
Archive issue  vol.6 No.4
No. 
Author(s)  Title 
Pages 
1. 
 70th Anniversary of Professor Zdzisław Kembłowski 
831832 
2. 
V.M.Soundalgekar, R.M.Lahurikar and B.S.Jaiswal  Unsteady combined convection through a porous medium bounded by an infinite vertical isothermal plate 
833842 
3. 
V.Sharma and G.C.Rana  Thermosolutal instability of Walters' (model B') viscoelastic rotating fluid permeated with suspended particles and variable gravity field in porous medium 
843860 
4. 
C.V.Sri Krishna  Suctioninjection effects on the onset of convection in suspensions occupying a porous medium 
861883 
5. 
P.I.Andharia, J.I.Gupta and G.M.Deheri  Effect of longitudinal surface roughness on the behaviour of squeeze film in a spherical bearing 
885897 
6. 
J.Galicki and M.Czech  Compression strength of pine wood in the main orthotropy plane 
899912 
7. 
T.Paul, B.K.Jha and A.K.Singh  Transient natural convection in a vertical channel 
913922 
8. 
J.N.Sharma and P.K.Sharma  On the transient waves in a thermoelastic half space 
923946 
9. 
D.Filip, R.Trîmbitas and I.Pop  The dynamics of an ideal fluid flow into an inclined cavity of a paraboloid form 
947968 
10. 
W.Eckart and A.Sadiki  Polar theory for electrorheological fluids based on extended thermodynamics 
969998 
11. 
C.Fetecau and G.Fetecau  Some properties of a 3D solution to the heat equation 
9991006 
12. 
J.R.Lin  The effects of couple stresses in the squeeze film behavior between isotropic rough rectangular plates 
10071024 
13. 
M.Massoudi  Averaged equations for developing flow of a fluidsolid mixture 
10251049 
14. 
G.Donzella, A.Mazzu and L.Solazzi  Prediction of the elastic shakedown limit in elastohydrodynamically lubricated line contacts 
10511060 
15. 
C.Carmignani and P.Forte  Active squeeze film dampers in rotordynamics 
10611072 
16. 
F.Sorge  A theoretical and experimental search for the stickslip inversion threshold 
10731087 
17. 
V.D'Agostino, D.Guida, A.Ruggiero and A.Senatore  On the influence of labyrinth seals on the dynamic behaviour of rotors 
10891098 
18. 
V.D'Agostino, D.Guida, A.Ruggiero and A.Senatore  Active magnetic bearings test rig for experimental investigation of seals 
10991107 
19. 
C.Bignardi, M.P.Cavatorta, A.Maggiora and P.M.Calderale  A finite element model for the wear analysis of polyethylene inserts in total knee joints 
11091117 

2.
UNSTEADY COMBINED CONVECTION THROUGH A POROUS MEDIUM BOUNDED BY AN INFINITE VERTICAL ISOTHERMAL PLATE
V.M. SOUNDALGEKAR
31A12, Brindavan Society, Thane (400 601), INDIA
R.M. LAHURIKAR
Department of Mathematics, Elphinstone College
Mumbai (400 023), INDIA
B.S. JAISWAL
Birla College, Kalyan (421302), INDIA
A finitedifference solution to the unsteady free and forced convection flow of a dissipative fluid through a homogeneous porous medium past an infinite vertical isothermal plate is derived. Velocity and temperature profiles are shown graphically whereas the numerical values of the skinfriction and the rate of heat transfer are listed in a table. It is observed that the velocity decreases when the permeability parameter 'sigma' or the Grashof number G or the Eckert number E increase. Temperature and the rate of heat transfer are found to increase with increasing 'sigma' but the skinfriction decreases with increasing 'sigma'. The skinfriction decreases with increasing 'sigma'. The skinfriction increases but the rate of heat transfer decreases with increasing G, E (Eckert number) or time t.

