Issue 4

JTAM, Sofia, vol. 19 Issue 4 (1988)

Remarks on Two Problems of the Dynamics of Absolutely Solid Bodies

T. Boyadjiev
Sofia University, Faculty of Mathematics and Informatics

The analysis is based on the condition that the reactions of links imposed on a material system are ideal. Hence equations of motion of some solid bodies are obtained for cases where links undergo degeneration.

JTAM, Sofia, vol. 19 Issue 4 pp. 011-016 (1988)

On the Nonexistence of New First F(p, r, γ,γ') = const Integrals of the Problem of Body Motion around a Fixed Point

S. Popov
Inst. Metal Research and Technology, 53 Chapaev Bld., Sofia

The paper studies a property of the new first integral of the problem of body motion around a fixed point. The theorem that n-l independent solutions of systems of l linear partial differential equations of first order and with n variables exist is used, where the system has the form Xi(f) = ∑k=1n aik df/dxk = 0, i = 1, 2,..., l. However, the sufficient and necessary condition for the existence of such a solution is that all Poisson brackets (xi, xj), i, j = 1, 2 ... li, i > j be expressed linearly by the operators X1(f), X2(f), ... Xl(f). It is shown that if γ2 + (γ')2 + (γ")2 = C3, where 0 < C3 < ∞, then an integral of type F(p, q, r, γ, γ') = const exist.

JTAM, Sofia, vol. 19 Issue 4 pp. 017-023 (1988)

Analysis of the Effect of the Scheme Error on the Accuracy of Gearing of a Localized Conic Gear with Straight Teeth

A. Miller, W. Bricki

The authors present results of the theoretical analysis of ensurance of a contact simul- neous localization and prescribed accuracy of gearing of a noncoupled (approximate) gear. However, this is how the so-called scheme error, due to the gear cutting theme, affects the gearing accuracy. The authors have obtained numerical results, which give the effect of correction displacements on gearing accuracy. The gear geometrical parameters have been taken into account as well.

JTAM, Sofia, vol. 19 Issue 4 pp. 024-031 (1988)

Numerical Investigation of Wave Propagation in Layered Media. Part I. Propagation of SH-Waves

G. Brankov, Ts. Ivanov, T. Angelov
Inst. Mech. Biomech., Bulg. Acad. Sci.

The paper studies propagation of SH-waves in elastic, izotropic half-space, consisting of non-parallel layers, and appropriate initial-boundary value problems are solved. The FEM-method is used for a spatial discretization, while Wilson's method is employed for time discretization. The main difficulty here is that the whole space can not be dissreticized by means of finite elements. This implies an analysis in a finite region, whereas the boundary conditions at the additional boundary are to be such that no wave reflection would occur back into the region. Various types of boundary conditions are analysed in detail, the latter compensating the reduction of the half-space into a finite region. Displacement diagrammes of surface points are obtained, which can be compared with the results obtained by employing other approaches or experimental data. All results are obtained by using the SH-computer programme complex.

JTAM, Sofia, vol. 19 Issue 4 pp. 032-041 (1988), [Full Article]

Solution of Gravimetrical Problems for Homogeneous, One-Connected Solids Obtained by Employing of Analogue Display Device

Ir. Lukarska
Inst. Nucl. Research and Nucl. Techn., Sofia

The paper proposes a method for solving real gravimetric problems, as well as a model approach to the inverse problem of the potential theory. An analog electronic device is employed for that purpose. Sufficient accuracy is attained and the results verify the method effectiveness.

JTAM, Sofia, vol. 19 Issue 4 pp. 042-047 (1988)

Asymptotic Investigation of the Instability of a Liquid Compound Jet

V. Epihin1, S. Radev2, V. Shkadov1
1Lomonosov Moscow State University, Moscow, USSR
2Institute of Mechanics and Biomechanics, Bulgarian Academy of Sciences, Sofia

Dispersion equation for the amplification rate of small disturbances in the irrotational flow of an axisymmetric compound jet is obtained for the case when the core and coaxial layer are moving with a uniform but different velocities. It is shown that in the longwave region this equation can be simplified to the equation arising from the one-dimensional equations of motion of the jet. In the shortwave region the instability is controlled by the capillary instability of the core and the instability of Kelvin-Helmholtz type, connected with the discontinuity of the jet undisturbed velocity profile.

JTAM, Sofia, vol. 19 Issue 4 pp. 048-057 (1988)

Numerical Analysis of the Hydrodynamic Interaction and Convective Mass Transfer between Two Spherical Particles Submerged into a Viscous Flow

E. Toshev, Z. Zapryanov
Inst. Mech. Biomech., Sofia

The authors analyse the problem of hydrodynamic interaction and mass transfer occurring during the outflow of two spherical particles by a viscous fluid. The Navier-Stokes equations and the equations of convective diffusion are solved by employing a numerical method. Steady axisymmetric proplems are solved. Regarding the hydrodynamic problem, it is supposed that the particles are submerged into a flow, uniform at infinity. As for the concentration problem, it is assumed that a model 1-st order chemical reaction takes place upon the spheres. A number of numerical experiments are performed, varying Reynolds and Bio numbers. Resistance, acting upon the spheres, is obtained, showing good agreement with other numerical results and experimental data.

