Issue 1
JTAM, Sofia, vol. 11 Issue 1 (1980)

On Chaplygin's Reducing Multiplier

I. Iliev
Plovdiv, Asen Halachev street, 42


The problem for the existence of Chaplygin's reducing multiplier in a nonholonomic system with K degrees of freedom is considered. A relationship between the conditions for the existence of Chaplygin`s reducing multiplier and Jacob's last multiplier is established. For a rigid body moving parallely to a plane – Chaplygin's example, it is proved that the introduction of the quasi coordinate makes Chaplygin's approach inapplicable for the normalization of this multiplier.

JTAM, Sofia, vol. 11 Issue 1 pp. 013-020 (1980)

On the Determination of the Peculiar Positions of Four and Five Chain Links by the Relative Transfer Functions

M. Konstantinov, V. Chifchieva
VMEI – Darvenitza

In the present paper the relation between the relative transfer functions and the peculiar positions of four and five chain links is subject of consideration, i.e. the cases when there is no solution of the problem for determining the angular velocities of the links. Conclusions are drawn for all variations of the relative transfer functions for the cases leading to peculiar configurations of the above chains. The existence of dependences between the relative transfer functions at a five chain link is presented.

JTAM, Sofia, vol. 11 Issue 1 pp. 021-026 (1980)
Translation Functions for Centroidal Type Mechanisms

V. Galabov
VMEI – Darvenitza

The effect of different exponential, trigonometric and exponential-trigonometric translation functions on the geometric characteristics of centroidal type mechanisms is considered. Subjects of determination are: the extreme values of the translation functions and the intervals in which they change their parameters and for which technically expedient solutions are obtained. An approach for selection of the translation function with respect to the desired properties of the designed mechanism is presented too.

JTAM, Sofia, vol. 11 Issue 1 pp. 027-035 (1980), [Full Article]

Analysis of the Optimal Parameters of Multistage Framed Buildings Subjected to Seismic Effects

A. Killimnik

Subject of consideration is the optimization of the structures to seismic effects. An optimization criterion is proposed on the basis of obtaining the extremum of the dissipation velocity functional of the energy or the degree of dissipation.

JTAM, Sofia, vol. 11 Issue 1 pp. 036-041 (1980)
To the Problem of the Calculation of Reinforced Concrete Thin-Walled Beams

Sp. Pamukchiev
VIAS, Bul. H. Smirnenski 1, Sofia

The problem for defining the transverse forces of reinforced thin-walled beams is considered. The longitudinal forces are determined on the basis of Professor V. Z. Vlahov's general theory of thin-walled beams. The determination of the transverse forces is based on the moment theory of sloping long cylindrical shells. As a result of the use of an appropriate generalization of the moment theory equations, expressions for the forces Mx and Nx are obtained. The reinforced thin-walled beams are measured out for these forces.

JTAM, Sofia, vol. 11 Issue 1 pp. 042-051 (1980)
To the Problem of the Stability of a Visco-Elastic Beam under Vibro-Creep Conditions

L. Hadjikov, H. Hristov, P. Bekjarova
IMB, Bulg. Acad. Sci, bl. 8, G. Bonchev str.

Subject of consideration in the presented paper is the solution of a system of integro-differential equations by which the stability of a visco-elastic beam under vibro-creep conditions is studied. The effect of the different parameters, involved in the equations, on the extent of the critical time is examined. The results are compared with the available experimental data. The solution is obtained on the basis of the generalized Maxwell-Gurevich-Rabinovich equation with rheologic constants varying depending on the parameter.

JTAM, Sofia, vol. 11 Issue 1 pp. 052-058 (1980)
On a Canonical Distribution of the Stochastic Processes and Its Application in Turbulence

H. Hristov
IMB, Bulg. Acad. Sci., G. Bonchev Str. block 8

A new canonical distribution of some steady stochastic processes is proposed and on this basis an equation of a freely degenerating Burgers turbulence is derived. The correlation function, the energy spectrum and the law of attenuation are obtained. The results are compared with the numerical experiments for attenuation of Burgers turbulence. The agreement is satisfactory.

JTAM, Sofia, vol. 11 Issue 1 pp. 059-066 (1980)
Dynamics of the Water Volume in Hidropneumoaccumulators for Impulse Irrigation

V. Georgiev, V. Mednikarov
IMB, Bulg. Acad. Sci., G. Bonchev str., block 8

Differential equations for the dynamics of the water volume in water-air reservoirs of hydropneumoaccumulators for impulse irrigation are derived. Subject of consideration are the cases of hydropneumoaccumulators without preliminary air compression in their reservoirs with complete and partial ejection of the accumulated water volume; as well as the cases of hydropneumoaccumulators preliminary pressurized to the low allowable limit of the pressure necessary for the normal operation of the impulse shower-watering systems which use the volume of their reservoirs with increased efficiency.