Key words: 
combined convection, unsteady, porous medium. 
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3.
ON THE TRANSIENT WAVES IN A THERMOELASTIC HALF SPACE
J.N. SHARMA
Department of Mathematics, Regional Engineering College,
Hamirpur (H.P.)  177005 INDIA
email: jns@recham.ernet.in
P.K. SHARMA
Department of Mathematics,
Government Girls Senior Secondary School Dharamsala,
Kangra (H.P.)  176215 INDIA
The distribution due to line source in a homogeneous isotropic thermoelastic half space has been investigated by applying a combination of the Laplace and Fourier transform technique in the context of generalised theories of thermoelasticity. The inverse transform integrals have been evaluated by using the Cagniard method to obtain the exact closed algebraic expressions for the displacement and temperature as a function of time and horizontal distances, which are valid for all epicentral distances. The displacement and temperature so obtained in the physical domain have been computed numerically and are presented graphically for an aluminum epoxy composite material. A comparison of results valid in different theories of thermoelasticity has also been made.

Key words: 
transient wave, relaxation time, Cagniard technique, conformal mapping, wave fronts. 
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4.
SUCTIONINJECTION – EFFECTS ON THE ONSET OF CONVECTION IN SUSPENSIONS OCCUPYING A POROUS MEDIUM
C.V. SRI KRISHNA
Department of Mathematics
Sir M. Visvesvaraya Institute of Technology
Bangalore  562 157, INDIA
email: cvsrikrishna@hotmail.com
The effect of the SuctionInjectionCombination (SIC) on the onset of RayleighBenard convection in suspensions is studied in a porous medium using the RayleighRitz technique. The critical eigenvalue is obtained for freefree, freerigid and rigidrigid boundary combinations with isothermal or adiabatic temperature condition. The microrotation of the suspended particles is assumed to vanish at the boundaries. The effect of the SIC on the critical eigenvalue is shown to be dependent on whether it is gravityaligned or antigravity. The classical results on the effect of suspended particles on convection is found to be unaltered by the SIC. The problem has industrial applications.

Key words: 
RayleighBenard, convection, suspension, suctioninjection, porous medium. 
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5.
EFFECT OF LONGITUDINAL SURFACE ROUGHNESS ON THE BEHAVIOUR OF SQUEEZE FILM IN A SPHERICAL BEARING
P.I. ANDHARIA and G.M. DEHERI
Department of Mathematics, Sardar Patel University,
Vallabh Vidyanagar 388 120, Gujarat, INDIA
email: gjbhatt@hotmail.com
J.L. GUPTA
(Retd.) Department of Mathematics, BVM Engineering College,
Vallabh Vidyanagar 388 120, Gujarat, INDIA
Efforts have been made to study the effect of longitudinal surface roughness on the performance of a hydrodynamic squeezefilm between a nonrotating spherical surface and a hemispherical bearing under a steady load using the general stochastic analysis without using a specific probability distribution for describing random roughness, It is assumed that the bearing surface as well as the surface of the approaching sphere have random roughness, which is distributed throughout the surfaces. The stochastic film thickness characterizing the roughness is considered to be symmetric with nonzero mean ('alpha') and variance ('sigma'^{2}). In order to get the expression for pressure the modified Reynolds equation is solved. Then by making use of this expression we obtain the expressions for load carrying capacity, which in turn is used to find the expression for response time. These expressions are numerically computed and the results are presented graphically as well as in tabular form. It is observed that the composite roughness of the surfaces affects the performance of the bearing significantly.

Key words: 
longitudinal, surface roughness, squeeze film bearing, Reynolds equation, pressure, load carrying capacity, squeeze time. 
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6.
COMPRESSION STRENGTH OF PINE WOOD IN THE MAIN ORTHOTROPY PLANE
J. GALICKI, M. CZECH
Chair of Applied Mechanics, Białystok Technical University
15351 Białystok, ul. Wiejska 45C, POLAND
email: mceh@cksr.ac.bialystok.pl
The paper presents a description of pine wood failure under compression. From among various failure criteria, the anisotropic failure Ascenazi criterion was used for description, assuming that wood is an orthotropic material. The experiments and description were carried out in one of the main orthotropy planes. An attempt to describe the dependence of compression strength on the density mass was made. The tests confirmed that for some assumptions the failure description of pine wood using the Askenazi criterion was possible.

