

JTAM, Sofia, vol. 15 Issue 3 pp. 053-063 (1984)

Stochastic Model of Two Types of Magnetic Fields

D. Vandev, N. Trendafilov
Inst. Mech. Biomech., Bl. 8 Geo Milev

The paper presents a model of the cosmic magnetic field, taking into account "point" magnetic sources. The investigation follows the famous Holzmark's work, where the distribution function of the gravitational field of a system of planets has been obtained. The basic idea of the paper consists in the determination of the distribution function of the cosmic magnetic field. The effective tool herein is the characteristic function, whereas its logarithm is of a stable, and not of Gaussian, distribution. From a practical point of view, however, the paper turns to be a basis for the derivation, ot statistical estimates of the cosmic field characteristics, involving real observations.

JTAM, Sofia, vol. 15 Issue 3 pp. 064-069 (1984), [Full Article]

Interaction between Gravitational and Nongravitational Convective Flows in a Thin Layer of Viscous Fluid

Sl. Slavchev, J. Kojuharova
Inst. Mech. Biomech., Bl. 8 Geo Milev

An analysis of the basic relations characterising the unstable convective flows of a thin layer of a viscous fluid, has been performed. Flows occur as a result of the nonuniform distribution of temperature and/or concentration of the surface-active substance on the layer free surface. A possibility to the regulation of the capillary convection has been revealed, employing suitable heating and cooling regimes (the latter, however, have to be combined with a specific mass flux of the substance, adsorbing on the fluid surface).

JTAM, Sofia, vol. 15 Issue 3 pp. 070-078 (1984)

On the Mechano-Mathematical Modelling of Irradiated Austenite Steel

D. Kolarov, A. Baltov, Em. Manoah
Inst. Mech. Biomech., Bl. 8 Geo Milev

The authors propose a model describing the mechanical behaviour of irradiated austenite steel, which undergoes plastic deformation. The model is based on experimental data available in literature. A yield limit relation which approximates data on austenite steel G-304 has been proposed.

JTAM, Sofia, vol. 15 Issue 3 pp. 079-093 (1984)

On the Statical Investigation of Rotational Shells of Zero Gaussian Curvature and Variable Thickness

M. Mishonov, Hr. Hristov
KNIPIOIUS, 6 Lenin Blvd.

The basis equations of statics, geometry and physics are given. They concern a conical shell with a variable thickness along the meridian. The shell, however, undergoes arbitrary loading. The investigation is based on the general moment shell theory and the basic system of partial differential equations has been derived in displacements. Furthermore, defferential relations, expressing loads by means of displacements, have been obtained. The problem is considered to be physically and geometrically linear. The effect of the elastic foundation, following Winkler's model, has been taken into account in meridional, parallel and normal direction. Effects of uniform and nonuniform temperature field are revealed as well. Equations, describing the special cases of cylindrical shells and circular and ring-shaped plates, have been simplified. The external load (including temperature effects) and the unknown displacement functions, forces and moments are expanded in Fourier series, but in parallel direction only. This reduces the problem to the one-dimensional case. The basic system of equations for the determination of the Fourier displacement coefficients, as well as formulas for the force and moment Fourier coefficients, have been derived.

JTAM, Sofia, vol. 15 Issue 3 pp. 094-103 (1984)

Application of the Method of Enlarged Fragments (MEF) to the Statical Investigation of Arch-dome Walls/Shells

Hr. Ganev, Ch. Dimitrov
Inst. Water Problems, Bl. 8 Geo Milev

The paper treats the problem of the verification of a new discretization method, employed for the investigation of the stressed and strained state of arch-dome shells walls. The method is similar to the finite element method (FEM). Moreover, it constitutes both a FEM generalization and formal contradiction. Increasing the degree of the interpolation polynomials, it is possible to decrease the number of the finite elements and to enlarge them correspondingly. Thus they are transformed into enlarged fragments and the whole region Ω may be represented by a single fragment – a polygon with curvilinear sides. Furthermore, the polygon region could overlap effectively the region Ω'. The Lagrange principle of virtual displacements is employed for the reduction of the system of differential equations to a discreticized system of linear algebraic equations that calculates the variational parameters. The system to be discreticized presents the boundary value problem concerning moment shells of a double curvature and variable thickness. Two examples are solved and comparisons are made accordingly. a) What is calculated at first is a cylindrical arch wall of a constant thickness that has been considered in Zienkiewicz's book [5]. Results of MEF and FEM calculations have been compared. A comparison to results, obtained by employing the method of test loads, has been made as well. b) Secondly, an example of the calculation of the arch-dome "Antonivanovtsi" dam wall is given as an illustration. Comparison to results obtained by model investigation has been made. However, tests have been performed in the Moscow Civil Engineering Institute.

JTAM, Sofia, vol. 15 Issue 3 pp. 104-110 (1984)

On Crack Problems for Ductile Porous Medium

I. Michovski
Inst. Mech. Biomech., Bl. 8 Geo Milev

Some aspects of the elastic-plastic problem for an opening mode crack in a ductile porous medium are revealed. A standard dilatation approach is employed. It is shown that this approach, when coupled with the existing experimental data on cracks in ductile porous medium, implies a reasonable crack growth criterion. The latter is presented in an explicit form. An analytical estimation of the experimentally observed relation between the material fracture toughness and its porosity is given.

JTAM, Sofia, vol. 15 Issue 3 pp. 111-116 (1984), [Full Article]