Journal of Theoretical and Applied Mechanics

Volume 40, Number 1, 2010

 

Contents

 

V. S. Jivkov

 

Department of Theory of Mechanisms and Machines,

Faculty of Machine Technology, Technical University of Sofia,

8, Kliment Ohridski Str., BG-1000 Sofia, Bulgaria,

e-mail: jivkov@tu-sofia.bg

 

STABILITY OF STEADY-STATE VIBRATIONS OF A ROTOR IN HOMOGENEOUS ELASTO-VISCOUS FIELD

 

Abstract. The aim of the present paper is to study virtual steady-state vibrations in the neighborhood of resonance conditions of a rotor with six degrees of freedom in linear homogeneous elasto-viscous field. Unstable frequencies zones are determined by "limited" power of an electric motor with linear characteristic and only one time-constant. Bogoliubov-Mitropolsky`s asymptotically method is applied in the neighborhood of single basic resonance by small difference between natural and driving frequencies. The influence of the motor’s time-constant is analyzed on the value of unstable frequency zones by quasi steady-state increasing/decreasing frequencies (jump phenomenon). Experimental result is applied.

 

Key words: Stability, Rotor dynamics, “Limited” excitation, Sommerfield's effect.

 

 

K. Georgiev

 

Institute for Parallel Processing, Bulgarian Academy of Sciences,

25-A, Acad. G. Bonchev, BG-1113 Sofia, Bulgaria,

e-mail: georgiev@parallel.bas.bg

 

Z. Zlatev

National Environmental Research Institute,

University of Aarhus,

Frederiksborgvej 399, P.O. Box 358, DK-4000 Roskilde, Denmark,

e-mail: zz@dmu.dk

 

COMPARISON RESULTS OF RUNNING THE DANISH

EULERIAN MODEL FOR LONG-RANGE TRANSPORT OF

AIR POLLUTANTS ON DIFFERENT HIGH

PERFORMANCE COMPUTERS *

 

ABSTRACT. The Danish Eulerian Model (UNI-DEM) is an Eulerian model for studying the transport of air pollutants on large scale. Originally, the model was developed at the National Environmental Research Institute (NERI) of Denmark (Roskilde, Denmark). The model computational domain covers Europe and some neighbour parts belong to the Atlantic Ocean, Asia and Africa. If the model is to be applied by using fine grids, then its discretization leads to a huge computational problem which implies that it must be run only on high-performance computer architectures.

The implementation and tuning of such a complex large-scale model on each different computer is a non trivial task. Here, some comparison results of running of this model on different kind of vector (CRAYC92A, Fujitsu, etc.), parallel computers with distributed memory (IBMSP, CRAY T3E, Beowulf clusters, Macintosh G4 clusters, etc.), parallel computers with shared memory (SGI Origin, SUN, etc.) and parallel computers with two level of parallelism (IBM SMP, IBM BlueGene/P, clusters of multiprocessor nodes, etc.) will be presented. The main idea in the parallel version of UNI-DEM is domain partitioning approach. The OpenMP Application Program Interface is used in the versions of the code for shared memory parallel computers. The MPI (Message Passing Interface) standard library routines are used as a communication library for the UNI-DEM version for distributed memory parallel computers. While, both communication libraries are used in the code prepared for parallel computers with two levels of parallelism. Discussions according to the effective use of the cache and hierarchical memories of the modern computers as well as the performance, speed-ups and efficiency achieved are presented. The results obtained prove that the parallel code ofDEM, created by using MPI standart library, appears to be highly portable and with good efficiency and scalability on different kind of parallel computers both wit shared and distributed memories.

Key words:  environmental problems, air pollution modeling, mathematical modeling, computer modeling, high-performance computer architectures.

 

S. Tabakova

 

Department of Mechanics, TU – Sofia, branch Plovdiv,

25, Tzanko Djustabanov, 4000 Plovdiv, Bulgaria,

Institute of Mechanics, Bulgarian Academy of Sciences,

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

e-mail: stabakova@gmail.com

 

S. Radev

 

Institute of Mechanics, Bulgarian Academy of Sciences,

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

e-mail: stradev@imbm.bas.bg

 

LINEAR STABILITY OF A FREE VISCOUS FILM UNDER

THE VAN-DER-WAALS FORCE ACTION*

 

ABSTRACT.. In the present work a free viscous film, attached on a rectangular frame surrounded by an ambient gas is considered. The film linear stability is analyzed, when small disturbances are imposed on its steady state. The non-linear system for the disturbances is solved numerically by the method of differential Gauss elimination. It is found that when the van-der-Waals forces are not active, the film steady shapes are stable. The inclusion of the van-der-Waals forces creates unstable film steady shapes at some combinations of the process parameters, while at other combinations the steady shapes remain stable.

 

KEY WORDS: free thin film, van-der-Waals force, linear stability, differential Gauss elimination, eigenvalue search.

