Issue 3
JTAM, Sofia, vol. 24 Issue 3 (1993)

Some Numerical Methods of Linear Design: Time Invariant Cases

V. Larin1, A. Cheremensky2, N. Dakev2
1Institute of Mechanics, Ukrainian Academy of Sciences, Kiev
2Institute of Mechanics, Bulgarian Academy of Sciences, Sofia


A linear affine manifold approach is opposed versus the Riccati equation method and the Youla parametrization one in order to take into account the interaction of internal and external uncertainty and to solve design problems in the cases when classical techniques based on the separation principle are not applied. In the most important time-invariant finite-dimensional case a linear affine manifold can be constructed by the help of very effective procedures of polynomial factoring, rational separation and solving matrix algebraic Riccati equations based on orthogonal projections and matrix sign-function. A high precision computer realization of the corresponding algorithms is created using Turbo C on IBM PCs and close compatibles.

JTAM, Sofia, vol. 24 Issue 3 pp. 017-021 (1993), [Full Article]

Reduce Sensitivity to Local Minima in Optimal Structural Design

V. Iliev
Technical University, Sofia

The reasons for convergence to local minima in Optimal Structural Design Problem are discussed. It is well known that if current design point is in neighbourhood of some minimum, the iterative solution process converges to this minimum. The strategy to hold current design point far from bounds of feasible domain is suggested. Application of this strategy to some examples and results are presented. It is found that strategy reduces sensitivity to local minima in comparison with other works.

JTAM, Sofia, vol. 24 Issue 3 pp. 022-026 (1993), [Full Article]

Dynamic Analysis of Three-Degrees-of-Freedom Parallel Type Manipulators

T. Tanev
Institute of Mechatronics, Bulgarian Academy of Sciences, Sofia

The dynamics of three-degrees-of-freedom parallel manipulators of types 3-RPS and 3-RRS has been discussed in the paper. The equations of motion have been derived using Lagrangian approach. A simulation of dynamics has been developed and examples of computer simulation have been shown.

JTAM, Sofia, vol. 24 Issue 3 pp. 027-035 (1993), [Full Article]

Combinatorial Approach to Plane Figure Modelling

S. Grozdev, N. Sirakov
Institute of Mechanics, Bulgarian Academy of Sciences, Sofia

It is shown in the paper, that three directions are sufficient to describe the boundaries of plane figures. A new approach is proposed to create models of plane convex figures. The approach uses the terms of regularities and consistencies of regularities. Several corollaries in connection with some practical applications are introduced.

JTAM, Sofia, vol. 24 Issue 3 pp. 036-044 (1993), [Full Article]

On Automated Deriving and Solving Differential Equations of Dynamics by REDUCE and FORTRAN

J. Jordanov
Technical University, Gabrovo

The potentialities of the REDUCE system for deriving differential equations of dynamics and writing them in FORTRAN programmes are investigated in this paper. Two methods of approach for designing of these programmes are compared – preliminary analytical solving of the differential equation system (DES) against generalized accelerations ​̈q by the REDUCE system and numerical solving of the DES against ̈q for every current step of integration. An optimal version of automated system which integrates all the stages – from deriving the differential equations to plotting graphics of the transient processes – is proposed.

JTAM, Sofia, vol. 24 Issue 3 pp. 045-052 (1993), [Full Article]

Synthesis of a Mechanical System for Microcomputer Magnetic Tape Storage Device

I. Sarafov, V. Galabov
Technical University, Sofia

This paper presents a scientific aspect of the synthesis of a mechanical system of microcomputer magnetic tape storage device in order to optimize the functions, interaction, dimensions and allocation of the individual mechanisms. A matrix method for the synthesis of linkages is used which reduces the calculation procedures for determination of the main dimensions. Tact diagrams for the three main linkages are composed and the mathematical model for synthesis of a crank-silder mechanism by three given absolute positions of the coupler is deduced. The model is converted for synthesis of a double gilder mechanism. Numerical solutions are obtained for the three mechanisms under definite conditions.

JTAM, Sofia, vol. 24 Issue 3 pp. 053-059 (1993), [Full Article]

On the Synthesis of Skew-Axes Gears with Plane Region of Mesh

V. Abadjiev, D. Petrova
Institute of Mechanics, Bulgarian Academy of Sciences, Sofia

What are considered are non-orthogonal gears generated by Olivier's second principle. The plane character of the working tooth surfaces of one of the gears and their preliminary defined position with respect to the axis of this gear determine uniquely the approach to mathematical modelling taking into account the region of mesh characteristics. The conditions for the existence of ordinary nodes and nodes of undercutting in the region of mesh are obtained. The analysis of these occurrences is bound in this type of mathematical modelling.

