Journal of Theoretical and Applied Mechanics

Volume 38, Numbers 3, 2008




Clementina D. Mladenova


Institute of Mechanics, Bulgarian Academy of Sciences,

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



Ivaïlo M. Mladenov


Institute of Biophysics, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str., Bl. 21, Sofia 1113, Bulgaria,



Spacecraft Dynamics Under the Influence of Gravity Torques


Abstract. On the basis of the general theory of kinematics and dynamics of a rigid body, this paper studies the dynamics of a rigid spacecraft under the influence of the gravity torques. The dynamics equations are obtained in a first-order form with a coefficient matrix which allows its eigenvalues to be obtained in an analytical form. An appropriate parameterization of SO(3) group is used, which has nice and clear geometrical properties and it is quite efficient in computational aspect. An example is given, which demonstrates the stability of the model.


Key words: rigid body, kinematics and dynamics, parameterizations of rotation group, eigenvalue problem.


G. Rosenhouse, F. Kirzhner, Y. Zimmels


Faculty of Civil and Environmental Eng. – Technion,

Israel Institute of Technology, Haifa, 32000, Israel,




Soil replacement for isolation of structures against underground vibrations


Abstract. Strong Soil vibrations can be intruding and leading on the extreme to damages. They are a reason for defects in delicate products of machinery and adverse effect on vibration sensitive instruments. In order to avoid such results, vibration amplitudes should be restricted to the limits specified in standards. Vibrations that exceed or are expected to exceed standard limits call for protective measures. In this work we consider design configurations that provide effective isolation against vibrations and in certain cases reduced differential settlements, using ground replacement by an elastic layer. Numerical examples using elastic layers, for example of 0.5 m thickness, result in effective vibration isolation within wide frequency range.


Key words: vibrations, isolation, ground replacement, structures.


Al. B .Kazakoff


Institute of Mechanics, Bulgarian Academy of Sciences,

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



D. P. Karaivanov


University of Chemical Technology and Metallurgy-Sofia,

8, Kliment Ohridski Blvd, 1756 Sofia, Bulgaria,



S. Troha


University of Rijeka, Technical Faculty,

58, Vukovarska Str., Rijeka, Croatia,





Abstract. Vibration characteristics of a generalized model of a robocrane – the model itself is an abstraction combination of a transmanipulator and a robocrane, are investigated in a vertical base plane with simultaneous linear travelling and lifting load motion. The investigation is based on the developed three mass dynamic model of a robocrane considering the variable load mass according to a certain time function. The system non-linear differential equations of motion are analyzed in different case studies of formation of reactive force with a definite crane control. The objective of the work presented in this paper is a derivation of the system motion differential equations, considering the accelerating and decelerating working modes and the equilibrium at linear variation of the brake torque. The stoppage time is defined at which the vibration amplitudes of the robocrane construction are minimal and the necessary gradient of the variation of the brake torque as a function of the system parameters is defined. Computer code MATLAB is used in the dynamic system computer modelling.


Key words: robocrane vibrations, crane vibrations, crane dynamics, ordinary differential equations of second order, computer modelling, frequency analysis, brake torque characteristics.


N. Petrov


Institute of Mechanics, Bulgarian Academy of Sciences,

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



A. Szekeres


Department of Applied Mechanics,

Budapest University of Technology and Economics,

Muegyetem 1-3, Budapest H1111, Hungary,





Abstract. The aim of the present study is to offer a non-classical model able to solve the problem connected with the paradox of the infinite speed of propagation of the thermal perturbation. The principle assumption is that the momentary dependence between the entropy and heat fluxes in Clausius–Duhem inequality does not take into account the relaxation phenomena due to the micro-structural formation and degradation processes. We reformulate this dependence as memory type. As a result a hyperbolic partial differential equation for the caloric balance is obtained instead of parabolic one, by which the above mention paradox is eliminated. Also we obtain a new heat conduction equation which is a generalization of the equations offered by Maxwell, and Green and Lindsay.


Key words: non classical, heat, conduction, claussius, duhem, thermodynamics, caloric, hyperbolic, parabolic.


Yongbin Zhang


Zhejiang Jinlei Electronics, Zhejiang Province, P. R. China,



When should the Boundary Lubrication Be Considered in a Hydrodynamic Contact?


Abstract. The mixed lubrication with mixed boundary lubrication and conventional hydrodynamic lubrication films in the whole contact in a one-dimensional problem is studied. The boundary lubrication is formed by the physical adsorbing of the fluid molecules to the contact surfaces. It is modelled by the flow factor approach suggested recently. The conventional hydrodynamic lubrication is modelled by the conventional fluid mechanics equation. Theoretical analysis is derived and analytical solution is obtained for the studied contact for different critical boundary lubrication film thickness, different surface patterns and different boundary lubrication film thickness. The results show that the critical boundary lubrication film thickness for the boundary lubrication should be considered in the modelling of a mixed lubrication may practically be on the 0.001 scale. The model as well as the previous model for studying the similar contact developed by the author indicates that 0.005 can often be regarded as the critical boundary lubrication film thickness for the boundary lubrication to be considered in a practical mixed lubrication modelling.


Key words: boundary lubrication, hydrodynamic contact, model.


Mohamed Elajrami, Mohamed Benguediab


Laboratory of Material and Reactive Systems,

Department of Mechanical Engineering, University of Sidi bel Abbes,

Ben M’Hidi City B.P 89 22000, Sidi Bel Abbes, Algeria,



Guillèn Ronald


Research Center and Transfer of Technology –GeM (EMM),

University of Nantes, France


Effects of various drilling procedures and of the cold expansion on the fatigue life of rivet holes


Abstract. The use of riveting as assembly technique, especially in the aeronautical construction, requires the implementation of several holes in aluminium alloy sheets, which leads to an inhomogeneous stress and strain field distribution and to stress localization in the drilled zones which will affect the fatigue life of 2024-T3 aluminium alloy.

In addition, the machining process used for drilling can increase or decrease the fatigue life of materials. This paper presents the results of an experimental study whose main objective is firstly to determine which drilling procedure least affects the fatigue life and to show the role of the residual stresses introduced by each process on the fatigue behaviour of the material, and secondly to evaluate the effects of the residual stress field caused by the cold expansion of the hole on the fatigue life improving and on the crack initiation and propagation in the 2024-T3 aluminium alloy.

For that four drilling procedures are compared in fatigue: directly drilling bit of the wanted diameter, drilling a small diameter hole called a pilot hole in the rivet hole location prior to drilling the final diameter using a reamer, a water jet and finally punching.

            The hole quality is compared in two parameters: conicity and surface quality, which are observed using a Scanning Electron Microscopy (SEM).

X-ray diffraction is used to determine the residual stress profile resulting of each drilling procedure and to measure the residual stresses resulting of the cold expansion on the hole edge.


Key words: drilling procedures, cold expansion, rivet holes, residual stresses, fatigue life.