Key words: 
failure criterion, orthotropy, pine wood, compression. 
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7.
TRANSIENT NATURAL CONVECTION IN A VERTICAL CHANNEL
T. PAUL, B.K. JHA and A.K. SINGH
Department of Mathematics
Banaras Hindu University, Varanasi  221005, INDIA
email: trishna_paul@rediffmail.com
This paper describes a theoretical analysis of transient motion of a viscous incompressible fluid in a vertical channel. The motion of the fluid is caused by the buoyancy force arising from the temperature gradient as a result of constant heat flux at one wall and an adiabatic condition on the other wall. Expressions for the velocity and temperature fields are derived with the help of the Laplace transform technique. The influence of the various parameters is extensively discussed with the help of graphs. It has been observed that the temperature is not influenced by the presence of an adiabatic condition on the other plate for large values of the Prandtl number.

Key words: 
natural convection, adiabatic condition, constant heat flux. 
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8.
ON THE TRANSIENT WAVES IN A THERMOELASTIC HALF SPACE
J.N. SHARMA
Department of Mathematics, Regional Engineering College,
Hamirpur (H.P.)  177005 INDIA
email: jns@recham.ernet.in
P.K. SHARMA
Department of Mathematics,
Government Girls Senior Secondary School Dharamsala,
Kangra (H.P.)  176215 INDIA
The distribution due to line source in a homogeneous isotropic thermoelastic half space has been investigated by applying a combination of the Laplace and Fourier transform technique in the context of generalised theories of thermoelasticity. The inverse transform integrals have been evaluated by using the Cagniard method to obtain the exact closed algebraic expressions for the displacement and temperature as a function of time and horizontal distances, which are valid for all epicentral distances. The displacement and temperature so obtained in the physical domain have been computed numerically and are presented graphically for an aluminum epoxy composite material. A comparison of results valid in different theories of thermoelasticity has also been made.

Key words: 
transient wave, relaxation time, Cagniard technique, conformal mapping, wave fronts. 
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9.
THE DYNAMICS OF AN IDEAL FLUID FLOW INTO AN INCLINED CAVITY OF A PARABOLOID FORM
D. FILIP, R. TRIMBITAS and I. POP
Faculty of Mathematics and Computing Science
"BabeBolyai" University
R3400 ClujNapoca, ROMANIA
email: popi@math.ubbcluj.ro
The present paper is a theoretical study of the motion of an inclined cavity of a paraboloid form filled with an ideal and incompressible fluid. The cavity is placed in the gravity field and its rototranslation motion is unknown. We look for determining the translation and rotation velocities of the cavity, the velocity potential of the fluid particles as well as the form of the fluid free surface. To this end, we shall use both the analytical and numerical methods. Numerical examples are presented in tables and graphs to elucidate the accuracy and efficiency of the proposed method.

Key words: 
cavity, ideal fluid, oscillations, eigenproblem. 
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10.
POLAR THEORY FOR ELECTRORHEOLOGICAL FLUIDS BASED ON EXTENDED THERMODYNAMICS
W. ECKART
Institute of Mechanics III, Darmstadt University of Technology,
Hochschulstr. 1, 64289 Darmstadt, GERMANY
email: eckart@mechanik.tudarmstadt.de
A. SADIKI
Institute of Energy and Powerplant Technology,
Darmstadt University of Technology,
Petersenstr. 30, 64287 Darmstadt, GERMANY
In this paper, we present a polar fluid model for electrorheological fluids using the methods of extended irreversible thermodynamics. In the first part of this paper, the fluid is described as a nonpolar fluid. We show that certain wellknown models emerge as special cases of our ratetype constitutive equations for the extra stress and the electric displacement. In the second part, we account for the induced structure in the fluid by using a polar theory. We derive ratetype constitutive equations for the (nonsymmetric) extra stress, the couple stress and the corresponding electric displacement. After discussing the transition from rate type to differential type, we compare the predicted shear stresses of both models for a viscometric flow configuration and show that only the polar model can account for different material responses, if the constant electric field is oriented either perpendicular or parallel to the flow direction.

Key words: 
electrorheological fluid, extended irreversible, thermodynamics, nonpolar theory, viscometric flow. 
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11.
SOME PROPERTIES OF A 3D SOLUTION TO THE HEAT EQUATION
C. FETECAU
Department of Mathematics,
Technical University of Iasi, R6600 Iasi, ROMANIA
G. FETECAU
Department of Electrical Engineering,
University of Galati, R6200, Galati, ROMANIA
In this note, we construct a 3D solution to the heat equation by means of the Fourier sine transform. If there exists no source of heat and the initial inner temperature of the body is zero our solution depends on x, y, z and t only by the similarity variables _ , _ and _ . Moreover, the corresponding 2D and 1D solutions appear as limiting cases for _ or _ and _ .

