Journal of Theoretical and Applied Mechanics

Volume 31, Number 4, 2001

 

Contents

T. Gichev

 

University of Architecture Civil Engineering and Geodesy,

1, Smirnenski Str., 1421 Sofia, Bulgaria

 

 

Processes with an Instantaneous Change of the Mass

 

Abstract. The work analyses instantaneous processes caused by the step-wise change of the mass. These instantaneous processes are studied with the help of approximating sequences of processes in intervals with length t when t 0. In each of these processes the mass changes continuously. A problem for determining the state of the basic quantities in the end of the instantaneous process is solved. The solution of this problem gives the initial conditions of the process immediately following the instantaneous process. The work considers processes described by ordinary differential equations and by hyperbolic partial differential equations.

 

 

Key words: instantaneous processes, change of mass.

 

S. Miladinova, D. Staykova

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G.Bonchev Str., Bl., 4, 1113 Sofia, Bulgaria,

e-mail: svetla@imbm.bas.bg

 

CONVECTIVE NATURE OF INSTABILITY IN NON-UNIFORMLY HEATED FALLING FILMS

Abstract. A non-uniformly heated falling film, which is susceptible to surface-wave and thermocapillary instabilities, is considered. The nature of both instabilities is studied regarding the absolute/convective instability criteria. The flat-film basic state with parabolic velocity profile is considered. An infinitesimal small localized perturbation of this state is imposed. The disturbance grows when the plate temperature increases downstream and decays when the plate temperature decreases. The speed of the most unstable mode decreases with the Marangoni number. It is shown that the instability is convective for thin weakly heated layers with relatively

large surface tension.

 

Key words: falling film, free-surface instability, thermocapillarity.

 

S. D. Iliev

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria,

e-mail: stani@bgcict.acad.bg

 

NUMERICAL INVESTIGATION OF THE STATIC LIQUID DROPS

ON HORIZONTAL HETEROGENEOUS SOLID SURFACE.

Part I: WITH RADIAL PATCHES

Abstract. A numerical investigation of the equilibrium state of the liquid drop, located on the smooth horizontal solid plane, is proposed. Our study considers the case in which the solid surface consists of the set of radial homogenous patches. We consider several types of non-homogeneity of radial patches. We assume at first that the contact angle varies sinusoidally with respect to j . Secondly we tackle the more realistic case when the contact angle in each radial patch has a random quantity.

 

 

Key words: liquid drops, contact line.

 

 

M. N. Koleva, Ch. D. Betchev

University of Chemical Technology and Metallurgy,

8, Kl.Ohridski Blvd, 1756 Sofia, Bulgaria

VISCOSIMETRIC INVESTIGATION OF UNSATURATED POLYESTER RESIN - HIGH IMPACT POLYSTYRENE BLENDS

Abstract. The influence of temperature and concentration on the viscosity of systems, based on an unsaturated polyester resin and a high impact polystyrene, are studied. The viscosity shows slightly negative deviating from an additivity because of a phase separation between systems, based on the resin and high impact polystyrene. The energy of activation of a flow as a function of polymer additive concentration is calculated. The temperature-invariant characteristics at various contents of the polymer additives are obtained.

 

Key words: polyester resin, rheology, temperature invariant characteristics.

 

Ts. Leontieva, Ch. Kouyumdjiev

University of Rousse “Angel Kanchev”,

8, Studenska Str, 7017 Rousse, Bulgaria,

e-mail: tsetsi@mech.ru.acad.bg

 

Determination of stress in multilayer coatings with rheological processes in them

Abstract. An algorithm of determining of stress-strain state in a multilayer coating by the bending strip method is proposed in the present work. It is supposed that during deposition and post deposition period some rheological processes in coating occur thus causing different creep changes in the different coating layers. A numerical example with real experimental data is considered about determining the stress in electrolytic coating deposited onto a strip substrate.

 

 

Key words: stress and strain in coatings, stress relaxation, multilayer coatings.

 

 

T. Penchev, I. Altaparmakov

 

Technical University of Sofia,

8, St. Kl. Ohridski Blvd., 1756 Sofia, Bulgaria,

e-mail: tpenchev@vmei.acad.bg

 

MODELLING OF GRAIN SHAPE IN COLD PLASTIC FORMING THROUGH THE FINITE ELEMENT METHOD.

PART II: THEORETICAL MODEL APPLICATION RESULTS

Abstract. Special features of the algorithm for application of the mathematical model for grain shape simulation, in the process of cold plastic deformation, are presented in this paper. Based on this algorithm a program for modelling single-phase material structures has been compiled as a subroutine to ANSYS FEM code. During various cold forming operations the microstructure modelling is done, and the results are compared with the microstructure of cold forged parts.

 

 

Key words: cold forming, grain shape, finite element, modelling.

 

 

V. Al. Dzhupanov

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria,

e-mail: dzhupan@imbm.bas.bg

 

TWelve METHODICAL NOTES ON THE Paradoxical results in a class of dynamical problems

(Part 2)

Abstract. The dynamics of a complicated mechanical system consisting of three components, namely: (i) cantilevered pipe, (ii) flowing fluid conveyed, and (iii) a linearly elastic resisting foundation is under methodical and consequent analytical investigation. In the first part 8 methodical notes were described. They prepared the understanding of the last 4 notes. However, here the concept of “critical combination of subcritical parameters” is formulated and discussed. Using the known (from the Hydroelasticity) concept of the added liquid mass, the concept of the joined rigidity (added stiffness) due to the dynamic structure-foundation interaction is introduced. By using the latter, as well as by using the concept of the local and global stability of the pipe, the dependence of the critical follower force on the stiffness of the resisting medium is proved. This contrasts to some paradoxical results for the problem on the dynamic stability of the Dzhanelidzes column supported by elastic foundation (considered in the text of Part 1).

 

 

Key words: Cantilevered pipe; fluid conveyed, resisting medium (foundation), added mass; added stiffness; local stability; global stability, critical velocities.

 

P. A. Djondjorov

Institute of Mechanics, Bulgarian Academy of Sciences,Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria,

e-mail: padjon@imbm.bas.bg

ON THE CRITICAL VELOCITIES OF PIPES ON VARIABLE ELASTIC FOUNDATIONSAbstract. The dynamic stability of straight cantilevered pipes on variable elastic foundation is studied. The rigidity of the foundation is assumed to be a linear function of the co-ordinate along the pipe axis. The aim is to analyze the influence of such elastic foundations on the critical flow velocities of the pipes under consideration and to draw conclusions about the stabilizing properties of various elastic foundations of the type considered. This problem is approached numerically using the Galerkin method. It is established that foundations that are weak at the free end and rigid at the other end have less stabilizing effect in comparison with foundations that are rigid at the free end and weak at the fixed end of the pipe.

 

Key words: pipe, variable elastic foundation, critical flow velocity, dynamic stability, Galerkin method