JTAM, Sofia, vol. 11 Issue 1 pp. 067-071 (1980)
On the Structure of a Non-Collision Shock Wave with Due Accounting of the Magnetic Viscosity

M. Kartalev
IMB, Bulg. Acad. Sci., G. Bonchev street, block 8

The problem of the structure of non-collision shock wave in plasma with anisotropic pressure is considered in one-dimensional steady formulation. The dissipation is accounted by the introduction of a finite electric conductivity. The longitudinal entropy is assumed to be preserved. For the obtained system the existence and singularity of the solutions for this type shock wave structure is studied. Further, the well known Jermen evidence for the existence and singularity of rapid shock waves in isotropic magnetic hydrodynamics is generalized. Some difficulties arise, however, with respect to the complification of the thermodynamic functions and of the free energy in particular. Difficulties occur too with the lack of identity in the mutual positioning of the characteristic velocities. The existence of a structure is proved under definite provisions. The obtained result is valid for an arbitrary dependence of the magnetic viscosity on the parameters of the medium. The exact kind of such dependence is not discussed in the paper.

JTAM, Sofia, vol. 11 Issue 1 pp. 072-082 (1980)
On the Usage of a Two-Layer Model for Description of the Bending Moment Relaxation of a Beam Placed In a Fluid Medium

K. Popov, K. Hadjov
VHTI, Darvenitza

A model is proposed on the basis of which the cross-section of the beam is divided into two regions in which the material manifests constant in time properties-dry and saturated. Thus the equations for the stress-strain relationship could be referred to a material with constant properties. The problem for the relaxation of the bending moment of a beam with a constant curvature and which is placed in a fluid medium is solved by the coupling equations of the type Boltzmann-Voltera linear inherited theory.

JTAM, Sofia, vol. 11 Issue 1 pp. 083-086 (1980)
On the Stability of a Two-Layer Cylindrical Shell Subjected to Axial Pressure

P. Kolev
VIAS, bul. H. Smirnenski 1, Sofia

In this paper the elastic stability of a two-layer cylindrical shell loaded along its contour with uniformly distributed and parallelly to the axis load is considered. The shell is freely supported on both ends – average length and consists of two isotropic layers: basic layer with thickness and higher physical characteristics and supporting layer with thickness.

JTAM, Sofia, vol. 11 Issue 1 pp. 087-091 (1980)
On the Stability of a Panel from Elliptic Cylinder

H. Kunchev
VIAS, bul. H. Smirnenski 1, Sofia

The stability of a thin elastic panel from elliptic cylinder without initial irregularity is studied. The panel is loaded with uniformly distributed axial load. The upper and lower limits of the critical load are obtained by the method of Bubnov and Galjorkin. The problem is solved in a first approximation with an approximation function for the radial displacements accounting the peculiarity that the depth of the sinking depends on the radius of the curvature.

JTAM, Sofia, vol. 11 Issue 1 pp. 092-096 (1980)
A New Approach to the Solution of Thin Elastic Plates

V. Drumev, N. Kurdjiev
VIAS, bul. H. Smirnenski 1, Sofia

The approximate solution of a plate bounded by mutually perpendicular segments is sought by the introduction for the unknown: of the derivative ∂4w/∂x2∂y2 of the sagging w. It is assumed to be step-like on an uniform rectangular net, i.e. it is constant in an element of the net. Owing to the fact that its values are presented at appropriate unique states spread on only 9 adjacent elements, the solution of the fixed plate reduces to the solution of a system of linear equations with a band matrix. This approach could be considered as an original displacement method of the method of the finite elements with coordinated states in case the latter method is comprehended in a broader sense.

JTAM, Sofia, vol. 11 Issue 1 pp. 097-105 (1980)
Variation of the Lateral Strain Coefficient at Elastic, Plastic and Elasto-Plastic Strains

S. Mandjakov
VMEI – Darvenitza

In this paper a theoretical study is carried out on the variation of the lateral strain coefficient at elastic, plastic and elasto-plastic strains. The concept “lateral strain coefficient" is specified and it is differentiated from and compared with Poisson's ratio. It is shown that the lateral strain coefficient reflects the geometric dependences which are not connected with the physico-mechanical properties of the deformable material. The variation in the lateral strain coefficient is studied on the basis of a relation (in geometric interpretation) between the coefficient and the relative variation in the volume and in the longitudinal strain and a definite dependence between the variation in the volume and in the longitudinal strain is accepted.

JTAM, Sofia, vol. 11 Issue 1 pp. 106-109 (1980)