Issue 3
JTAM, Sofia, vol. 26 Issue 3 (1996)

On the Chaotic Behaviour of a System from Rigid Body Dynamics

O. Christov
Faculty of Mathematics and Informatics, Sofia University


In this paper we prove existence of horseshoes in the dynamics of a system consisting of a rigid body and a particle oscillating in it around its fixed point. The presence of horseshoes implies chaotic behaviour and hence nonintegrability.

JTAM, Sofia, vol. 26 Issue 3 pp. 09-16 (1996), [Full Article]

Modified Legendre's Polynomials Used in the Theory of Differential Equations

A. Iarovici, V. Visarion
Institute of Solid Mechanics, Rom. Acad. Sci., Bucharest

Some special functions Pn(x) obtained from Legendre polynomials Pn(x) are introduced, so that one obtains complete series if we arrange these functions in a special way. All these functions together with their derivatives of order m(0<k<m<n) vanish in the points x=± 1. In the differential equations theory with differential type limit conditions the solution is developed in a series of such functions. The problem is reduced to a system of linear algebraic equations and limit conditions are "exactly" satisfied (independent of the polynomials number retained from the infinite series).

JTAM, Sofia, vol. 26 Issue 3 pp. 17-24 (1996), [Full Article]

Model for Calculation of the Dynamic Characteristics and Loadings of the Electric Platform Truck in the Case of Controlled Start or Stop

P. Petrov
Balcancar Engineering Ltd. Sofia

A dynamic plane model of the platform electric truck is created. The characteristics of the basic units in the electric power circuit are considered and the mechanical system is presented in terms of fine concentrated masses and seven generalized coordinates, associated with the rigidities and resistances. The effect of the controlled braking moment in the fore and back wheels is considered, as well as the road resistance and the controlled moment of the electric traction motor. A mathematical model and a computer programme are created to perform the motion parameters calculation, their velocities and the loadings in some assemblies, units and joints, under either contactor or pulse control of the electric traction motor in controlled start and stop mode; forward and backward motion mode. The results of a calculation experiment are presented.

JTAM, Sofia, vol. 26 Issue 3 pp. 25-39 (1996), [Full Article]

On the Critical Velocities of a Pipe Conveying Fluid and Subjected to an External Loading

V. A. Dzhupanov, V. M. Vassilev, P. A. Djondjorov
Institute of Mechanics, Bulg. Acad. Sci., Sofia

The work is dealing with the vibration behaviour of a supported one span pipe conveying inviscid flowing fluid. Along the pipe an external smoothly and continuously distributed transversal load is dynamically acting. Just the analytical particularities of the boundary-value problem generated by the interactive combination of both perturbations: (i) internal longitudinal fluid (liquid) flow and (ii) transversal dynamic load, are under investigation. The problems arisen are treated numerically by using the finite difference method (FDM) in combination (for comparisons) with Galerkin method. As a result of the numerical analysis a relation between the flow velocity and the forced vibration frequency is found out to exist when the amplitudes of the pipe transversal vibrations get inadmissible high values, i. e. exceeding the limit under which the linear model under consideration is applicable. On the basis of this relation a new design criterion is suggested to be introduced into the engineering practice.

JTAM, Sofia, vol. 26 Issue 3 pp. 40-51 (1996), [Full Article]

Topmost Speed Effect and Some Other Frictional Effects in a Reciprocal Joint

Y. Smirnov
Tula State University, Tula, Russia

An analysis attempt was made for self-excited vibrations of a slide-block within the framework of multivariant modelling of a friction contact interaction of rigid bodies. A topmost speed effect was discovered and the possibility of an interrupting motion caused by dynamical selfbracing was demonstrated.

JTAM, Sofia, vol. 26 Issue 3 pp. 52-56 (1996), [Full Article]

A Note on Rayleigh Waves

Ts. Ivanov1, R. Savova2
1Faculty of Mathematics and Informatics, University of Sofia
2Institute of Mechanics, Bulg. Acad. Sci., Sofia

In this note the case of surface waves of an assigned frequency in classical elasticity is considered. It is proved that the waves of Rayleigh type which correspond to the complex roots of the secular equation are inadmissible.

JTAM, Sofia, vol. 26 Issue 3 pp. 57-61 (1996), [Full Article]

Digital Filter for the Visioplasticity Method

D. Kisselkov
Institute of Metal Science, Bulg. Acad. Sci., Sofia

In the visioplasticity method for investigation the plastic flow the initial experimental data are principally "noisy". It is described a procedure for building a digital filter for smoothing experimental data, subject of thrice-repeated differentiation. Application of the five-term smoothing formula is compared with such one based on "homomorphous" functions (applied for valid signal multiplied with the noise signal). Unsatisfactory result obtained with "homomorphous" filter let to conclude, that the noise in our data has an additive character, and that more suitable for present data is proposed filter.

JTAM, Sofia, vol. 26 Issue 3 pp. 62-65 (1996), [Full Article]

Non-axisymmetric Static Drops on a Horizontal Plane: Numerical Analysis

S. Iliev
Institute of Mechanics, Bulg. Acad. Sci., Sofia

Here is presented parametric investigation of the shape of the equilibrium liquid drops with fixed volume and undergo surface tension and gravity on a horizontal plane. For this analysis is used a numeral method to minimize the energy of the system, and directly to simulate virtual displacements of the considered system. We have studied here a sessile drop on the heterogeneous solid surface, liquid drop hanging from a square and the drop with limits of the space locations.

JTAM, Sofia, vol. 26 Issue 3 pp. 66-74 (1996), [Full Article]