 

M.Hennenberg

 

Microgravity Research Center, Fac.Sc.Appl., Universite Libre de Bruxelles, Av.F.D.Roosevelt, Brussels 1050, Belgium

e-mail: mhennenb@ulb.ac.be

 

S.Slavtchev

Institute of Mechanics, Bulgarian Academy of Sciences,

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

e-mail: slavcho@imbm.bas.bg

 

B. Weyssow

 

Physique Theeorique, Fac.Sciences, UniversiteLibre de Bruxelles, Boulevard du Triomphe, Brussels 1050, Belgium,

e-mail: bweyssow@ulb.ac.be

 

OSCILLATORY MAGNETIC FIELD ACTION ON A FERROFLUID LAYER

 

ABSTRACT. We develop here the formulation of a linear stability problem for an isothermal ferrofluid layer, submitted to a magnetic field that contains a constant and an oscillating part. The Laplace boundary condition describing the liquid free surface deformation, is reduced to a generic Hill’s equation in two important cases, the first one corresponding to a hearly inviscid case, the second one assuming the validity of the lubrication approximation.

 

KEY WORDS: ferrofluid, oscillating magneting field, marginal stability, parametric resonance, Hill’s equation.

 

P. Boyanova

 

Institute for Parallel Processing, Bulgarian Academy of Sciences,

25A, Acad. G. Bontchev, BG-1113 Sofia, Bulgaria,

e-mail:petia@parallel.bas.bg

 

S. Margenov

 

Institute for Parallel Processing, Bulgarian Academy of Sciences,

25A, Acad. G. Bontchev, BG-1113 Sofia, Bulgaria,

e-mail:margenov@parallel.bas.bg

 

 

ON MULTILEVEL ITERATIVE METHODS FOR

NAVIER-STOKES PROBLEMS *

 

ABSTRACT. Two projection schemes which are based on nonconforming Crouzeix-Raviart finite element approximation of the velocities and piece-wise constant approximation of the pressure are considered. The important advantage of these approximations is that the divergence of the velocity field is zero inside each element, i.e. the approximation is locally conservative. We show that optimal order Algebraic MultiLevel Iteration (AMLI) preconditioners can be successfully applied to the decoupled scalar elliptic problems at the Prediction step as well as to the mixed FEM problem at the Projection step. As a result, the related composite time-stepping solution methods have a total computational complexity of optimal order.

 

KEY WORDS: time dependent Navier-Stokes, nonconforming FEM,

projection scheme, multilevel PCG solver.

 

E. E. Gdoutos

 

Office of Theoretical and Applied Mechanics of the Academy of Athens,

School of Engineering, Democritus University of Thrace,

Institute of Mechanics, Bulgarian Academy of Sciences,

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

GR-671 00 Xanthi, Greece,

e-mail: egdoutos@civil.duth.gr

 

 

TRIAXIAL STATE OF STRESS AT CRACK TIPS STUDIED

BY CAUSTICS

ABSTRACT.. The optical method of caustics is used to study the triaxiality of the stress field in the neighbourhood of a crack tip in a tension specimen. It is found that the state of stress in the vicinity of the crack tip is three-dimensional up to a limiting distance from the tip, after which it approaches to plane stress. This distance depends mainly on the ratio of the crack length to specimen thickness.

 

KEY WORDS: Stress triaxiality, stress intensity factors, cracks, caustics,

plane stress, plane strain.

 

M. Abdennadher, W. Siala, L. Hammami, M. Haddar

 

Research Unit of Mechanical, Modelization and Manufacturing,

National School of Engineers of Sfax, B.P.W. 1173 Sfax, Tunisia,

e-mails: moezabd@yahoo.fr, siala w@yahoo.fr,

lotfi.hammami@enis.rnu.tn, mohamed.haddar@enis.rnu.tn

 

 

DYNAMIC BEHAVIOUR AND NOISE TRANSMISSION OF

A SANDWICH PLATE WITH VISCOELASTIC THICK

CORE*

ABSTRACT. The dynamic response and noise transmission of a thick sandwich plate were investigated by using a mixed method, based on Finite Element (FE) and Boundary Finite Element (BFE) methods. The sandwich plate was composed of three perfectly glued layers, two thin elastic face layer and a three dimensional viscoelastic core. The integration through thickness of the functional of energy leads to bi-dimensional problems. A refined 2D finite element is developed and applied in modelling of the dynamic equation. The proposed model can correctly describe the damping developed inside the thick viscoelastic core by considering a complex Young and shear modulus of viscoelastic material. The noise transmission was obtained by using BFE. The influences of the viscoelastic core thickness and geometrical parameters on modal damping and dynamic behaviour are also discussed. Results show that the viscoelastic core thickness in the sandwich structure has a great effect on the energy dissipation of sandwich plate.

KEY WORDS: composite (sandwich) structure, noise, dynamics.

 

I.Jordanov

 

Institute of Mechanics, Bulgarian Academy of Sciences,

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

e-mail: ivan@imbm.bas.bg

 

Z.Dimitrova

 

“G.Nadjakov” Institute for Solid State Physics, B ulgarian Academy of Sciences, 72, Tsarigradsko Chausee, BG-1784 Sofia, Bulgaria,

e-mail: zdim@phys.bas.bg

 

ON NONLINEAR WAVES OF MIGRATION

 

ABSTRACT. We study waves caused by migration of the members of interacting populations. We consider the migration as diffusion process influenced by the changing values of the birth rates and coefficients of interaction between the populations. We show that kink solutions of the obtained model equation are possible. We obtain an approximate solution of for small value of the ratio between the coefficient of diffusion and the wave velocity.

 

KEY WORDS: nonlinear dynamics, population dynamics, migration, solitary waves, kinks, asymptonic stability.