JTAM, Sofia, vol. 24 Issue 3 pp. 060-066 (1993), [Full Article]

Determination of the Theoretical Profile of a Grinding Wheel Relieving Cylidric Archimedean Hob with Non-Symmetric Thread Profile

V. Kirov1, V. Abadjiev2
1Technical University of Rousse
2Institute of Mechanics, Bulgarian Academy of Sciences, Sofia

Profiling of a relieving grinding wheel for cylindric hob with non-symmetric and linear in axial section profile of threads is presented in this article. The research is part of the technology for cutting high-reduction skew-axes gears, their surfaces being generated by Olivier's second principle. An algorithm for calculation of the basic geometry of relieving grinding wheel profile is created.

JTAM, Sofia, vol. 24 Issue 3 pp. 067-072 (1993), [Full Article]

Modelling of the Kinematical Contact of Hypoid Tooth Mechanisms

K. Minkoff
Institute of Mechanics, Bulgarian Academy of Sciences, Sofia

A mathematical model for synthesis and analysis of hypoid tooth surfaces is given in this paper. This general approach for determination of optimal geometry and mutual motion of the blanks, tools and machines secure the best contact of the designed mechanism.

JTAM, Sofia, vol. 24 Issue 3 pp. 073-079 (1993), [Full Article]

Manufacturing Fine Pitch Spiral Bevel Gears with the Generated Duplex Helical Cutting Method. Principal Problems

Zd. Wólcik
Warsaw University of Technology, Poland

This paper shows how to calculate the main geometrical quantities of the technological systems in the duplex helical method of generated fine putch spiral bevel gears production. The angles determined are sufficient to calculate the other machine setting parameters.

JTAM, Sofia, vol. 24 Issue 3 pp. 080-089 (1993), [Full Article]

Investigation of Load Distribution in Statically Non-Determinable Planetary Gears

K. Arnaudov, P. Parushev, V. Guenov
Institute of Mechanics, Bulgarian Academy of Sciences, Sofia

The reasons for the unequal load distribution in the statically non-determinable planetary gears are analyzed. Mechanical and mathematical models of two satellite planetary gears of that type are created and analytical load distribution expressions are deduced. An experimental programme for investigation of the impact of the inaccuracies, elasticities, load, planetary gear structure, and central bearing windages is formed. A software for investigation automation is created and the results from the computer aided research are discussed.

JTAM, Sofia, vol. 24 Issue 3 pp. 090-096 (1993), [Full Article]

A Mechanical-Mathematical Model of Balancing Spring Suspension with Asymmetric Springs

V. Petrov, G. Gabrovski
Technical University of Rousse, Rousse

A mechanical-matematical model was designed of balancing spring suspension with asymmetric springs for a heavy-freight semi-trailer car. The spring investigation was carried out from a new point of view, which made it possible to examine its independent bending in both ends. A software system was designed for modelling the vertical vibration in the trailer-semi-trailer mechanical system travelling over a random microprofile. The software system and the mechanical-mathematical model, designed, give possibilities for optimization in the structure and characteristics of the suspension.

JTAM, Sofia, vol. 24 Issue 3 pp. 097-101 (1993), [Full Article]

An Evaluation of an Integrated Approach to Biomechanical Modelling in the Design of Products

D. Wright1, K. Leibrandt2, R. Brown2
1Brunel University, London, U. K.
2Cardiff Institute of Higher Education, Cardiff, Wales

A methodology is proposed to include user's environment in the design of products. Both the way in which the product is perceived and the image created are considered. The methodology considers the user and product as parts of an integrated mechanical system.

JTAM, Sofia, vol. 24 Issue 3 pp. 102-106 (1993), [Full Article]

Theoretical Investigations of Residual Strain in Left Ventricle

St. Stoytchev
Institute of Mechanics, Bulgarian Academy of Sciences, Sofia

Kinematics of the left ventricle, assumed as an ellipsoid of revolution, is modelled on the basis of Continuum Mechanics. In accordance with published experimental data, it is supposed that in an unloaded state there exist residual stresses in the left ventricle wall. The analysis of the results show that stress distribution in unloaded state is nonuniform throughout the wall and connected with compressive residual stress in the endocardial region and tensile stress in the epicardial region. At the same time, in loaded state, which is associated with the end-diastolic state, the stress and strain distribution is more uniform. It is shown that the uniformity of the deformation field in loaded state strongly depends on the residual stress parameters.

