Journal of Theoretical and Applied Mechanics

Volume 37, Number 2, 2007



M. A. Ferman


Aerospace & Mechanical Engineering Department,

Parks College, St. Louis University, St. Louis, MO, USA,



E. Aguilar


Consultant for ABGAM, GAMESA Co., Madrid, Spain


Experiences with Experimental and Analytical Flutter Studies of a Rhomboid Wing Flutter Model


Abstract. Rhomboid type, joined-wing, designs are receiving significant attention by aircraft designers. While these designs are superior to conventional aircraft wings in structural properties such as aeroelasticity, and in performance requirements, only limited experimental work has been done with flutter testing. Thus, this research was carried out to provide experimental flutter results by testing models in the Low Speed Wind Tunnel at Parks College, Saint Louis University. Analytical methods were used to guide the model design and to compare with vibration and flutter test results. Close correlations were found between the analytical and experimental results for vibration and flutter, thus confirming a sound approach was taken from the model design and construction stages to analyses and testing.


Key words: aeroelasticity, joined wing, flutter, wind tunnel.


S. P. Radev


Institute of Mechanics, Bulgarian Academy of Sciences,

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



F. Onofri, L. Tadrist


PolytechMarseille- IUSTI-UMR CNRS no 6595, Technopole de Chateau Gombert,

University of Provence, 5, rue Enrico Fermi, Marseille 13453, France,




Sinuous Instability of a Viscous Capillary jet into an immiscible non-viscous fluid.

Part Ii: different forms and numerical analysis of the dispersion equation


Abstract. In the present (second) part of the paper a linear instability analysis of a viscous capillary jet flowing into an inviscid immiscible fluid is performed. The analysis is based on the full 3D-Navier-Stokes equations written in respect of the moving trihedron of the jet axis. A dispersion equation of the sinuous disturbances is derived accounting for the effect of the jet viscosity and ambient density, while the viscosity of the surrounding fluid is neglected. Two limiting cases are considered and corresponding reduced forms of the dispersion equation are obtained. They concern the small wave number case as well as the case of non-viscous jet. Some numerical results illustrating the growth rate and speed of propagation of the disturbances are shown.


Key words: capillary jet, sinuous instability.


L. Parashkevova, N. Bontcheva


Institute of Mechanics, Bulgarian Academy of Sciences,

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



P. Petrov, G. Petzov


Technical University Varna,

1, Studentska Str., BG-9010 Varna, Bulgaria,



Finite element simulation of gears warm die forging


Abstract. Warm die forging of improved stainless steel type 304 AISI with preliminary obtained fine microstructure is considered. The forging process is examined by means of FE simulation. Temperature, stress and strain fields are defined. By varying with the preheating temperature and forging velocity the operative forging parameters are depicted.


Key words: stainless steel, warm forging, gear, FEM.


S. Cherneva, R. Iankov, V. Kavarjikov


Institute of Mechanics, Bulgarian Academy of Sciences,

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




D. Stoychev


Institute of Physical Chemistry, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str., Bl. 11, Sofia 1113, Bulgaria,



Numerical modelling of microindentation experiment for determination mechanical characteristics of metals and alloys


Abstract. The present paper aims at proposing an appropriate mathematical model and a finite element model of the microhardness test describing the deformation process. The finite element numerical simulations of Vickers microhardness test are performed. Different 2D axisymmetric and 3D-numerical finite element models are considered to describe the deformation processes. For the two-dimensional finite element model a substituting rigid conical indenter is used as an equivalent to the standard tetrahedral Vickers’ pyramid. As a result of 2D and 3D finite element simulations, the load-penetration depth (P-h) curves are obtained numerically and compared with the P-h curves obtained from the experimental data. The results, obtained by numerical simulations give good coincidence with the experimental results.


Key words: microindentation hardness test, finite element method, mechanical characteristics, load-penetration depth curve.


H. S. Takhar


Manchester Metropolitan University, Manchester, M5, England, U.K.,



R. Bhargava, S. Rawat


Indian Institute of Technology, Roorkee-247667, India,



T. A. Bég


Engineering Mechanics/Earthquake Engineering Consultant,

18 Milton Grove, Manchester, M16 OBP, UK,

e-mail: ihd001@


O. Anwar Bég


Engovation Aerodynamics and Biomechanics Research,

15, Southmere Avenue, Great Horton, Bradford, BD7 3NU, England, UK,



T. K. Hung


Civil Engineering and Neurosurgery, University of Pittsburgh,

Pennsylvania, USA.


Biomagnetic Hydrodynamics in a 2-Dimensional non-Darcian Porous Medium: Finite Element Study


Abstract. In this paper we consider the two-dimensional fully developed steady, Newtonian hydrodynamic flow of a non-conducting biomagnetic fluid (blood) in a two-dimensional (X-Y) non-Darcy porous medium. A drag force model is used to simulate the porous Darcian linear impedance and Forcheimmer quadratic drag in both X and Y directions. The porous biomagnetic flow equations are transformed into a set of coupled dimensionless partial differential equations which are then solved used a finite element model. We study the influence of biomagnetic number (NH), Darcy number (Da) and also Forcheimmer number (Fs) on the X- and Y-direction velocity profiles in detail and also the interactive effects of these parameters. A number of special cases of the flow model are also mentioned. The model finds applications in biomedical device technology, haemotoligical filtration systems, and also in transport in tumors, soft connective tissue zones and electromagnetic therapy modelling.


Key words: biomagnetic, fluid dynamics, non-Darcy porous media, finite element method, magneto-biomedical devices, tissue transport modelling.


S. Nikolov, V. Kotev


Institute of Mechanics, Bulgarian Academy of Sciences,

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



E. D. Yankulova


Faculty of Biology, University of Sofia,

8, Dragan Tzankov Blvd, 1421 Sofia, Bulgaria




Abstract. A likely mathematical model of the Human Immunodeficiency Virus (HIV) infection (describing the interaction between the HIV viruses and the immune system) is proposed by application of the logistic growth function to a HIV viruses population. We investigate the dynamical and bifurcation behaviour of this model on the basis of Lyapunov-Andronov’s theory. It is found that: (i) the HIV infection can be of three types; (ii) the boundary of stability in a latent type infection (the most uncommon one) and an active type infection (being most common) is dangerous; (iii) in the transition zone from a controlled infection to an active infection, the model has basic oscillations with period two and quasiperiodic oscillations near the basic one.


Key words: HIV infection, mathematical model, bifurcation analysis.