Issue 4
JTAM, Sofia, vol. 16 Issue 4 (1985)

Registration of Singular Points of Contact in a Generation of Surfaces by T. Olivier's Second Approach

V. Abadjiev, D. Petrova
Inst. Mech. Biomech., Bulg. Acad. Sci., Bl. 8 Geo Milev


The paper treats the appearance of singular knot points of contact, the existence of which causes undesirable phenomena, such as undercutting and interference. Simple analytic relations to registrate undercutting in a generation of gear working surfaces by T. Olivier's second approach are proposed.

JTAM, Sofia, vol. 16 Issue 4 pp. 011-014 (1985)

Restricted Length Configurations

A. Dontchev, G. Iliev, M. Konstantinov
Center Math. Mech., Bulg. Acad. Sci., Bl. 8 Geo Milev

The problem of finding a restricted length plane curve, which minimizes a convex functional invariant under isometric transformations, is considered. Necessary and sufficient conditions characterizing the solution are given. The problem of determining the restricted length minimal energy configuration of an elastic string is considered in details.

JTAM, Sofia, vol. 16 Issue 4 pp. 015-021 (1985), [Full Article]

Nonlinear Oscillations of a Deployable SAR-Satellite Antenna

M. Hiller
Gallenklingenstr. 1, Stuttgart, Germany

A dynamical model of the folding truss for a satellite antenna with large dimensions is proposed. The nonlinear oscillations of the outer panel of the truss are investigated. Of particular interest are the rapidly changing time period of the oscillations and the shocklike increasing angular velocity and acceleration in a neighbourhood of the equilibrium position.

JTAM, Sofia, vol. 16 Issue 4 pp. 022-024 (1985), [Full Article]

Individual Forecasting of the Creep in Structures by Using the

Yu. Samarin, Yu. Eremin, V. Radtchenko
Kuybishevski Politehnicheski Institut, USSR

A reduction method from creep stochastic equations describing similar structures bearing to deterministic equations with entirely defined values of the casual parameters involved in the corresponding casual functions is developed. A tension measured or stand tested individual forecasting of the corresponding product becomes possible. The investigation results show that the method is correct.

JTAM, Sofia, vol. 16 Issue 4 pp. 025-033 (1985)
Investigation of Heat Processes in a Cylindrical Bar under Heating and Cooling

P. Marinov, P. Kiriazov, N. Kalkanov
Inst. Mech. Biomech., Bulg. Acad. Sci., B1. 8 Geo Milev

A suitable mechano-mathematical model of an infinite axissymmetric cylindrical bimetal bar is constructed. It is possible to forecast the time distribution of temperature across the bar during a given environment heat interchange and an ideal contact of the boundary surface between the two metals. Heating and cooling conditions without heat sources inside the cylindrical bar are designed. The Laplace transform is applied to the solution of the initial boundary value problem and the system of partial differential equations is reduced to a system of Bessel type ordinary differential equations. Two propositions concerning the order of the characteristic zeroes are proved. An algorithm for solving the heating problem of a cylindrical bar is pointed out and a numerical realization is given.

JTAM, Sofia, vol. 16 Issue 4 pp. 034-044 (1985)
Steady Nonlinear Waves on the Surface of a Vertical Liquid Film

O. Tsvelodub, Y. Triffonov

Periodic and soliton solutions of an ordinary differential equation with one nonlinearity and modelling the propagation of steady-state travelling waves on the surface of a vertical viscous film for moderate Reynolds numbers are numerically obtained. The wave profiles and the wave velocities dependence on their amplitudes are compared with experimental data of other authors and this shows a good agreement in the case of different values of similarity criteria.

JTAM, Sofia, vol. 16 Issue 4 pp. 045-048 (1985)
Computation of Stabilized Turbulent Fluid Flow and Heat Transfer in Circular Smooth Pipes for Moderate Prandtl Numbers. Part 2. – The Limiting Heat Transfer Coefficieuts

M. Mikhailov, N. Valchanov, V. Zimparov
High. Inst. Mech. Electr. Eng., Dârvenitsa

Data for the limiting heat transfer coefficient under I and H kind boundary value conditions for the pipe wall are presented. The basis is the exact solution of the Graetz problem for a hydrodynamic entirely stabilized turbulent fluid flow of an incompressible fluid in circular smooth pipes for moderate Prandtl numbers, as well as the turbulent flow transport described in Part 1 of this study. The case of I kind boundary value condition is examined numerically by using a modification of a recently published algorithm for the estimation of Sturm-Liouville operator eigen values and eigen functions. The results that have been obtained are compared with correlations and previously published references.

JTAM, Sofia, vol. 16 Issue 4 pp. 049-054 (1985), [Full Article]

Hydromechanic Model of a Flow Jump after a Flowing below a Shield

V. Matakiev, V. Simeonova, R. Petkov
Inst. Water Problems, Bulg. Acad. Sci., Bl. 1 Geo Milev

A mathematical model of a flow jump after a flowing below a shield is proposed. What is assumed for the solution according to the scheme from Fig.2 is a rectangular canal with a backward to the flow infinite length and a critical form of the level conjugation beyond the shield opening. The problem is two-dimensional and is divided into two sub-problems,. The first one defines a boundary value condition for the second one. Initial positions for both the problems are the Navier-Stokes equations (averaged by Reynolds method) and the equation for continuity. The systems (9) and (10) are closed by using Prandtl hypothesis for both the turbulent stress tensor and the stresses along the vertical walls 1-1 and 2-2. A particular constant k is introduced and the flow is recognized by means of it.

JTAM, Sofia, vol. 16 Issue 4 pp. 055-060 (1985)
The Three-Dimensional Problem for Anisotropic Media and Solids

D. Kolarov
Inst. Mech. Biomech., Bulg. Acad. Sci., Bl. 8 Geo Milev

An algorithm for solving in a most general formulation the three-dimensional problem for stresses and deformations in media and solids is developed. This algorithm is based on the analytical method previously proposed by the author for obtaining large classes of solutions for linear systems partial differential equations of high order. It is possible for the material to be with a most general anisotropy with 21 constants or with less modules, too. The solution containing a great number of integration constants which depend on two free parameters enables the fulfilment of the most complex boundary value conditions. The method is completely adapted to modern high efficient computing technics.

JTAM, Sofia, vol. 16 Issue 4 pp. 061-067 (1985), [Full Article]

On the Behaviour of an One-Storey Steel Frame with Barrage Walls under a Horizontal Earthquake. Part II – Theoretical Investigation

B. Yanev
P. B. 1100, N. Y. C., N. Y. 10023, USA

A mechano-mathematical modelling of the behaviour of a steel frame with barrage walls under a horizontal earthquake effect is carried out by using system identification methods. Experimental results from Part I (No 3, 1985, "Theoretical and Applied Mechanics") of this study are used. The necessity to apply combinations of the classical methods of mechanics of continua is well-grounded.

JTAM, Sofia, vol. 16 Issue 4 pp. 068-074 (1985)
Reducing the System of Differential Equations for the Momentum Theory of Shell Structures with Changing Thickness to the Integro-Differential Equations of

H. Ganev, T. Dimitrov
Inst. Water Problems, Bulg. Acad. Sci., Bl. 1 Geo Milev

A reduction of the total system of the differential equations of shells to the integro-differential equation of "plate" lying in elastic pliant groove is made by using the V. Z. Vlassov general momentum shell theory. The theoretical results are confirmed by a numerical experiment for arc-dome wall shell with peripheral joint.

JTAM, Sofia, vol. 16 Issue 4 pp. 075-085 (1985)