JTAM, Sofia, vol. 19 Issue 4 pp. 058-066 (1988)

Radiation Heat Exchange during Drawing of Optical Fibres

P. Gospodinov
Inst. Mech. Biomech., Sofia

Heat exchange in the furnace-product system is studied, when optical fibres are drawn from a cylindrical preform. The radiation energy transfer is considered, whereas shadowing, autoradiation and furnace diffusion reflection is taken into account. The results can be used when modelling drawing of microcapillaries from glass tubes.

JTAM, Sofia, vol. 19 Issue 4 pp. 067-073 (1988)

The Influence of Nonlinear Mass Transfer on the Laminar Boundary Layer

N. Vulchanov1, Chr. Boyadjiev2
1High. Inst. Chem. Eng., Sofia
2Inst. Chem. Eng., Bulg. Acad. Sci., Sofia

The dependence of the normal velocity of a laminar bondary layer flow at the solid-fluid boundary on the intensive mass transfer at the boundary for different Schmidt numbers is studied. The original boundary value problem for forced convection boundary layer flow is transformed via similarity of the variables into a two-point boundary value problem for a system of ordinary differential equations and the latter is integrated numerically. Computed results are reported and discussed.

JTAM, Sofia, vol. 19 Issue 4 pp. 074-078 (1988), [Full Article]

Determination of the Dynamic Coefficient during Impulsive Loading, the Latter Stopped before Attaining the Maximum Deformation

M. Zefirov, Ya. Stoilov
High. Inst. Arch. Civ. Eng., Sofia

The dynamic analysis of structures needs the determination of the dynamic function and its extremum value the dynamic coefficient. The present paper takes into account bending and shear stresses together, in order to understand properly the structure's real behaviour. The method proposed here for the determination of the dynamic coefficient is valid when the impulse load acts till attaining maximum elastic deformations. The authors' approach is verified by a numerical analysis. Proper conclusions are made.

JTAM, Sofia, vol. 19 Issue 4 pp. 079-084 (1988)

Plastic Localization Bands at Nonhomogeneous Plain Strain and Coupled Thermoplastic Processes

N. Boncheva, A. Baltov, St. Todorov, M. Pesheva
Inst. Mech. Biomech., Sofia

Bifurcation conditions in bands of plastic localization are derived under plain starin and for plastically hardening materials. The latter, however, are sensitive to strain rate and their yield limit depends on temperature. Heat, produced owing to plastic deformation, is taken into account as well. The ideal case is considered, where the localization band is reduced to a localization line, and jump conditions on the latter are derived.

JTAM, Sofia, vol. 19 Issue 4 pp. 085-094 (1988), [Full Article]

Application of BEM for Solving the Contact Problem

E. Ganchev
High. Inst. Mech. Electr. Eng., Sofia

The author proposes a method for solving the contact problem, where the surface of the contact region and the load distribution there is sought. However, the system geometry, points where load is applied, value of the distance between body centres after load is applied and the body elastic properties are given. The method is built on the basis of the indirect BEM version and bodies are taken to be ideally rigid. It is assumed that the distance between body centres, before applying the load, is empiricaily determined in advance. An algorithm is developed for the practical realization of the proposed approach. The difficulties that are to be overcome during the computer-aided realization of the method, are outlined.

JTAM, Sofia, vol. 19 Issue 4 pp. 095-100 (1988)

Analysis of the Coupled Electro-elastic Field in Piezo-electric Materials

D. Kolarov, K. Lilova
Inst. Mech. Biomech., Sofia

The development of modern piezo-technique requires the solution of dynamic problems' involving piezo-elements with a complex geometry and spatial-time distribution of the initial and boundary conditions. Such problems are usually solved by employing numerical methods or by simplifying both the physical and mathematical models. This paper presents D. Kolarov's analytical-numerical method for solving the linear dynamic problem of piezoelectricity in spatial formulation. The dynamic behaviour of a piezo ceramic plate, polarized through its thickness, is studied. The initial and the complex boundary conditions at both surfaces are satisfied analytically. The additional boundary conditions at the side contour are satisfied either by development into power, or trigonometric series, or numerically (by discretization) Hence, it is very convenient to use computing algorithms or programmes.

JTAM, Sofia, vol. 19 Issue 4 pp. 101-116 (1988)

On the Note by C. I. Christov Concerning the Solution of the Stokes' Problem for a Circullar Cylinder

K. Shulev
High. Inst. Arch. Civ. Eng., Sofia

JTAM, Sofia, vol. 19 Issue 4 pp. 117-118 (1988)

On the Remark by M.M. Konstantinov Concerning the Solution of the Stokes' Problem for Circuilar Cylinder

K. Shulev
High. Inst. Arch. Civ. Eng., Sofia

JTAM, Sofia, vol. 19 Issue 4 pp. 119-119 (1988), [Full Article]

On the Incorrectness of a Mathematical Proof about Unsolvability of the Stokes' Paradox

K. Shulev
High. Inst. Arch. Civ. Eng., Sofia

JTAM, Sofia, vol. 19 Issue 4 pp. 119-121 (1988), [Full Article]