Issue 1

JTAM, Sofia, vol. 2 Issue 1 (1971)

Nikolai Ivanovich Muskhelishvili (On the Occasion of His 80th Anniversary)

G. Brankov

JTAM, Sofia, vol. 2 Issue 1 pp. 009-010 (1971)

Dynamical Criterion for the Motion Mode of the Machines

I.I. Artobolevski

Different criterions for the motion, mode of the machines are surveyed. A more detailed investigation of the characteristical criterion of the motion mode of the machines and of the dynamic coefficient of unevenness of the machine pace is made.

JTAM, Sofia, vol. 2 Issue 1 pp. 011-024 (1971)

Functional and Basic Variational Equation in the Theory of Thermo-Visco-Plasticity

D. Kolarov, A. Baltov

A thermomechanical structural process based on the general model of a body with internal parameters of thermodynamic state, is studied in variational way. The action functional and the basic variational equation of the model are obtained. The variational equation is a basis for application of variational methods for solving of concrete initial-boundary problems. The total system of equations describing the considered process is obtained from this equation. This investigation is applied for thermo-visco-plasticity which makes possible the obtaining of new results for this theory.

JTAM, Sofia, vol. 2 Issue 1 pp. 025-036 (1971)

Stability of Elliptical Cylindric Shells

M. Kozarov

Thermostability of elliptic cylindric shells is considered in Linear formulation in the presented investigations. The external tangential temperature gradient which varies irregularly does not affect the elastic properties of the material. The problem for the thermostability of the shell is brought to a problem for the static stability of the same shell. Two cases are considered : a) stability of an elliptical cylindric shell subjected to axial pressure, b) stability of the elliptical cylindric shell to bending. The solution of the same problem when the temparature gradient varies along the axis is shown.

JTAM, Sofia, vol. 2 Issue 1 pp. 037-044 (1971)

Characteristic Equation in Complex Region for a Circular Cylindric Shell and Investigation of its Roots

G. Minchev

The characteristic equation in complex region according the moment theory is found for a closed thin-walled circular cylindric shell. The roots of the equation are determined and investigated. They are divided in two groups: two rather big roots, which solution according the moment theory are from boundary effect kind, and two other rather small roots, which solution according the moment theory is extended along a rather long shell. Approximate expressions, practically very convinient, are given for the sought roots, at small values of k.

JTAM, Sofia, vol. 2 Issue 1 pp. 045-048 (1971)

General Integral of the System of Integro-Differential Equations (I) and Stability

R. Krastev

The system of integro-differential equations (I) is considered. For the system are proved the following theorems: 1st theorem for existence and uniqueness of the solution, 2nd and 3nd theorems for the kind of the general integral, 4th theorem for stability and so on. For the equation (70) are proved the stability theorems 9, 10, 11. Examples are given. The new results for stability are obtained due to the kind of the general integral (18), (45).

JTAM, Sofia, vol. 2 Issue 1 pp. 049-060 (1971)

Solving Problems of Cone Shells with Variable Thickness

I. Ganev

Cone shells which thickness varies in a linear way along the generating lines and is constant along the parallels are considered. Differential equations obtained after a variational principle are compiled for investigation of this kind of shells. Thus the properties symmetry and positive definiteness are quaranteed for the system of equations. These properties are important conditions when a solution is sought. The operations for compilation of equations and for their solution are presented in matrix form which is convenient when using computers. A concrete numerical example is solved as an illustration of the considered methods.

JTAM, Sofia, vol. 2 Issue 1 pp. 061-074 (1971)

On the Space Action of Long Slope Shells with Variable Thickness

M.G. Kolchako

Formulae in closed form are obtained on the basis of the slope shells theory with the premise that the shells are long. This formulae render a possibility to take into account the space action of arc shells with variable moment of inertia of the arc and variable thickness. The elastic-characteristics which ought to be introduced for some non-isotropic materials – reinforced concrete, glassplastic etc., are given. Formulae in closed form are given for some partial cases often met in practice.

JTAM, Sofia, vol. 2 Issue 1 pp. 075-090 (1971)

A Method for Approximate Integration of Non-Linear Equations in the Mechanics of Polymers

A.L. Rabinovich, R.A. Turusov

A general numerical method for solution of the problems in rigid polymer mechanics when a relaxation times spectrum is available, is surveyed in the paper. The relationship between the stresses and the visco-elastic deformations is accepted according the generalized Maxwell’s law, proposed from Gruevich.

JTAM, Sofia, vol. 2 Issue 1 pp. 091-094 (1971)

Stability of the Periodical Solutions of Non-Autonomous Quasilinear Neutral Type Systems rat Double Roots of the Main Amplitudes Characteristics

D. Bajnov, B. Vesselinov

A neutral type quasilinear non-autonomous system is considered. The sufficient conditions for assymptotic stability of the 2n periodical solutions of the system (I) at double roots of the main amplitude equations are found.

JTAM, Sofia, vol. 2 Issue 1 pp. 095-098 (1971)

Optimal Synthesis of a Machine Aggregate with Elastic Cardan Transmission

A.M. Pisarev

When definite simple correlations between the elasticity of the driven schafts, as well as between the moments of inertia of the engine and working machines rotors, are observed, the aggregate is discharged from dynamic loadings. The deduced necessary and sufficient conditions for optimal synthesis of an aggregate with a cardan schaft are practically realized in a very simple way and show a big practical effect. This is confirmed from the carried out theoretical and experimental investigations, surveyed in the paper.

JTAM, Sofia, vol. 2 Issue 1 pp. 099-104 (1971)