Issue 2

JTAM, Sofia, vol. 16 Issue 2 (1985)

Bi-Frequency Asymptotic Solutions of an Autonomous System in the Case of Resonance of Arbitrary Rank

B. Cheshankov, M. Slavkova
High. Inst. Mech. Electr. Eng., Darvenitsa

The solutions of an autonomous system in the case of resonance of arbitrary rank are considered. Rank of resonance is the number which shows the power of the resonant terms in the equations of motion. Canonical systems which describe wholy the resonant solutions are obtained. A qualitative investigation for some concrete canonical systems is performed. The study of the systems in the phase plane permits a comprehensive idea to be obtained with regard to all possible resonant solutions.

JTAM, Sofia, vol. 16 Issue 2 pp. 011-026 (1985), [Full Article]

On the Optimization Synthesis of the Arrow Four-bar Linkage of a Gantry Crane by Using the Method of Nonlinear Programming

S. Stoikov, K. Enchev, V. Pirgosliev
High. Techn. Sch. "A. Kanchev", Russe

The author has designed a method for the optimization synthesis of the trajectory of the crane point to which the load is attached. However, the point trajectory approximates the horisontal straight line. The method accounts for the mechanism structure characteristics that provide suitable trajectory and effective design of the mechanism itself. An example is given where the method is applied to the improvement of the structure of an actual mechanism.

JTAM, Sofia, vol. 16 Issue 2 pp. 027-033 (1985)

Proof of Coiter's Problem for the Second Variation in the Theory of Elasticity

Ts. Ivanov
Inst. Mech. Biomech., Bulg. Acad. Sci., Bl 8

What is considered is an elastic body which is in equilibrium owing to the action of conservative external loading. It is supposed that the potential energy functional might be expressed as a sum of homogeneous functionals of various crdcrs. What is proved as a next step is that if the second-order functional in the relation for the potential energy is positively definite and the rest of the funetionals remain regular, then the body equilibrium state is stable.

JTAM, Sofia, vol. 16 Issue 2 pp. 034-038 (1985), [Full Article]

Statistical Models Describing the Rheology Behaviour of Metals and Alloys

T. Balevski
Inst. Met. Res. Techn.. Geo Milev

Two statistical mechano-mathematical models are designed to describe the visco-elasto-plastic behaviour of real deformable media. However the models consist of an infinite number of parallel-bonded Maxwell's or Bienheim's elements. Involving the model structure-equations, the author performs an analysis of processes of deformation with constant strain rates, as well as stress relaxation for a constant total deformation.

JTAM, Sofia, vol. 16 Issue 2 pp. 039-044 (1985)

Aggregation in Problems of Nonlinear Creep by Using the

Yu. Samarin, Yu. Eremin
Kuybishevski Politehnicheski Institut, USSR

The investigation of creep in structures is performed by employing the "black box" principle, popular in cybernetics. Such an approach might be treated a sa physical hypothesis which is the basis for the design of determining relations that enable to treat a complex structure as a system of separate units. This, however, provides a comparatively simple multidegree schematization of the structure, when solving problems of nonlinear creep of structures that undergo unsteady loading.

JTAM, Sofia, vol. 16 Issue 2 pp. 045-054 (1985)

Computation of Stabilized Turbulent Fluid Flow and Heat Transfer in Circular Smooth Pipes for Moderate Prandtl Numbers. Part I – Fluid Flow and Eddy Diffusivity

M. Mihaylov, N. Valchanov, V. Zimparov
High. Inst. Chem. Eng., Darvenitsa

The authors develop a model that is based on models already published. Moreover, they propose an algorithm to calculate the velocity field and eddy diffusivity, regarding flow of an incompressible liquid in smooth and circular pipe. However, flow is hydrodynamic and fully developed and moderate Prandtl numbers are considered. The model reliability is proved by comparing the calculated values of Fanning's resistance coefficient to experimental data and correlations that have been published in advance.