Key words: 
heat equation, initial boundary value problem, similarity variables. 
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12.
THE EFFECTS OF COUPLE STRESSES IN THE SQUEEZE FILM BEHAVIOR BETWEEN ISOTROPIC ROUGH RECTANGULAR PLATES
J.R. LIN
Department of Mechanical Engineering,
Nanya Institute of Technology, P.O. Box 267,
ChungLi, 320, R.O.C., TAIWAN
email: jrlin@ms18.hinet.net
On the basis of the Stokes microcontinuum theory and the Christensen stochastic model, a theoretical study of squeeze film performance for isotropic rough rectangular plates with couple stress fluids as lubricants is presented. A stochastic nonNewtonian Reynoldstype equation is derived and solved analytically for the mean film presure distribution. Squeeze film characteristics are then evaluated. According to the results, bearing surfaces with isotropic roughness pattern result in poor bearing characteristics as compared to the smoothsurface case. However. the isotropic rough plates with a nonNewtonian couple stress fluid provide a significant increase in the mean loadcarrying capacity, and compensate the response time by more than the reduction caused by surface roughness.

Key words: 
Stokes microcontinuum theory, Christensen stochastic model, surface roughness, squeeze films, rectangular plates. 
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13.
AVERAGED EQUATIONS FOR DEVELOPING FLOW OF A FLUIDSOLID MIXTURE
M. MASSOUDI
U.S. Department of Energy
National Energy Technology Laboratory
P.O. Box 10940, Pittsburgh, PA 152360940, USA
email: Massoudi@netl.doe.gov
A mathematical description of a mixture of a Newtonian fluid infused with particulate solids is presented within the context of Mixture Theory. In the absence of any thermal effects, the balance of mass and balance of linear momentum equations for each component are averaged over the cross section of the flow to obtain ordinary differential equations describing developing flow between parallel plates. The resulting coupled equations describe the variation of the average velocities and volume fraction in the direction of flow, and represent a simplified approximate set of equations which are used in engineering applications.

Key words: 
mixture theory, developing flows, multiphase flows, averaging method, granular materials. 
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14.
PREDICTION OF THE ELASTIC SHAKEDOWN LIMIT IN ELASTOHYDRODYNAMICALLY LUBRICATED LINE CONTACTS
G.DONZELLA, A.MAZZU, L.SOLAZZI
University of Brescia, Department of Mechanical Engineering,
25123 Brescia, ITALY
email: donzella@bsing.ing.unibs.it
email: mazzuan@bsing.ing.unibs.it
email: solazzi@bsing.ing.unibs.it
Different failure mechanisms are possible in cyclic contact phenomena, from wear to surface or subsurface fatigue. The limit of the material elastic shakedown is a critical parameter, because an early failure has to be expected when it is exceeded. It depends on all the tribological quantities involved in the process, which determine the effective stress field in the bulk of contacting bodies. This paper presents a program developed just to solve sequentially both the EHDL problem and the stress problem. A complete interface between these two parts of the program has been developed, thus permitting the user to make a fast evaluation of the failure risk. The effects of the rheological parameters on the limit of elastic shakedown are finally shown. The hypothesis of surface hardened components, i. e. in the presence of a material with strength varying along the depth, is also taken into consideration.

Key words: 
elastohydrodynamic lubrication, elastic shakedown, orthogonal shear stress, shear yield stress. 
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15.
ACTIVE SQUEEZE FILM DAMPERS IN ROTORDYNAMICS
C. CARMIGNANI and P. FORTE
Department of Mechanical, Nuclear and Production Engineering,
University of Pisa, Via Diotisalvi 2, 56126 Pisa, ITALY
email: carmi@ing.unipi.it
email: p.forte@ing.unipi.it
Electrorheological and magnetorheological fluids react to electric and magnetic fields respectively undergoing changes in their mechanical characteristics, viscosity and stiffness in particular. Their macroscopic behaviour is represented by the Bingham plastic model. In the last decade there has been an increasing attention toward the employment of ER and MR fluids in active bearings and active squeeze film dampers in rotordynamics. In the literature some applications of ER fluids in rotor squeeze film dampers can be found. However, nothing is reported on similar test rigs set up for MR dampers. After a review of the theoretical and experimental work reported in the literature, a feasibility study of an ER squeeze film damper and an MR one is presented and the two solutions compared.

