Journal of Theoretical and Applied Mechanics

Volume 39, Number 3, 2009





Evtim V. Zahariev


Institute of Mechanics, Bulgarian Academy of Sciences,

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



Juana M. Mayo


Department of Mechanical and Materials Engineering, University of Sevilla,

Camino de los Descubrimientos s/n, 41092 Sevilla, Spain,





Abstract. In the paper the graphical methods of Routh’s and Impulse Momentum Equations (IME) are presented. A novel iterative methodology for solution of spatial frictional impact of multibody systems is proposed. The iterative procedure consists in descretization of the normal velocity and consequential computation of IME. At every iteration the tangential velocity is pre-calculated analyzing the condition for sliding and sticking. Examples of spatial frictional impact are presented. The sliding trace is computationally derived. The paper will be of use for lecturers and scientists dealing with the problems of frictional contact and impact and presents short but the major references of the scientific investigations in the field.

Key words: impact, friction, multibody systems.


Ilker Sugozu


Firat University, Institute of Science, Machine Education Department,

Elazığ, Turkey,



Ibrahim Mutlu


Afyon Kocatepe University, Technical Education Faculty,

Afyonkarahisar, Turkey,




Abstract. Brake pads of automotive are composite materials composed of more than ten different ingredients. Asbestos has been used as a friction material but it has been prohibited to use in brake pad due to its harmful effect on human health. Therefore, new material investigation to replace the asbestos gained acceleration.

In this study, Waste Tire Rubber (WTR) was used as a new friction material in brake pads. Newly formulated brake lining material with five different ingredients has been produced by using WTR. WTR is used in different amount in the mix of other regular ingredients in brake pad. Conventional techniques have been used in the production of brake lining. In the experimental studies, the change of friction coefficient, the temperature of friction surface and amount of wear were measured. In addition, micro-structural characterizations of braking pads are carried out by using Scanning Electron Microscopy (SEM). The strategy proposed in this paper can be considered as an alternative to revalorize this kind of waste products. As a result, WTR can be used as friction materials in the brake pads.


Key Words: brake pad, composite materials, friction, wear, Waste Tire Rubber (WTR).


Nikolay K. Vitanov


Institute of Mechanics, Bulgarian Academy of Sciences,

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



Optimum theory of turbulence: Ideas, methods and results


abstract. It is not possible to obtain closed mathematical expressions for the complex velocity, temperature and other fields describing the turbulent motion of the fluids. Instead of this we must use direct numerical simulations or other methods to obtain analytical results for the flow quantities. There are few such methods. One of them is the optimum theory of turbulence. This theory leads to upper bounds on energy dissipation, transport of momentum, heat transport, etc. The bounds are obtained by solution of the Euler - Lagrange equations of variational problems formulated on the basis of the systems of model equations.

Two methods of the optimum theory of turbulence are widely used. The Howard-Busse method is based on modelling of the flow fields by coupled modes with different wave numbers (multi-α-solutions). The Doering - Constantin method is based on a decomposition of the flow fields on background field which satisfies the boundary condition and fluctuation field which satisfies zero boundary conditions. The Doering - Constaintin method does not lead to better bounds but it is more flexible with respect to

the boundary conditions.

In this paper we discuss the main ideas, the areas of application, and selected upper bounds obtained by the optimum theory of turbulence. The two methods are illustrated by their application to different fluid systems. The Howard - Busse method is applied for obtaining of upper bounds on the

thermal convection in a fluid saturated porous layer. The Doering – Constantin method is applied for obtaining upper bounds on the energy dissipation of Couette - Ekman flow.


Key words: fluid dynamics, turbulence, variational problems, upper bounds, optimum theory of turbulence, Howard - Busse method, Doering - Constantin method.


S. Slavtchev, P. Kalitzova –Kurteva,


Institute of Mechanics, Bulgarian Academy of Sciences,

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



A. Oron


Department of Mechanical Engineering,

Technion-Israel Institute of Technology,

Haifa 32000, Israel,





Abstract. The emergence of a mass flux in binary mixtures, due to temperature gradient, is known as thermodiffusion or Soret effect. When the latter is present, in addition to the classical diffusive flux, the total mass flux also contains a thermodiffusive flux. Thermodiffusion is usually small, but it can be important in various separation processes. The Soret effect is called nonlinear when the thermodiffusive flux is proportional to a nonlinear function of the solute concentration in the mixture. The nonlinear Soret effect is significant in very dilute solutions. Recently, taking into account this effect, the long-wavelength monotonic Marangoni instability in a thin horizontal layer of a binary liquid mixture heated from below was studied by the present authors [1]. Here, the study is completed by considering the case of oscillatory Marangoni convection.


Key words: binary mixture, nonlinear Soret effect, Marangoni oscillatory instability, long waves.


Valentin Velev, Todor Dimov


Konstantin Preslavsky University - Shumen, 9712 Shumen, Bulgaria,



Anton Popov


University "Prof. Dr. Assen Zlatarov" - Bourgas, 8000 Bourgas, Bulgaria,



Christo Betchev


University of Chemical Technology and Metallurgy, 1756 Sofia, Bulgaria,



Deformation behaviour of amorphous uniaxially oriented polyester samples caused by simultaneous thermal and mechanical treatments


Abstract. The deformation behaviour of as-spun polyester filaments, subjected to simultaneous thermal and mechanical treatments has been studied. Amorphous Poly(Ethylene Terephthalate) (PET) bundles produced on the industrial spinning machine Furnet (France) were used as samples. The heat mechanical treatments and the birefringence measurements were conducted using devices constructed and produced in the authors’ laboratories. Thermal deformation experiments were carried out on conditions of linear samples heating from room temperature up to 473 K while they were subjected to a well-defined constant strain force. The results obtained show the role of the strain stress on the causing samples deformation and in the control of the rival processes of the fluid like deformation and stress-induced crystallization.


Key words: poly(ethylene terephthalate), amorphous filaments, linear heating, strain stress, deformation behaviour, birefringence.


Richard Berenyi


Department of Electronics Technology,

Budapest University of Technology and Economics,

3, Goldmann, H-1111 Budapest, Hungary,



Mechanical Study of a Micro-Machined Flexible Substrate


Abstract. A new Three-Dimensional (3D) laser micromachining method of 3D flexible structures has been introduced to enhance the current micromachining technology. The machining is carried out with a simple Two-Dimensional (2D) movement of the laser beam on the work piece. This method can be applied for machining 3D geometries or bending edges in various materials. The purpose is to extract the material by an ablation of matter in order to achieve “V” shape for multi-bend structure. The process is well controlled and only selective polyimide material removing on bending edges was used. Two-layered polyimide-copper assembly was considered. This is a practical case for multilayer structures such as layered composites and coatings. The mechanical bending analysis of the system with residual stress was carried out with COMSOL Multiphysics. Variations in strain and stress of the structure are demonstrated. Dynamic bending features were also measured and compared to a non laser cut and bended substrate. Its mechanical reliability is improved.


Key words: micro-machining, 3D package, laser processing, laser ablation of polyimide, mechanical structures in polyimide, reliability test.