Journal of Theoretical and Applied Mechanics

Volume 33, Number 1, 2003






Al. B. Kazakoff


Institute of Mechanics, Bulgarian Academy of Sciences,

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




Abstract. This paper describes investigation of spatial vibrations of mechanical filters presented as a double mass vibration dynamic system utilising viscoelastic properties and natural frequency prediction of dynamically scaled models of the mechanical filters subjected to a half sine wave shock input. The mechanical and mathematical modelling is performed on the basis of a double mass dynamic model with twelve degrees of freedom in the spatial variant: six for each mass - three for the linear and three for the angular motion. A forced response analysis was used to determine the resonant frequencies of viscoelastically damped structures. Finite Element Analysis (FEA) is used to predict the vibration characteristics of the viscoelastic systems. The frequency dependant properties of the Young’s modulus and loss factor are incorporated in the FEA, in which a commercial code ABAQUS is used. The results of FEA are partially validated by means of analytical analysis using the energy approach and the classical Lagrange’s differential equation of second order. Natural frequencies and amplitudes of displacement are obtained by means of computer experiment in the three dimensional solution and compared with the results of finite element analysis. In this paper an optimisation of the double mass dynamic system has been performed in two basic directions: with respect to material and geometry optimisation of dynamically scaled bodies.



Key words: vibrations, mechanical filters, viscoelastic material properties,

frequency dependence, forced response calculations.


D. M. Simeonova


Technical University of Sofia,

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


An Interaction of Forced and Self-Excited Oscillations during a Cutting of Metals


Abstract. Dynamical models, in which the basic reasons of self-excited oscillations during the cutting of metals are taken into account, are considered. A new feature is the consideration of the variable thickness of the cutting metal layer, which leads to appearance of a periodic component in the cutting force. In the governing system of non-linear differential equations there are both reasons of self-excited oscillations and reasons of forced oscillations. The obtained solution is studied quantitatively. The interaction of the self-excited oscillations leads not only to quantitative variations but to qualitative ones also. The obtained results can be used for a dynamic synthesis of the system.



Key words: self-excited oscillations, cutting of metals, non-linear oscillations.


A. D. Polyanin, A. I. Zhurov


Institute for problems in Mechanics, Russian Academy of Sciences,

101, Vernadsky Avenue, 117526 Moscow, Russia,




N. T. Kovacheva


Institute of Mechanics, Bulgarian Academy of Sciences,

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






Abstract. One-, two- and three-dimensional linear non-homogeneous unsteady boundary-value heat and mass transfer problems when the coefficients of the equations are arbitrarily dependent on the time and spatial coordinates are considered. General formulae, which allow expressing the solutions of the problems by the Green function for all basic types of the boundary conditions, are obtained. The results can be used in order to investigate the heat and mass transfer processes in immovable and movable medium for isotropic and anisotropic cases (in case of volumetric and surface chemical reactions).

Key words: heat and mass transfer, linear non-homogeneous differential equation, Green function.


A. Baltov, V. Kavardzhikov, K. Sokolova

Institute of Mechanics, Bulgarian Academy of Sciences,

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



Theoretical-experimental study on mechanical behaviour of wood under compression


Abstract. A theoretical-experimental approach to determining the mechanical characteristics of wood is proposed, in which the fact that wood is a composite material with anisotropic properties and sensitive to the type of loading is taken into consideration. The mechanical-mathematical model introduces a number of subspaces defining equal types of stress states into a six-dimensional vector space of stresses. A method of obtaining wood elastic characteristics in case of a two-dimensional stress state is developed. Special attention is paid to a correct preparation of the experimental specimens. Quadratic surfaces of “Pinus sylvestris L” wooden material constant deformations levels at the elastic stage of deformation, as well as the components of the matrix of elastic deformation, are determined.



Key words: wooden material, anisotropic properties, elastic characteristics, two-dimensional stress state.



V. A. Dzhupanov


Institute of Mechanics, Bulgarian Academy of Sciences,

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




Sv. V. Lilkova-Markova

University of Architecture, Civil Engineering and Geodesy,

1, Chr. Smirnenski Blvd., 1421 Sofia, Bulgaria,




Statement ruses of the problem on the dynamic stability of cantilevered pipe conveying liquid and lying on elastic foundation (Part II)


Abstract. Following the hypothesis of Winkler the Foundation response = - c1w, where w is current vertical displacement of the points of the pipe neutral axis, and c1 is constant proportionality coefficient. The sense of c1 is “a local foundation response force due to local unit displacement of the pipe”. This hypothesis was generalized by Pasternak who proposed the Foundation response = - c1w – c2w,x, where c2 is also constant proportionality coefficient. The sense of c2 is “a local foundation response bending moment due to local unit rotation of the pipe”. Due to their good engineering sense and to their visible simplicity these hypotheses are broadly used in the engineering practice up to now. The hypothesis of Pasternak started a process of other (additional) generalizations. Different rough features in these proposals generated a set of investigations especially directed to correct these features and make clearer their nature. In the present investigation, by using the problem on the dynamic stability of a cantilevered pipe conveying fluid and lying on elastic medium, is accented on the theory and examples of some structural realizations of multi-parametric foundation media.



Key words: beam-like pipe, dynamic stability, flutter, elastic resisting, foundation, joined stiffness.



Kalinka P. Bakalova

Solar-Terrestrial Influences Laboratory, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str., Bl. 3, 1113 Sofia, Bulgaria,



Estimation of the flat Earth model error in evaluation of the double scattered Sun radiation

Abstract. The present paper considers the transmission of double scattered sunlight through a fluid medium like the earth atmosphere. In many cases, the flat earth-atmosphere approximation is quite acceptable and preferable in atmospheric optics, especially for describing the propagation of beams with zenith angle smaller than 75o, or for short distant processes. Obviously, the primary scattered beams coming from all sides do not satisfy the first condition. Moreover, it is not evident that the attenuation in the atmosphere restricts the length of the primary scattered beams to extent allowing the use of the flat earth simplification. The estimation of the error of the flat earth model should indicate if the latter is adequate for description of the amount of the secondary scattered sun radiation.

The subject of the present paper is the exploration and estimation of the error due to ignoring the earth curvature when the amount of the radiance of the double scattered sunlight is evaluated by means of the flat earth model.


Key words: atmosphere, transmission of light, atmospheric models, multiple scattering.



A. K. Haghi


Department of Textile Engineering, The University of Guilan,

P. O. Box 3756, Rasht 41938, Iran,






Abstract. The microwave and convective drying of industrially prepared bundle of natural silk yarn has been experimentally investigated on a laboratory scale. The experiments were performed at different levels of heating temperature. The results obtained from the two drying techniques show less damage to the silk yarn by microwave radiation and a strong relationship between applied microwave power and drying time of natural silk samples.



Key words: natural silk, convective drying, microwave drying, scanning electron