Volume 29 Number 1 1999

**CONTENTS**

**K. Istev, A. Ianakiev,
F. Filipov.**

*K. Istev*
*Faculty of Automation,
Technical University of Sofia,*
* 8, St.Kl.Ohridski
Str., 1000 Sofia, Bulgaria*
*e-mail: kish@vmei.acad.bg*
*A.Ianakiev*
*Faculty of Mechanical
Engineering, Technical University of Sofia,*
*8, St.Kl.Ohridski Str.,
1000 Sofia, Bulgaria*
*F. Filipov*
*Central Laboratory for
Seismic Mechanics and Earthquake Engineering,*
*Bulgarian Academy of
Science,*
*Acad. G. Bonchev Str.,
Bl. 4, 1113 Sofia, Bulgaria*

Application of Condensation Techniques for Modelling of a Group of Mechanical Systems

Abstract. The current trend
to analyze more and more complex finite element models of mechanical systems
increases the size of the corresponding matrices, which impose obstacles
for synthesis and simulation of control. The paper presents a possible
approach to overcome the problem by employing models based on transfer
functions between the Laplace operators of the signals at specified points
and the inputs. Apart from being more compact the transfer functions in
these models provide an easy approach for reduction of the models, keeping
at the same time the necessary level of accuracy for the required frequency
range. The introduction and eventually the correction of the damping is
a simple task in the above models.

*Technical University of Sofia,*
*8, St.Kl.Ohridski Str., 1000 Sofia, Bulgaria*

Synthesis of Open Kinematics Chains for Robot Mechanisms by Using Relative Conditions for Position Input-Output Synchronization, Part 2 - Models Based on System of Vectorial-Matrix Equations

Abstract. The generalized
mathematical model for dimensional synthesis of open kinematics chains
for specialized robots in this part is built on the base of vectorial-matrix
equations. The synthesis of such a chain is performed using the same relative
conditions for synchronization of the finite linear and angular displacements
of the output link with the finite relative rotations of its links, as
shown in part one of the paper. A computer programme, incorporating the
two types of generalized mathematical models discussed, is used for the
design of the open kinematics chain of the GRIPMAT specialized robot. This
robot is used for serving of horizontal presses for casting under pressure.
The two types of generalized models are compared and analysed with respect
to linearity and non-linearity.

*Technical University of Sofia,*
*8, St.Kl.Ohridski Str., 1000 Sofia, Bulgaria*

An Investigation of the Dynamic Loads in a Two-Stage Spur Gear Machine Aggregate - Part II

Abstract. A model of a two-stage
spur gear machine aggregate with 12 degree of freedom is treated. The influence
of the gear meshing parameters: the elasticity of the meshing, period of
the meshing, gear modulus number of teeth, gear wheels width and the distribution
of the gear ratio on the dynamic loads in shafts, bearings and meshings
is investigated in a wide frequency area, as well as the impact forces
in teeth at beginning of contact out of the theoretical meshing line.A
model of a two-stage spur gear machine aggregate with 12 degree of freedom
is treated in this paper. The model, the differential equations, parameters
nomenclature and constant values of the parameters are the same as in part
I. The aim is investigation of the following gear meshing parameters: the
elasticity and period of meshing and the distribution of gear ratio upon
dynamic loads in a two-stage spur gear machine aggregate.

*A.M'chirgui, L.Tadrist*
*Institut Universitaire
des systemes Thermiques Industriels*
*(IUSTI),CNRS - UMR 6595
Technopole de Chateau Gombert,*
*13453 Marseille
Cedex 13 France*
*St.Radev*
*Institute of Mechanics,
Bulgarian Academy of Sciences,*
*Acad. G. Bonchev Str.,
Bl. 4, 1113 Sofia, Bulgaria*

Particle Size Distribution Effect on a Solid Carryover of Particles in a Fluidized Bed

Abstract. The effect of particle size distribution (PSD) on the carryover of solid phase from a gaz-solid fluidized bed has been investigated. Solid entrainment rate and carried solids size measurements have been performed. The variation laws of the solids entrainment rate and the mean diameter of the entrained solids with the gas velocity were found to depend strongly on the breadth of the PSD. The wider the PSD function of fluidized material, the more progressive the transition from weak to sharp removal of solids. An analytic approach based on the single particle model has been developed. This approach gives formula to predict the PSD of the entrained solids in a reasonable agreement with experiments.

