Issue 2
JTAM, Sofia, vol. 1 Issue 2 (1970)

On the Stabilization of a Non-Linear Controlled System in the Case of 2k Pure Imaginary Roots

N. V. Stoyanov, G. H. Gerov


The problem of stabilization in the critical case of k pairs pure imaginary roots is considered. A continuous equation non-linear regarding the critical 2k variables is introduced. The problem of making the system stable (non-stable) is brought to the problem of defining of some square form depending only on the critical variables.

JTAM, Sofia, vol. 1 Issue 2 pp. 011-016 (1970)

Obtaining of Indiscrete Information about the Stress State Tensor and about the Equivalent Stresses at Dynamic Loadings

P.L. Ganev, K.D. Daskalov

The problem for obtaining of indiscrete information about the stress state tensor and about the equivalent stresses, when the loading is a function of the time, is considered. The algorithms are deduced, after which the equivalent stresses and the stress state tensor components can be determined by means of rosettes of surface deformation. It is shown that it is practically impossible to realize these algorithms mentally and the necessity to perform this realization with specialized computers is well grounded. More precise attention is paid to the realization to the eqivalent stresses algorithms according to Mohr, Coulomb, Mariot aud Huber.

JTAM, Sofia, vol. 1 Issue 2 pp. 017-022 (1970)
Stress and Strain State of Slope Shells with Double Curvature on Rectangular Basis Taking into Account the Creeping of the Material

R.P. Rangelov, A.A. Popov

A non-reinforced and a reinforced slope shells with double curvature on a rectangular basis, made of creaping material are investigated. The basic  premises of the technical theory of slope shells and the premises of the linear hereditary theory of creeping are accepted. On this basis the integral-differential equations of the shell at arbitrary vertical loading are obtained. The equations are solved by means of Bubnov-Gal’orkin’s method and the expressions for the forces and strains of the shell are obtained. A slope shell, supported on ideal diaphragms, loaded with sine load, is examined as an example. The creeping effect on the strains for the theory of the elastic heredity and the theory of ageing is taken into account.

JTAM, Sofia, vol. 1 Issue 2 pp. 023-038 (1970)
On the Dynamic Theory of Elasticity for Different Modular Orthogonal-Anisotropic Media

I.Tr. Minchev

The problem for determining the stress and strain state of indescrete different modular orthogonal-anisotropic media, subjected to a propagating plain elastic wave, is considered. By means of D’Alambert’s method a solution of the dynamic system of partial differentia! equations is obtained (1). The existence of three different values for the velocity of the stress wave propagation is proved, the directions of the waves coinciding with the main directions of the orthotropy. The solution for the stress wave propagation in different modular orthogonal-anisotropic semispace is given as an example.

JTAM, Sofia, vol. 1 Issue 2 pp. 039-044 (1970)
Dynamic Stability of Orthotropic Cone Shells from Pulsating Axial and Hydrostatic Load

M.M. Kozarov

The dynamic stability of circular cone shells, reinforced with ribs in two directions are examined. The investigations are carried out in linear aspect using energetical approach. The basic system of differential equations treating the dynamic stability of the considered cone shell, is introduced by means of the Ostrogradski-Hammilton’s variational principle at given boundary conditions. The obtained scheme is Matheux-Hilts type. The general solution makes possible the obtaining of partial solutions and it is also possible at their programming to take into account the effect of the different geometric and elastic characteristics on the stability of the shells.

JTAM, Sofia, vol. 1 Issue 2 pp. 045-052 (1970)
On the Mechanical Stability of Shock Waves Generated at One-Dimensional Free Oscillations

A. Rachev

A necessary condition imposed on the elastic potential is obtained, at which satisfying the shock waves generated at one dimensional free oscillations, are stable. The condition is applied in the cases of longitudinal and shear oscillations at concrete forms of the elastic potential.

JTAM, Sofia, vol. 1 Issue 2 pp. 053-058 (1970)
On the Plain Problem of the Non-Linear Theory of Elasticity for Rectangular Area

J. Stoichev

An iterative solution of the first boundary problem in the non-linear theory of elasticity is proposed for a rectangular area at comparatively general boundary conditions and for a partial case of non-linear relation between deformation and translation.

JTAM, Sofia, vol. 1 Issue 2 pp. 059-064 (1970)
Stationary Motions of a Gyroscope Hung on a Filament

L. Stariradeva

The problem for the motion of a gyroscope hung on a filament is considered. The gyroscope has not dynamic symmetry, it is hung on the filament in the mass center and it is subjected only to the weight forces of the system. At stationary motion of the mass center, the gyroscope moves as cone pendulum, while the motion around the mass center is permanent rotation around the vertical. The position of the permanent axis in the system, connected with the gyroscope, depends on the hydrostatic moment and in the general case, the generatrice of the second order cone serves as axis of the permanent rotation – the cone of the permanent axes in the problem for the motion of gyroscope fixed in the mass center. The sufficient conditions for stability of the established stationary motions with regards all parameters of the motion, are obtained by means of the direct Lyapunov’s method.

JTAM, Sofia, vol. 1 Issue 2 pp. 065-072 (1970)
Effect of the Motion of a Point Mass on the Rotation of a Body Bearing It

V. Mileva

The mechanical system considered consists of a bearing body and point mass, which moves in the body and causes its spherical motion. The closed trajectories of the relative motion of the point securing a given finite rotation of the bearing body, are sought. The case in which the rotation is zero is also investigated. Mostly the plain problem is considered: the point moves in the main inertional plain of the bearing body, which plain rotates around its perpendicular axis. Optimum trajectories with minimum longitude, which at known initial conditions determine a given finite rotation, are selected from the obtained class of curves. A quantitative analysis of the trajectories obtained this way, is made in the approximate solution.

JTAM, Sofia, vol. 1 Issue 2 pp. 073-082 (1970)
Dimensioning of a Profiled Nozzle for Ship Propeller with Computer

M. Popov, K. Varsamov

A numerical method for dimensioning of a profiled nozzle is described. The main premises from (3) are accepted, but the ringwise peculiarities (vortexes and sources) are iteratively transferred on the frame line and their intensities are expressed according to (7). The problem is programmed for a computer „Minsk-22“, as first the frame line is determined, after which is determined the profile itself. The counter velocity, the parameters of the boundary layer, the resistance cofficient of the nozzle and the velocities in the interior, after which the propeller can be dimensioned for a specific case are also determined.

JTAM, Sofia, vol. 1 Issue 2 pp. 083-090 (1970)
On the Equilibrium Positions of a Satellite-Gyroscope on a Circular Eguatorial Orbit and Their Stability

A. Anchev, P. Atanasova, B. Bonev

The relative equilibrium positions of a satellite-gyroscope which moves on a circular equatorial orbit, are investigated. The effect of the flattenness of the Earth, the magnetic interaction between the satellite and the Earth and the aerodynamic resistance are taken into account. Classes of equilibrium positions as well as the necessary and sufficient conditions for century stability of these equilibrium positions are obtained.

JTAM, Sofia, vol. 1 Issue 2 pp. 091-102 (1970)