Key words: 
rotordynamics, squeeze damper, active control, electrorheological fluid, magnetorheological fluid. 
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16.
A THEORETICAL AND EXPERIMENTAL SEARCH FOR THE STICKSLIP INVERSION THRESHOLD
F. SORGE
University of Palermo, Department of Mechanics and Aeronautics,
90128 Palermo, ITALY
email: sorge@dima.unipa.it
This paper addresses the inversion threshold between equilibrium and selfsustained oscillations through an energybalance approach quite suitable for moderately nonconservative mechanical systems with nonlinear friction/speed characteristics. The analysis leads to the definition of an inversion surface in the coordinate space of the variables, emphasizing the influence of the friction curve shape. A global insight into the system stability is presented. Several experimental results for the dry contact between a rubber belt and a pulley are also shown.

Key words: 
tribology, friction, stickslip, inversion threshold. 
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17.
ON THE INFLUENCE OF LABYRINTH SEALS ON THE DYNAMIC BEHAVIOUR OF ROTORS
V. D'AGOSTINO, D. GUIDA, A. RUGGIERO and A. SENATORE
Department of Mechanical Engineering
University of Salerno, 84084 Fisciano (SA), ITALY
email: dagostino@unisa.it
The influence of the labyrinth seals on the dynamic behaviour of a flexible rotor in journal bearings is investigated. In particular a code which makes possible the determination of the stiffness and damping coefficients and the calculus of the stability threshold in the absence of unbalance is discussed. The pressure field in journal bearings and in the labyrinth seal is determined using Warner's hypothesis and the bulkflow model with twocontrolvolume, respectively.

Key words: 
labyrinth seals, hydrodynamic journal bearings, fluid film force, stability. 
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18.
ACTIVE MAGNETIC BEARINGS TEST RIG FOR EXPERIMENTAL INVESTIGATION OF SEALS
V. D'AGOSTINO, D. GUIDA, A. RUGGIERO and A. SENATORE
Department of Mechanical Engineering
University of Salerno, 84084 Fisciano (SA), ITALY
email: dagostino@unisa.it
A test rig for the experimental validation of the rotordynamic coefficients of annular and labyrinth seals using Active Magnetic Bearings (AMBs) exciters is presented. The rotordynamic coefficients for annular and labyrinth seals are obtained, with two computer programs using the Reynolds' gas lubrication equation and the bulk flow model with two volume control, respectively. The AMBs exciters allow the rotor to levitate without contact, and to excite it with userdefined sinusoidal forces at the same time. The dynamic experiments can be conducted at various rotor speeds, whirling speeds, and with different pressure drops across the seal.

Key words: 
seals, hydrodynamic journal bearings, fluid film force, active magnetic bearings. 
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19.
A FINITE ELEMENT MODEL FOR THE WEAR ANALYSIS OF POLYETHYLENE INSERTS IN TOTAL KNEE JOINTS
C. BIGNARDI, M.P. CAVATORTA, A. MAGGIORA, P.M. CALDERALE
Department of Mechanical Engineering, Technical University of Torino
Corso Duca degli Abruzzi, 24  10129 Torino, ITALY
email: cavatorta@polito.it
In the present work, a wear evaluation of the UHMWPE tibial insert of a total knee joint is attempted based on a simple wear model. A user subroutine has been written and integrated into a commercial finite element program to allow for a structuralkinematic model of the joint. The kinematic model simulates the relative angular velocity and linear movements between tibia and femur during walking. The input data consist of internalexternal rotation and flexionextension angle as taken from the literature. In the simulation, the femoral and tibial components are compressed vertically under gait loads, while at different orientations as determined by the kinematic model. A stress history of each element during the gait cycle is determined. The calculation of the product between the contact pressure and the node relative velocity, as given by the kinematic model, is then used for a qualitative determination of wear maps.

Key words: 
total knee replacement, knee kinematics, wear, finite element model, UHMWPE. 
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