JTAM, Sofia, vol. 16 Issue 2 pp. 055-059 (1985), [Full Article]

On the Mathematical Modelling of the Unsteady Plane Seepage Flow in Inhomogeneous Multilayered Systems

G. Simeonov
Inst. Mech. Biomech., Bulg. Acad. Sci., Bl. 8

To model the above natural seepage systems, the author employs Girinskiy-Myatiev-Jacob's hypothesis. Supposing that the seepage flow regime in semipervious layers is elastic, formulas that express fluxes through semipervious layers by means of the hydraulic heads in adjacent leaky aquifiers are derived. However, the method of boundary integral identities is einploved for that purpose. Thus a system of integro-differential equations for the piezometric heads is obtained to model seepage through permeable strata. Explicit exnressions for kernels of the integral terms are found that hold for large and small values of time. A simple interpretation of these terms is made. The integro-differential equations that have been obtained are suitable for the economical numerical modelling of the systems into consideration.

JTAM, Sofia, vol. 16 Issue 2 pp. 060-071 (1985)

On the Minimal Density of Irrigation of a Two-Layered Liquid Film Flowing Down a Vertical Wall

H. Karagyozov, I. Parvez
High. Inst. Chem. Eng., Burgas

The authors attempt to calculate the minimum density of irrigation of a two-layered liquid film. However, the film flow is laminar. A system of two equations is obtained on the basis of the criterion for balance of surface and inertial forces. The equations allow for the calculation of both the minimum thickness and irrigation density of the internal and the external film.

JTAM, Sofia, vol. 16 Issue 2 pp. 072-075 (1985)

Investigation of the Field of Application of Some Models of Elastically Deforming Robot Elements

A. Baltov, Y. Ivanova, S. Todorov
Inst. Mech. Biomech., Bulg. Acad. Sci., Bl. 8

The authors analyse the problem of selecting a suitable model to satisfy the accuracy demands when investigating structure elements undergoing dynamical impacts. A typical structure element – clamped beam, is considered for reasons of concreteness. What is introduced is a "rational model", which is to satisfy the accuracy demands and is at the same time the simplest one from a set of models that describe the element behaviour by accounting for the elastic deformaticns. The paper analyses the range of model validity, when varying both geometry and mechanical characteristics. However, ranges of applicability are determined with respect to the model effectiveness. The investigation provides prospects and calculation procedure to select a suitable model, which until now has been done by intuition.

JTAM, Sofia, vol. 16 Issue 2 pp. 076-083 (1985)

Plane Steady State Flow of the Lubricant in Elasto-Hydrodynamical Bearings Regarding Inertia Forces

V. Alexandrov
High. Inst. Arch. Civ. Eng., 1 Hr. Smirnenski blvd.

The author presents a solution of the steady, isometric and contact-hydrodynamical problem. The lubricant is considered to be Newtonian fluid. The original differential equations of the plane lubricant flow account for the inertial members as well. What is obtained after their substitution for values, averaged through the lubricant layer thickness, is Prandtl's systems of equations which is reduced to a single first-order ordinary differential equation. The latter is solved numerically by employing the Runge-Kutta method. The curves obtained reflect the effect of both the lubricant velocity (the Reynolds number) and the deformations of the rubbing surfaces on the distribution of the hydrodynamical pressure within the lubricant layer.

JTAM, Sofia, vol. 16 Issue 2 pp. 084-090 (1985)

A Fracture Criterion for Anisotropic Hardening Materials

N. Boncheva, R. Yankov, A. Baltov
Inst. Mech. Biomech., Bulg. Acad. Sci., Bl. 8

The authors propose an energetical fracture criterion for anisotropically hardening materials. What is achieved is the capability to predict the change of the angle of the crack propagation, as related to the existance of preliminary plastic deformations. Good agreement with experimental data is obtained.

JTAM, Sofia, vol. 16 Issue 2 pp. 091-097 (1985), [Full Article]