Issue 1
JTAM, Sofia, vol. 5 Issue 1 (1974)

On the Principles of Gauss and Chetaev about Systems with Non-Ideal Bonds

V.V. Rumyantsev
USSR, Moscow-B-333, Computer Centre of the Academy of Sciences of the USSR, 40 Vavilov Street


A generalization is presented of the theorem of Chetaev, of the principle of Gauss, and of the principle of Chetaev for discrete material systems limited by non-ideal bonds. These results are extended to cover continuous media which are treated generally as systems with non-ideal bonds.

JTAM, Sofia, vol. 5 Issue 1 pp. 009-014 (1974)

On the Set of Mechanisms with Triangular Circuit

L. Kandov, V. Chifchieva
Sofia, Higher Institute of Mining Engineering and Geology, Department of Mechanics

The problem of determining the set of all mechanisms with which a movement of triangle is effected can be related to the problems of the theory of mechanisms. On the basis of the method of transfer functions, determination is made in the article of the set of all movements of the vectorial circuit with one, two, three and four degrees of mobility, and examples are given of mechanisms through which the above movements are realized. Unified formulae are given by means of which it is possible to determine the speeds of each mechanism.

JTAM, Sofia, vol. 5 Issue 1 pp. 015-024 (1974)
Strength of a Pre-Stressed Thick-Walled Pipe

E. Zlatanova
Sofia, Higher Institute of Mechanical and Electrical Engineering, Department of Machine Drawing

This is an examination of the strength of a pre-stressed thick-walled pipe made of non-compressible elastic material. The pipe is subjected to extreme tension and uniform external pressure. The strain is divided into two stages, namely, extreme preliminary strain and additional small strain. The equilibrium equations have been worked out and an attempt has been made at finding an approximate solution of the problem by the introduction of a small parameter. A strength condition has been also worked out, from which it is possible to calculate the critical values of the parameter of strain.

JTAM, Sofia, vol. 5 Issue 1 pp. 025-036 (1974)
Determining the Temporary Unevenness in the Operation of Hydro-Units with Jet Turbines upon Picking up the Load

I.S. Ivanov
Sofia, Institute of Mathematics and Mechanics with Computing Centre, Bulgarian Academy of Sciences, IV km

On the basis of an analysis of the universal and boost-up characteristic of high-speed turbines, an analytical method has been worked out for determining the temporary unevenness of the operation of the units upon picking up the load. An analytical formula has been obtained for the purpose of determining the maximum temporary unevenness. A certain average value is taken for the hydraulic impact.

JTAM, Sofia, vol. 5 Issue 1 pp. 037-044 (1974)
On the Strains of Certain Types of Seismic Diaphragms

L. Tsenov
Sofia, Institute of Geophysics of the Bulgarian Academy of Sciences, IV km

The author has investigated the strains of the composite girders modelling the diaphragms of various types of buildings built in seismic regions. A flexible line and maximum bending of the modelling composite girder have been obtained under different conditions of operation of the separate elements of its cross section. The parts of the overall loading, obtained, from each element of the girder's section, have also been determined. The results obtained and the method applied are undoubtedly of interest in the field of applied seismic mechanics.

JTAM, Sofia, vol. 5 Issue 1 pp. 045-056 (1974)
To the Problem of the Dynamic Interaction of Two Circular-Cylindrical Shells with Compressible Liquid

V. Dzhoupanov
Sofia, Institute of Mathematics and Mechanics with Computing Centre, Bulgarian Academy of Sciences, IV km

The potential has been determined of the speeds of a layer of compressible liquid when two vertical circular-cylindrical shells of the pilot type are vibrating in it according to an established harmonic principle. Account is taken of their interaction through the liquid. The solutions taken as a starting point are those for a single shell as infinite series according to Hankel's functions of the second order. The unknown constants in the series are determined from the equation of the speeds of the fluid and the surface of the shells. Infinite systems of algebraic equations are obtained which provide solution by the method of reduction. Determinations are made of the general expressions of the hydrodynamic pressure on the surface of one of the shells and the kinetic energy of the interaction between the shells and the fluid. A number of particular cases have been presented as well.

JTAM, Sofia, vol. 5 Issue 1 pp. 057-066 (1974)
On the Bifurcation and Stability of Stationary Movements

V.N. Rubakovski
USSR, Moscow-B-333, Computer Centre of the Academy of Sciences of the USSR, 40 Vavilov Street

The article offers an expansion of the theory of Poincare and Chetaev about bifurcation of the equilibrium of random systems whose equations of movement allow for time-independent integrals. Theorems about stability and instability of the stationary movements of mechanical systems have been proved.

JTAM, Sofia, vol. 5 Issue 1 pp. 067-080 (1974)
Studies into and Numerical Solution of the First Basic Problem of the Elasticity Theory about Transversally Isotropic Bodies through Integral Transformation of Fourier

S. Borshoukova
Sofia, Institute of Mathematics and Mechanics with Computing Centre, Bulgarian Academy of Sciences, IV km

The paper deals with the problems of determining the stressed and strained states of a long cylinder (solid and hollow) and the cylindrical cavity of transversally-isotropic material under arbitrary normal axial-symmetric loading. On the basis of the detailed analytical study of the problem of elastic equilibrium of a rotary body under symmetrical strain (belonging to S. G. Lehnitskiy) and elimination of the specificities at the points of interruption of the external loading, the solutions of the problems set have been reduced to calculation algorithms. The numerical results for one concrete problem have been presented graphically.

JTAM, Sofia, vol. 5 Issue 1 pp. 081-092 (1974)
On the Elasticity Theory of Media, with Independent Dilatation of the Particles

K. Markov
Sofia, Institute of Mathematics and Mechanics with Computing Centre Bulgarian Academy of Sciences, IV km

This is an exam nation of the statics of a microstructural medium in which the dilatation (volume expansion) is an independent deformational characteristics. The author has worked out the equilibrium equations for such a medium and has formulated the two basic boundary problems – in displacements and in stresses. He has worked out a general solution of the Papkovich-Neuber type and Greene's tensor for an unlimited area. Further examined is a micropolar Kossera's medium with independent dilatation of the particles.

JTAM, Sofia, vol. 5 Issue 1 pp. 093-100 (1974)
Investigation of Thin-Walled Cylindrical Shells of Polymeric Material under Bidimensional Stressed State of Tension and Shear

R. Dobrev, N. Bogdanova-Boncheva
Sofia, Institute of Mathematics and Mechanics with Computing Centre, Bulgarian Academy of Sciences, IV km

Following experimental studies of an alkaline polyamide PA-A, a theoretical dependence has been worked out connecting the intensities of the deformations in the case of bidimensional stressed state of tension and shear. It is demonstrated that the model of the unified curve cannot be applied to the polymeric material under this type of stressed state.

JTAM, Sofia, vol. 5 Issue 1 pp. 101-113 (1974)