Issue 2
JTAM, Sofia, vol. 22 Issue 2 (1991)

Theory of Lyapunov's Characteristic Exponents for Impulsive Differential Systems II. Inequalities of Wazewski and Lyapunov for Impulsive Systems. Reducible Systems

P. Simeonov1, D. Bainov2
1Higher Military School, Pleven
2University


In relation to the theory of Lyapunov's characteristic exponents for differential impulse systems analogues with the inequalities of Wazewski and Lyapunov are found in the present paper. Necessary and sufficient conditions are also found to reduce such systems.

JTAM, Sofia, vol. 22 Issue 2 pp. 009-013 (1991), [Full Article]

Poincare's Initial Conditions in Dynamics of Walk Phase for Space Model of Legged Locomotion Robot. A Case of Internal and External Resonance

M. Peikova
Technical University, Sofia

The dynamics of an antropomorph robot model in the walk phase has been studied in the present paper. Certain conditions have been called initial value conditions, which are assumed to be satisfied. They define some relations between the initial values of the generalized coordinates and the generalized velocities. Two cases are possible in studying periodic solutions: a nonresonance case and a resonance one (the resonance is external or it is internal and external simultaneously). In both these eases the initial value conditions are obtained in different ways. The method of Poincare's small parameter is one of the methods to determine these conditions. The application of this method to the case of an internal and an external resonance has been shown in the paper.

JTAM, Sofia, vol. 22 Issue 2 pp. 014-021 (1991), [Full Article]

On Planar Oscillations of Gyrostat on Elliptic Orbit

O. Hristov
Technical University, Russe

The equation of gyrostat planar oscillations on an elliptic orbit has been obtained. The stability of these oscillations has been studied in some cases.

JTAM, Sofia, vol. 22 Issue 2 pp. 022-028 (1991), [Full Article]

Solution Ways of a Classical FSI Problem

V. Dzhupanov, A. Gancheva
Institute of Mechanics and Biomechanics, Bulg. Acad. Sci., Sofia

The article is a first methodical step in clarifying some complicated cases of interaction between a fluid and the elastic walls of a channel (FSI = fluid-structure interaction). The hydroelastic system (HES) under consideration consists of a vibrating elastic wall and an ideal, compressible and heavy liquid. The rest of the walls have been assumed to be absolutely stiff. The liquid is flowing in the channel with a velocity which is much smaller than that of the sound, so the problem becomes planar. Different kinds of loading on the elastic wall have been considered in details. Before discussing the way to determine the proper frequency spectrum of the HES, the free vibrations of the HES-components have been considered. The advantages of the different solution ways have been emphasized.

JTAM, Sofia, vol. 22 Issue 2 pp. 029-037 (1991), [Full Article]

Delaminafion of Multilayered Plates in Bending under Monotone Boundary and Non-monotone Interlayer Conditions. A Variational-Hemivariational Inequality Approach

G. Stavroulakis, P. Panagiotopoulos
Aristotle University, 54006 Thessaloniki, Greece

Delamination effects arising in multilayered plates in bending under general boundary conditions are studied herein. Delamination is modelled by means of complete, nonmonotone phenomenological, binding constitutive laws, which give rise to hemivariational inequality problems through the generalized gradient operator in the sense of Clarke applied on appropriately defined nonconvex superpotentials. Boundary conditions (or monotone interlayer phenomena) are general monotone, multivalued laws, which give rise to variational inequality problems through the subdifferential operator of convex analysis applied on appropriate convex superpotentials in the sense of Moreau. The variational-hemivariational inequality problem is written here and existence and approximation results are given.

JTAM, Sofia, vol. 22 Issue 2 pp. 038-046 (1991), [Full Article]

A Direct Derivation of Dual Extremum Principles in Dynamic Anisotropic Coupled Thermoelasticity

A. Liolios
Democritus University of Thrace, 67100 Xanthi, Greece

Dual extremum principles are derived in a direct way for the initial boundary-value problem of fully coupled linear anisotropic dynamic thermoelasticity. This derivation is based on the Laplace transform, the Hypercircle method and the use of special weight functions to get back to the original time-domain. The dual principles assure the existence and uniqueness of the solution and provide a global measure of the error involved in numerical approximations.

JTAM, Sofia, vol. 22 Issue 2 pp. 047-054 (1991), [Full Article]

The Collective Effect in Disperse Systems – an Approach Based on the Renormalization Group Technique

A. Yarin
Institute of Mechanics Problems, 117526 Moscow, USSR

In the present paper consideration is given to the problem of the value of hydrodynamic drag on an individual spherical particle in a system of similar particles in an un-bounded fluid flow.

