Issue 1
JTAM, Sofia, vol. 21 Issue 1 (1990)

Can the Reputation of the Lagrangean Dynamical Equations Be Saved?

I. Chobanov
Sofia University, 5 A. Ivanov Bld., Sofia


Contrary to the wide-spread belief, not a single problem of the rigid body dynamics can be solved by means of the Lagrangean dynamical equations, since they cannot answer the question of the existence of a solution of the problem. The same holds for their numerous non-holonomic variants. While the postulate of ideal constraints is a question of a definition in the holonomic case, in the non-holonomic one it is a question of a demonstration; up to now this circumstance has been generally ignored in the traditional literature on analytic dynamics. The mathematically irreproachable means for solving holonomic as well as non-holonomic dynamical problems are the Eulerian dynamical axioms (laws (principles) of momentum and of moment of a rigid body).

JTAM, Sofia, vol. 21 Issue 1 pp. 011-018 (1990), [Full Article]

Stability of the Equilibrium Positions of a Satellite-Gyrostate System with a Damper

L. Lilov, O. Hristov
Sofia University, 5 A. Ivanov Bld., Sofia

A satellite-gyrostate system along a circular orbit in a central Newton tension field is considered. Three rotors have been balanced dynamically and statically. They have been directed along the inertia main axes. What oscillates along a fixed line in the satellite is a point that has been attached to a spring. Friction forces act to the point and they have been realized by a damper. The system equilibrium positions are defined and their stability is examined.

JTAM, Sofia, vol. 21 Issue 1 pp. 019-028 (1990)
Independent Joint Controllability of Manipulator Systems

P. Kiriazov, P. Marinov
Inst. Mech. Biomech., Bulg. Acad. Sci., Bl. 4

The inertial matrix plays a central role in designing a manipulator with appropriate dynamic characteristics. In the general case a weak condition is imposed on the matrix to provide independent joint controllability of the manipulator system. A1 most all non-redundant manipulators satisfy the condition. The case of a planar manipulator with three rotary joints is considered as well.

JTAM, Sofia, vol. 21 Issue 1 pp. 030-035 (1990), [Full Article]

Numerical Examination of the Free Convective Laminar Flow of Fused Metal at the Vertical Refrigeratable Tube Entrance

O. Iliev
Inst. Mech. Biomech., Bulg. Acad. Sci., Bl. 4

What is examined numerically in the paper is the steady free convective laminar flow of fused metal along the initial length of a flat cylindrical vertical refrigeratable tube. Some cases are considered before or after the tube wall constant phase formation when the flow is up or down the tube. All features have been pointed out in constructing computing algorithm in the cylindrical case. The flow dependence on mathematical and thermophysical problem parameters has been examined as well.

JTAM, Sofia, vol. 21 Issue 1 pp. 036-043 (1990)
A Solution of the Navier-Stokes Differential Equations

K. Shulev
High. Inst. Arch. Civ. Eng., 1 Hr. Smirnenski Bld., Sofia

An exact solution in explicit form of the initial-boundary value problem for the complete Navier-Stokes equations is derived. The problem corresponds to a viscous fluid flow that has been induced by transverse damping motion of a long circular cylinder with a given initial velocity. The problem allows a generalization by extended initial-boundary value conditions. In the case of null viscosity the solution is reduced to the Eulerian equations solution of a cylinder motion with a constant velocity.

JTAM, Sofia, vol. 21 Issue 1 pp. 044-048 (1990), [Full Article]

On the Applicability of Some Simple Turbulence Models to the Two-Dimensional Boundary Layer Modelling

D. Marinov, G. Simeonov
Inst. Mech. Biomech., Bulg. Acad. Sci., Bl. 4

Numerical results about the characteristics of a two-dimensional turbulent boundary layer on a flat plate are presented. Different combinations of simple algebraic models of the “inner” and the “outer” boundary layer regions are estimated via comparison with available experimental data. What is found out accounting for the Reynolds number and the characteristics under consideration are the cases of the best results that can be obtained by one of the following “inner”-„outer” models combinations: van Driest’s-Prandtl’s, van Driest’s-Clauser’s, Patankir & Spalding’s-Clauser’s and Patankar & Spalding’s-Clauser’s with Klebanoff’s intermittancy factor.

