Issue 3
JTAM, Sofia, vol. 4 Issue 3 (1973)

Wave Propagation in Visco-Elastic Rods Composed by Two Materials

G. Brankov1, H. Boncheva2, N. Petrov1
1Sofia, Centre for Research and Training in Mathematics and Mechanics, Bulgarian Academy of Sciences, Geo Milev District, Block VIII
2Department of Seismic Mechanics at the Institute of Geophysics, Bulgarian Academy of Sciences, Geo Milev District, Block IV


A solution for wave propagation in a rod composed by two visco-elastic materials (subordinated to different stress and strain laws) is proposed. The rod is loaded with f(t) pulse and the waves propagate from the first visco-elastic material to the second. Graphs of the displacements variation depending on time, on frequency and density, as well as the reflection and penetration coeifficients are shown.

JTAM, Sofia, vol. 4 Issue 3 pp. 011-019 (1973), [Full Article]

Investigation on the Stability and the Oscillations of a Hyperbolic Shell with One Surface Depending on a Symmetrical Axial Load

M. Kozarov, M. Kishkilov
Sofia, Higher Institute of Civil Engineering, 1 Hr. Smirnenski Blvd.

The stability and the oscillations of an isotropic hyperbolic shell with one surface are investigated. The load is assumed to be axial, symmetrical and evenly distributed along the edges of the shell. The law for its operation is P = P0 + Ptcosθt in the most general case. The boundary conditions of the shell are accepted as simple supporting. The basic equations are obtained proceeding from Vlassov's general theory on shells. The solution of the basic system of differential equations is carried out by means of the Bubnov – Galyorkin variational method. A Matier-type system of differential equations is obtained for the most general case. The poblems related to the oscillations and the static stability of the construction follow as particular cases. Finally a numerical example is deduced.

JTAM, Sofia, vol. 4 Issue 3 pp. 021-032 (1973)
A Method for Analytical Solution of Boundary Problems for the Geometrically Non-Linear Theory of Slope Shells

Y. Betev, V. Petrov
Moscow, USSR

The stress and strain state of slope shells with saggings comparable to their thickness is considered. The basic system of equations is linearized by means of the consequent loadings method. The Kantorovich method of restricted operators and the Vlassov-Kantorovich modified method are used for solving the system of equations.

JTAM, Sofia, vol. 4 Issue 3 pp. 033-040 (1973)
Distribution of the Stresses in Developed Plastic Strains in Thick-Walled Pipes

V. Kortenska1, D. Dimitrov1, B. Ivanov2
1Sofia, Higher Institute of Civil Engineering, 1 Hr. Smirnenski Blvd.
2Institute of Metal Science and Technology of Metals, Bulgarian Academy of Sciences, 53 Chapaev Blvd.

The stressed state of a thick-walled pipe subjected to heavy strains is investigated. The reinforcement function of the material is accepted as exponential. The cases of parabolic type reinforcement function and ideally plastic material are also considered. An approximate solution by means of summation functional series is proposed.

JTAM, Sofia, vol. 4 Issue 3 pp. 041-048 (1973)
Non-Linear Physical Equations and Their Application for Calculation of Visco-Elastic Shells

G. Zahariev
Sofia, Central Laboratory of Physical and Chemical Mechanics, Bulgarian Academy of Sciences, Geo Milev District, Block IV

Non-linear physical equations comprising stresses and strains in explicit form are deduced for elastic relaxive medium in the small deformations region (solid cross-linked polymers and glass-fibre-reinforced plastic obtained on their basis). The equations obtained are applied for calculation of statistically determinable visco-elastic shells under conditions of momentless stressed state and constant loading. A spherical cupola subjected to its own weight is considered as an example.

JTAM, Sofia, vol. 4 Issue 3 pp. 049-056 (1973)
On the Existence of Periodic Solutions of Some Quasilinear Delay Systems

M. Konstantinov, D. Baynov
Sofia, Higher Institute of Mechanical and Electrical Engineering, Durvenitsa; 11 G. Georgiu Dezh Str.

The problem of the existence and number of periodic solutions of the following system is investigated:
z̈(t) + Aż(t) = f(t) + εF(t, z(t-τ1), ż(t-τ1), ..., z(t-τr), ż(t-τr), ε)
and an iteration procedure for plotting the solutions is proposed.

JTAM, Sofia, vol. 4 Issue 3 pp. 057-062 (1973)
A Method for Determination of the Statically Permissible Stressed State for the Plane Problem of the Elasticity Theory

V. Droumev
Sofia, Higher Institute of Civil Engineering, 1 Hr. Smirnenski Blvd.

Determination of the stressed state which satisfies the equilibrium equations and static boundary conditions along the entire contour in the plane problem of the elasticity theory is the subject of the present paper. Determination of this state is a stage in the solution of this problem according to the method given in [1] and [2]. The following complex derivative is accepted as an unknown quantity ∂2τ/∂x∂y = ψ(0)(x, y). A uniform rectangular net is placed over the considered area. It is accepted that ψ(0) is constant in the different rectangles and consequently dependent on a finite number of parameters. The determination of ψ(0) becomes unambiguous through suitable additonal assumptions and there is no need to solve systems of algebratc equations of high order.

JTAM, Sofia, vol. 4 Issue 3 pp. 063-072 (1973)
Secondary Stationary Currents of a Liquid Placed between Rolling Cylinders

I. Bozdouganov
Sofia, Institute of Mathematics and Mechanics and Computer Centre of the Bulgarian Academy of Sciences, Geo Milev District

The problem of the ambiguity of the solution for a stationary spatial periodic problem for Navier-Stoks equations is considered. M. A. Krasnoselskiy's theorem for points of bifurcation of operator equations is at the basis of the method used. It is established that the appearance of secondary stationary currents of a given type for any Reynolds number is impossible before the emergence of secondary stationary currents that are periodic along z.

JTAM, Sofia, vol. 4 Issue 3 pp. 073-079 (1973), [Full Article]

Differential Equation for Axial Symmetrical Stability Loss of a Circular Cylindrical Shell

G. Minchev
Sofia, Higher Institute of Mechanical and Electrical Engineering, Durvenitsa

The differential equation of axial symmetrical stabilty loss of a thin-walled circular cylindrical shell pressed biaxially is deduced. The roots of its characteristic equation are found and studied and the charccter of the solution they describe is shown. The general integral of the eq nation obtained permits the investigation of a shell with arbitrary support along its curvilinear edges.

JTAM, Sofia, vol. 4 Issue 3 pp. 081-084 (1973)
Multyfrequency Resonance Oscillations of Third Rank in Conservative Systems

B. Cheshankov
Sofia, Higher Institute of Mechanical and Electrical Engineering, Durvenitsa

m-frequent resonance oscillations of a conservative system with n degrees of freedom are investigated and the problem is reduced to a study of cannonic systems describing the resonance phenomena. The degree of resonant terms in the equations (1,5) is called resonance rank. Three basic cases are possible for third rank resonance: 1) when the cannonic system has 2m-2 equations; 2) when the cannonic system has 2m-4 equations; 3) when the cannonic system has 2m-6 equations. Three-frequency and four-frequency resonance oscillations are considered in particular for the second and third basic cases.

JTAM, Sofia, vol. 4 Issue 3 pp. 085-092 (1973)