JTAM, Sofia, vol. 24 Issue 3 pp. 107-112 (1993), [Full Article]

On the Influence of the Solid Phase Polidispersity on the Viscosity of Disperse Systems

Ya. Ivanov, V. Stojanov
Central Laboratory of Physical and Chemical Mechanics, Bulgarian Academy of Sciences, Sofia

The concentrational dependence of viscosity and rhoelogical behaviour of suspensions with bi- and polydisperse solid phase is considered. The case when the solid phase is composed of monofractions, strongly differing in size, is discussed in particular. Rheologically optimal compositions are calculated for these systems at different volume fraction of the phase. The concrete mixture is considered as a bi- and trimodal disperse system.

JTAM, Sofia, vol. 24 Issue 3 pp. 113-119 (1993), [Full Article]

Floor Response Spectra

M. Kostov, D. Stefanov, H. Boncheva, G. Varbanov, N. Koleva
Central Laboratory for Seismic Mechanics and Earthquake Engineering, Bulgarian Academy of Sciences, Sofia

The generalization of floor response spectra for Units 1 and 2 of the NPP "Kozloduy" is discussed shortly. The structure response to seismic excitation is analyzed using different models (2D and 3D finite element models) and varying the soil and structure properties and the way of modelling. The soil-structure interraction is studied. Floor response spectra are generated by a direct method. Final spectra represent envelopes of combined (by the SRSS procedure) response spectra for different models. The design floor response spectra are smoothed and broaden. Attention is paid to the rotational effects due to seismic excitation.

JTAM, Sofia, vol. 24 Issue 3 pp. 120-126 (1993), [Full Article]

Earthquake Analysis of Roller Compacted Concrete Dams

St. Tasev
Institute of Water Problems, Bulgarian Academy of Sciences, Sofia

The construction of roller compacted concrete (RCC) dams has become widespread in the last few years. The advantages of this type of dams are well-known. Two of them – the absence of joints and the favourable against cracking temperature conditions are the basic for the present work. A computer programme with 3-D discretization through volumetric finite elements with a linear approximation of displacements – tetrahedrons – is used. The results of the dynamic numerical analysis by the FEM of two RCC dams are presented. Additionally the elasticity modulus influence is commented.

JTAM, Sofia, vol. 24 Issue 3 pp. 127-132 (1993), [Full Article]

Vortex-Induced Oscillations of Tandem Cylinders with Rectangular Cross Section

S. Martinov1, M. Matsumoto2, N. Shiraishi2, T. Takeuchi3
1University of Architecture, Civil Engineering & Geodesy, Sofia
2University, Kyoto, Japan
3SUMITOMO Heavy Industr. Ltd., Japan

Heaving vortex-induced oscillations (VIO) of tandem structures with rectangular cross section have been studied through wind tunnel tests and flow visualizations on two-dimensional models. Motion-induced type vortex oscillations (MIO) are identified in the velocity-amplitude response of tandem cylinders by a new method for dynamic measurement of Power Spectral Density. Flow pattern corresponding to MIO and Karman type VIO of tandem cylinders are distinguished. The mechanism of MIO and KV is discussed.

JTAM, Sofia, vol. 24 Issue 3 pp. 133-140 (1993), [Full Article]

Progressive Crushing of Plastic Cylindrical Shells Under Axial Impact

J. Ivanova
Institute of Mechanics, Bulgarian Academy of Sciences, Sofia

The theoretical predictions for the final and effective axial crushing distance, the average value of the crushing force and the number of complete lobes for the cases of pure diamond and transition crushing modes of shell are obtained. The method used is based on the variational principle of Hamilton, defined over the geometric approximation of the crushed shell middle surface of cylindrical plastic strain rate sensitive shell under axial impact. A comparison is made between the theoretical and experimental results, obtained at the Department of Mechanical Engineering at the University of Liverpool and a good agreement is observed.

JTAM, Sofia, vol. 24 Issue 3 pp. 141-149 (1993), [Full Article]

A Numerical Solution of the Plane Boundary Value Problem of Thermoelasticity through Non-orthogonal Meshes

O. Santurjian
Institute of Water Problems, Bulgarian Academy of Sciences, Sofia

There are problems, like the modelling of thermal stresses in incremental concrete dam blocks, which two-dimensional solution is more appropriate to be obtained by Airy's stress function, employing the equations of strain compatibility. A method for numerical integration of these equations with nonorthogonal and irregular meshes, based on the colocation principle by local approximation of the stress function and its second derivatives through incomplete polynomials of fourth degree, is briefly exposed in the report. The method could be used for other similar problems.

JTAM, Sofia, vol. 24 Issue 3 pp. 150-154 (1993), [Full Article]