Issue 4
JTAM, Sofia, vol. 15 Issue 4 (1984)

Mechano-Mathematical Modelling

G. Brankov


JTAM, Sofia, vol. 15 Issue 4 pp. 011-016 (1984)

On Linear Regulation in a Finite Dimensional Configuration Space

A. Cheremenski
Inst. Mech. Biomech. Bulg. Acad. Sci., Bl. 8 Geo Milev

As it is known, the separation of controlling and controlled parameters does not stand for a one-valued operation. However, the paper proves that both stability conditions and the synthesis of the stationary stabilization do not depend on the method of separation. Calculations involve a quadratic quality functional, including controlling parameters of non-degenerate form, as well as parameters that control the object conduct in the configuration space. Furthermore, an index of the system of parameters is created, whereas both the synthesis of the regulator and the surveillance of an object under "enemy's" control can be realized.

JTAM, Sofia, vol. 15 Issue 4 pp. 017-023 (1984)
Automated Design of Hyperboloid Gears of High Transmission Ratio

V. Abadjiev, D. Petrova
Inst. Mech. Biomech., Bulg. Acad. Sci., Bl. 8 Geo Milev

The paper presents a kinematic scheme of theoretically conjugate generated gears designed by using T. Oliver's second approach. The authors create as well an algorithm and a computing procedure for the mathematical securing of the following three problems: (i) calculation of the optimal geometry of billets and gears; (ii) calculation of the gear bearing supports; (iii) calculation of the cutter geometry. The problems underlined concern the design of hyperboloid gears of high transmission ratio.

JTAM, Sofia, vol. 15 Issue 4 pp. 024-030 (1984)
Kinematic Theory of the Infinitely Close Positions of a Solid Body with a Single Fixed Point III

S. Butchvarov
High. Inst. Mech. Electr. Eng., Durvenitsa

A solution of the problem for five infinitely close positions of a solid body with a single fixed point is presented and performed kinematically. The existance of Burmester's points and centres is proved and methods for their location are developed.

JTAM, Sofia, vol. 15 Issue 4 pp. 031-037 (1984)
`Robot' Programme System and Algorithms for the Kinematic Investigation of Manipulators

E. Peisah

The paper has been presented at the 4th National Congress of Theoretical and Applied Mechanics, Varna 1981.

JTAM, Sofia, vol. 15 Issue 4 pp. 038-041 (1984)
Dynamic Investigation of Structures with Switch on Connections

L. Tsenov
CLSMSI, Sofia

A dynamic investigation of such structures is performed. The approach adopted outlines prospects to the design of structures resistant to seismic impacts. Moreover, the values of the system basic parameters are sought to produce maximum effectiveness of the structure when resisting to seismic impacts.

JTAM, Sofia, vol. 15 Issue 4 pp. 042-049 (1984)
On the Composition of a Damping Matrix for the Solution of Dynamic Problems

P. Sotirov, P. Dineva, L. Hadjikov
Inst. Mech. Biomech., Bulg. Acad. Sci., B1. 8, Geo Milev

The authors propose a new approach for the solution of dynamic problems, i.e. seismic response of a soil-structure system. Since most of the computing programmes concern a model with viscous damping that requires less computing time and memory, solution is sought routinely, but what has to be calculated is the damping matrix that corresponds to the system real conduct. Such an equivalent damping matrix can be obtained through solving an inverse problem for the determination of the damping matrix coefficients, on the basis of the damping coefficients of the main oscillation forms. The latter, however, can be found by calculating the system complex eigen frequencies.

JTAM, Sofia, vol. 15 Issue 4 pp. 050-059 (1984)
Investigation of Nonlinear Oscillation Effects Occurring During the Interaction of Elastic Bodies

N. Kilchevskiy, D. Ilchishina, M. Shalda, L. Stoimenov

The paper has been presented at the 4th National Congress of Theoretical and Applied Mechanics, Varna 1981.

JTAM, Sofia, vol. 15 Issue 4 pp. 060-064 (1984)
Iterative Method for Determination of Equilibrium Shapes of a Floating Zone Free Surface

J. Kojuharova, S. Slavchev
Inst. Mech. Biomech., Bulg. Acad. Sci., Bl. 8 Geo Milev

An iterative method for determination of equilibrium shapes of a liquid free surface is discussed. The liquid is supported by surface-tension forces between two horizontally placed, parallel discs with limited radii. The solution of the problem gives the shape of the molten zone of a crystal worked by the floating zone method.

JTAM, Sofia, vol. 15 Issue 4 pp. 065-071 (1984)
The Effect of Temperature on the Long-term Strength of Д16T2 Alloy

V. Gorbatenko
High. Inst. Arch. Civ. Eng., 1 Hr. Smirnenski Blvd.

The long-term strength of Д16T2 alloy is investigated by testing specimens similar to sonde tubes and undergoing tension under high temperature. Values of stresses are close to the yield limit. Long-term strength – temperature nomographs are drawn for various intervals of time, where temperature varies in the 160-200°C range.

JTAM, Sofia, vol. 15 Issue 4 pp. 072-077 (1984)
Non steady Oscillations of a Rigid Rotor Supported by Roller Bearings

V. Kortenska
High. Inst. Arch. Civ. Eng., 1 Smirnenski Blvd.

A dynamic model of a rigid balanced rotor on two supports is presented. One of the supports is rigid while the other one is elastically-complient, with a nonlinear characteristics. The mechanical problem is reduced to an autonomous system of differential equations of the form d2Ψ/dt2 = CΨ+εf(ε, Ψ, dΨ/dt), where ε is a small parameter and C = ∥Cij∥ is a quadratic non-degenerate matrix with negative eigen values. Each coordinate of the vector function f(ε, Ψ, dΨ/dt) is an analytic function of the form fj(ε, Ψ, dΨ/dt)=∑(v=0)∞εvgiv(Ψ, dΨ/dt), whereas the following equalities hold giv(Ψ,-dΨ/dt) = giv(Ψ,dΨ/dt). Periodic trajectories are obtained in the R4 space as well.

JTAM, Sofia, vol. 15 Issue 4 pp. 078-085 (1984)
On a Method for the Identification of Mechano-Mathematical Models by Using a Statistical Approach in the Theory of Pattern Recognition

I. Nikolova
Inst. Mech. Biomech., Bulg. Acad. Sci., Bl. 8 Geo Milev

The paper proposes a method for the identification of mechano-mathematical models by using data obtained when applying an experimental wave method. Employing a statistical model in the theory of pattern recognition, a single model is chosen from a group of models to approximate most effectively (in the sense of minimum error probability) the material under consideration. Such a method does not depend on the generated impulse, i.e. on the particular wave experiment. Tests are performed for definite values of parameters involved in the model equation.

JTAM, Sofia, vol. 15 Issue 4 pp. 086- (1984)