Journal of Theoretical and Applied Mechanics

Volume 33, Number 2, 2003



Alexander  B.   Kazakoff


 Institute of Mechanics, Bulgarian Academy of Sciences,

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






Abstract. This paper deals with modal analysis of electrical stators, prediction of the natural frequencies and mode shapes of different vibration modes as affected by teeth, frame and laminations. The problems associated with thick cylindrical shells are of considerable engineering importance in numerous applications. One important application of such shells is the stator of electrical machines, where the thick stator-core with teeth and windings is encased by a thin frame. In order to design a quiet electrical machine, the accurate determination of resonant frequencies and vibration characteristics of the stator is essential. The vibration properties of an induction motor are investigated in this paper using a Finite Element (FE) method. The influence of teeth, frame and laminations on the overall vibration response of the stator is evaluated and a suitable modeling approach is suggested. The results presented should help design-engineers to determine resonant frequencies and natural response of stators accurately by proper incorporation of effects of teeth, frame and laminations. Also, the physical interpretations of the results, given in the paper, would help in acquiring a better understanding of the vibration behaviour of stators in relation to the problem of electromagnetic acoustic noise in electrical machines.


Key words: electrical stators, natural frequency prediction, noise and vibration, modal analysis


B. Marinov


Institute of Mechanics, Bulgarian Academy of Sciences,

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





Abstract. In this paper a theory is developed for sizing the shafts of a power transmission line. The behaviour of the line is investigated when the torsional and longitudinal vibrations act simultaneously. The angular velocity of the shafts varies in working mode and the system passes through different resonance zones. The purpose of this investigation is to establish the resonance zones provoked by the first two natural frequencies from the torsional and longitudinal vibrations, and to choose suitable values of the linear characteristics, so that the stresses of the power transmission line are smaller than the permissible values. This study is a base for the investigation of the complex dynamic loads generated by the joint action of torsional, bending and longitudinal vibrations in resonance and non-resonance modes.


Key words: shafts, sizing, frequency, vibrations, angular velocity, dynamic loads.


N. Pesheva, S. Iliev


Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev St. 4, 1113 Sofia, Bulgaria,



Numerical verification of the Cassie’s EQUATION

for well-defined heterogeneous substrates with “mesa” defects


Abstract. The wetting properties of model heterogeneous flat substrates are studied numerically. In the framework of the classical capillary theory the shapes of three-dimensional liquid drops in equilibrium with such substrates are obtained. The numerical method used is based on the local variations approach. It has been extended here to treat chemically heterogeneous substrates with “mesa” defects, i.e. sharp boundaries between surface patches with different surface tensions. We discuss the implications for the Cassie’s equation.


Key words: Cassie’s law, contact angles, heterogeneous substrates, liquid drops.


Ts. P. Ivanov,


Faculty of Mathematics and Informatics, University of Sofia” St. Kl. Ohridski”,

5, James Bourchier Blvd., 1126 Sofia, Bulgaria,


R. Savova

Institute of Mechanics, Bulgarian Academy of Sciences,

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


Motion and Stability of an Elastic and Asymmetric Heavy Top

 Abstract. Motion and stability of an elastic top with stress-free surface and a fixed point moving in a gravitational field is considered. The investigation is based on a direct approach in the energy momentum method split into two steps. The deformation of the top due to the gravitation and an arbitrary rotation is considered first and after that - the motion of the deformed top as a rigid one. This separation is possible since the elastic deformation is assumed static during the motion, which leads to relative equilibrium state of the top. It is stable if the top is in a stable state with respect to both of them - the deformation and the motion.  The Koiter's definition for non-linear stability with respect to the deformation and the usual Lagrange definition for stability of the motion of the deformed top as a rigid one are adopted. Relative equilibrium states are determined and criteria for stability are proved.


 Key words: top, elasticity, relative equilibrium, energy momentum methods, stability.


Tsviatko Rangelov


Institute of Mathematics and Informatics, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, Bulgaria,



Scattering from cracks in an elasto-anisotropic plane


Abstract. Scattering problem in cracked elasto-anisotropic plane is studied. A representation of the scattering field due to time-harmonic wave motion in the exterior of an arc crack is derived. Using Radon transform a fundamental solution in the frequency domain is obtained. In the case of a line crack an inverse problem for determining the crack opening area and stress intensity factors is presented. Numerical examples for solution of the direct and inverse scattering problem in orthotropic plane are given.


Key words: cracked elasto-anisotropic plane, direct and inverse problems, BIEM.


Rumen K. Krastev


Central Laboratory of Physical Chemical Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str, Bl. 1, 1113 Sofia, Bulgaria,



Mechanical properties and ratios of GF/POM under   three test regimes

Abstract. The present study concerns the prediction of the durability basic equation, which represents the relationship of lifetime under constant loading. Samples of glass-fiber reinforced poly(oxy)methylene (GF/POM) were tested under three point bending till fracture. The experimental work included two short-term loading experiments (at constant deflection rate and at constant force rate) indicating characteristic fracture behavior of the material for the two regimes, as well as experimental lifetime measurements under constant force loading. The dependencies of some specific properties on the regime and velocity of loading were described. Based on the two sets of short-term experimental data, the lifetime predictions were performed applying two methods. The predictive lines were compared with the experimental curve of durability.


Key words: loading regime, mechanical loading, lifetime prediction, GF/POM.


Svetlana V. Lilkova-Markova


University of Architecture, Civil Engineering and Geodesy,

1, Christo Smirnenski” Blvd., 1046 Sofia, Bulgaria,



Influence of Variable Middle Elastic Support to the Dynamic Stability of a Cantilevered Fluid Conveying Pipe with Two Additional Elastic Supports


Abstract. Two-span cantilevered pipes with two additional linear elastic supports are studied. The effect of mispositioning of the middle support on the dynamic stability of these pipes is thoroughly investigated. It is shown that when the flow velocity exceeds a certain value, depending on the spring constant, the tube is subject to flutter- type instability, buckling - type instability, or both with multiple stable and unstable ranges of flow velocity. The effects of the pipe parameters - mass ratio, spring constant on the dynamic stability are considered.


Key words: pipe, elastic supports, fluid flow, critical velocity, dynamic stability.