JTAM, Sofia, vol. 22 Issue 2 pp. 055-060 (1991), [Full Article]

Influence of Heat of Absorption on Thermocapillary Instability in a Thin Liquid Layer

V. Naidenov, S. Slavchev
Institute of Mechanics and Biomechanics, Bulg. Acad. Sci., Sofia

The stationary capillary instability of a horizontal liquid layer with a free surface at a non-isothermal gas absorption is studied. In this case the thermal flux due to the heat of absorption is proportional to the mass flux at the interface. The born capillary force causes instability of the equilibrium state of the gas-liquid system. In case of heating from above this contradicts the well-known fact that the layer is always stable. The unexpected result is explained by another mechanism for perturbation amplifying. The critical values of the Marangoni number depend strongly on the Lewis number.

JTAM, Sofia, vol. 22 Issue 2 pp. 061-068 (1991), [Full Article]

Tensions and Deformations in Circular Fillet Welding

M. Grois1, L. Dimitrov2
1VUT, Brno, Czechoslovakia
2Technical University, Sofia

The aim of this theoretical research is to determine the tensions in the weld and the deformations in the surface layer of a circular fillet welding. The typical simplifications and assumptions for similar cases have not been made in the consideration of the question. The theoretical prerequisite of the given thesis is the appearing of spatial tensions in the fillet welding which lead to a surface change of the shape of the longitudinal link fibres: It is suggested to look for the solution by a tension determination at the welding characteristic points.

JTAM, Sofia, vol. 22 Issue 2 pp. 069-072 (1991), [Full Article]

On the Optimal Control of the Oriented Plastic Forming Process of Perfectly Plastic Plates

A. Baltov, I. Trendafilova
Institute of Mechanics and Biomechanics, Bulg. Acad. Sci., Sofia

Considered is the plastic forming process of a thin plate that has been made of perfectly plastic material by an absolutely solid and spherical instrument. The aim is to obtain a spherical shell with given dimensions. The optimal control of the forming process problem has been solved in the paper. The criterion function is the consumed deformation energy while the control one is the motion velocity of the spherical instrument. The Robbins-Monro algorithm for stochastic approximation has been used to solve the problem. Some examples and results have been considered.

JTAM, Sofia, vol. 22 Issue 2 pp. 073-080 (1991), [Full Article]

A Static Strength Criterion

T. Balevski, D. Ruskov, V. Venkov
Institute for Metal Science and Technology, Bulg. Acad. Sci., Sofia

A strength criterion has been suggested to describe the influence of the first and the second main stresses on the fracture break. The criterion is linear with respect to the stresses and shows a good agreement to the experimental data which reflect the fracture behaviour of a wide material range in two-dimensional stress states.

JTAM, Sofia, vol. 22 Issue 2 pp. 081-090 (1991), [Full Article]

A Contribution to the Analysis of the Cor¬ner Cracking Problem in Masonry Veneer Walls by Means of the Theory of Hemivariational Inequalities

C. Baniotopoulos
Aristotle University, 54006 Thessaloniki, Greece

The present paper deals with the study of the corner cracking problem in brick masonry veneer walls within the framework of the theory of hemivariational inequalities.

JTAM, Sofia, vol. 22 Issue 2 pp. 092-101 (1991), [Full Article]

Static Analysis of Cracked Masonry Walls by Means of the Phenomenological Interface Concept

G. Stavroulakis
Aristotle University, 54006 Thessaloniki, Greece

Methods for the static analysis of cracked masonry walls are presented here which assumes that all nonlinear, strength degradation phenomena are phenomenologically summed up along predefined interfaces in the structure. Monotone and nonmonotone, possibly multivalued laws are introduced to model the mechanical behaviour along the normal and the tangential direction of each interface. Variational and hemivariational inequality formulation of the problem is derived by means of appropriate superpotentials and methods for the numerical solution of the problems are discussed. Coupling between normal and tangential to the interface mechanisms is also considered. Numerical examples illustrate some of the proposed algorithms.

JTAM, Sofia, vol. 22 Issue 2 pp. 102-113 (1991), [Full Article]

European Mechanics Colloquium No 278 "Microstructure and Effective Properties of Random Particulate Solids"

K.Z. Markov

JTAM, Sofia, vol. 22 Issue 2 pp. 114-115 (1991), [Full Article]