Key words: solid carryover,
particle size distribution, breadth of the distribution, transition zone,
fluidized bed.

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

On the Numerical Modelling of the Venus Planetosphere/Mantle

Abstract. A scheme for modelling
the interaction of solar wind with nonmagnetic planet is proposed. The
creation of the ionized gas, forming the planetosphere, is supposed to
be only due to the ionization processes in the existing neutral exosphere
of the planet. A self - consistent consideration of the planetosheath and
the planetopause (planetosheth boundary) is performed in gasdynamic approach,
supposing decoupling of the MHD system of equations. Mass- loading process
in both regions is taken into account. The pressure balance is establishing
the shape and position of the planetopause, determined in the solution.
A grid characteristic numerical scheme is applied. The results are demonstrating
quite satisfactory coincidence with some Pioneer Venus Orbiter measurements
around Venus. Modelling of the solar wind interaction with nonmagnetic
planets chronologically follows the ideas, arising in considering in the
literature the analogical problem for the magnetic planets.

*Department of Applied
Mechanics,*
*University of Chemical
Technology and Metallurgy*
*8, St.Kl. Ohridski Str.,
1756 Sofia, Bulgaria*
*e-mail veso@uctm.edu*

Mechanical Behaviour of Amorphous Materials on the Basis of a Micro-Structural Mode

Abstract. To model the transition micro-macro for the case of amorphous materials, the present article proposes a procedure for computer simulation of the mechanical material behaviour based on a simplified micro-structural model. The main idea of the model proposed is to substitute the discrete structural unit for a modelling homogeneous triangular finite element having equivalent mechanical behaviour. To further simplify the problem, we construct the model in a pseudo three-dimensional domain, based on the hypothesis that a qualitative insight of the stress-strain state of the representative bulk of material can be obtained by analyzing a finite number of plane sections. The simplified geometrical micro-structural model can be considered as composed of two types of finite elements: triangular, modelling the structural units; and triangular or quadrilateral, modelling the stiffness of the rings formed by bonding the structural units. The stiffness matrix of the elements is derived from a radial-symmetric potential of the central forces of the Lenard-Johnes type. The following summary of a stress distribution analysis for tension and shear within the micro-structure of the pilot material is to demonstrate how the procedure for computer simulation of the material mechanical behaviour at micro level works. The values obtained have been compared with those obtained by other methods.

Key words: mechanics of materials,
computer simulation, structural modelling.

*University of Architecture,
Civil Engineering and Geodesy,*
*1, Hr. Smirnenski Str.,
1421 Sofia, Bulgaria*

On the Application of a New Mixed Finite Element Model to In-Plane Problems

Abstract. The present paper
has a practical purpose and seeks to show some of possibilities of one
new mixed model in the finite element method to in-plane problem in the
theory of elasticity. Bilinear approximating functions for description
of the fields of the stresses and displacements, spread over the whole
area of the finite element, are proposed. The new model is applied for
an in-plane problem (wall beam) with non-symmetrical holes. The results
obtained are compared with those obtained by the program SAP'90 and a frame
model representing the plane problem as a frame construction.

*Institute of Engineering
Cybernetics of Academy*
*of Sciences of Belarus*
*6, Surganov Str., Minsk,
Belarus, 220012*

Wave Mechanisms Using Biomechanical Principles of Locomotion of Some Terrestrial Animals

Abstract. Investigations
of transport capability of travelling deformation waves on elongated deformable
bodies have led to new explanations of some methods of locomotion of such
a living creature as a caterpillar, an earthworm, a terrestrial snake.
This enables to create new engineering mechanisms and instruments using
these biomechanical wave methods of locomotion. The information about the
new linear wave mechanisms and transport devices without driving wheels
is given. The kinematic analysis of the travelling deformation waves running
along an elongate deformable body (a flexible filament) is also given.

**Acad. Alexander Nikolaevich
Guz (On an occasion of his 60 birth day)**

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