JTAM, Sofia, vol. 21 Issue 1 pp. 049-062 (1990), [Full Article]

A Link between the Dynamical and the Statical Criterion for Deformable Solid Stability

Ts. Ivanov
Inst. Mech. Biomech., Bulg. Acad. Sci., Bl. 4

In the present paper a comparison is made between the stability statical approach and Coiter’s stability dynamical criterion. What assumes a stability sufficient condition following the statical criterion in the case of kinematically admissible and arbitrary small equilibrium state deviation is that the stored or the dispersed energy of deformation should be greater than the outer conservative force work. Thus formulated the condition implies unique solution of the statical problem under given boundary value conditions and with respect to additional small deformation that has been applied to the finite one. The stability dynamical criterion is based on Lyapunov’s stability ideas that have been generalized for deformable solids. It is proved that the stability sufficient condition according to the statical criterion is no more sufficient with respect to the dynamical one. The forms of stability lost corresponding to both the statical and dynamical criteria coincide. The form existence of stability lost does not imply equilibrium state instability according to the dynamical criterion. Additional considerations are necessary in this case.

JTAM, Sofia, vol. 21 Issue 1 pp. 063-068 (1990)
On a Solution of the Coefficient Problem in Nonlinear Stochastic Geomechanics

M. Valkov
High. Inst. Min. Eng., Durvenitsa

What is defined in the paper are the global geomechanical characteristics of the rock massif under mould settling data. The inverse coefficient problem is solved using group properties of the nonlinear stochastic geomechanics basic equation. The investigations conclude that differential equations group analysis gives powerful means to solve concrete practical problems. The coefficient problem solution can be applied to preliminary calculation of the displacements that have appeared due to earth entrails geomaterial removing.

JTAM, Sofia, vol. 21 Issue 1 pp. 069-072 (1990)
Inverse Analysis of Tunnel Nature Measurements

V. Vassilev
Inst. Water Problems, Bulg. Acad. Sci., Bl. 1

The paper presents an algorithm and a program to carry out inverse analysis of nature measurements of rock massif displacements around underground constructions (tunnels). What is determined by the inverse analysis are the elasticity module and the rock massif natural stressed state. Afterwards, both of them are data input to examine the stressed state and the underground construction stability. A numerical example illustrates the accuracy of both the algorithm and the program.

JTAM, Sofia, vol. 21 Issue 1 pp. 073-077 (1990)
Numerical Determination or Plastic Localization during Extrusion of Metals

N. Boncheva
Inst Mech. Biomech., Bug. Acad. Sci., Bl. 4

The initiation of plastic localization bands during extrusion of metals is investigated by means of a program system that has been based on a combination of both the finite element method and the free point one. Strain-rate and temperature sensitivity of the material are taken into account. The coupled thermoplastic process is considered. The temperature distribution and the plastic zones detailed graphics are obtained in the domain that has been occupied by the treated material.

JTAM, Sofia, vol. 21 Issue 1 pp. 078-085 (1990), [Full Article]

Netlike Representation of the Thermoelastic Medium

G. Wrobel
Inst. Mech. & Mach. Constr., Technical University of Silesia

The paper presents the formal basis of the description and identification of the netlike elements of the thermoelastic medium. The example of the netlike model of symmetrical thermoelastic medium has been shown. The netlike model is alternative to the continual medium representation. Simultaneously, it gives the modelling language and interpretation of the problems which are solved due to the numerical method.

JTAM, Sofia, vol. 21 Issue 1 pp. 086-093 (1990), [Full Article]

Numerical Solution of the Heat Conductivity Problem for Dam Wall Blocks by a Non-Orthogonal Network

I. Etimova, O. Santurjian
Inst. Water Problems, Bulg. Acad. Sci., Bl. 1

A numerical solution of a problem is developed to determine a volume unsteady temperature field in concrete dam wall blocks. It is based on a modified colocalizing point method to boundary value problems that has been developed by the authors using a nonuniform non-orthogonal network. An application of the method is stated to model temperature regime of blocks accounting for their real form during construction and exploitation. The block heights increase by sections. The basic defining equations of the interior, the boundary and the section contact planes are presented after their derivation. What is presented in addition are the stability criterion and the investigation results of the solution accuracy and stability.

JTAM, Sofia, vol. 21 Issue 1 pp. 094-104 (1990)
On a Theoretical Possibility To Optimize Strength Calculations

N. Gospodinov
High. Inst. Mech. Electr. Eng., Durvenista

What is considered in the paper is the application of the extremal principle on an experimental base. It concerns the maximal plastic work when determining steel material high strength under thermic treatment. This principle is well known in the plastic theory. The investigations prove that the maximal plastic work theorem can be applied to determine the most favourable thermic regime of high strength steel material treatment. It is possible to solve wide range of complex optimization problems as well. The problems connect the product strength with both the treatment technological ability and economy, for instance.

JTAM, Sofia, vol. 21 Issue 1 pp. 105- (1990)