
Archive issue  vol.8 No.1
1.
NORMAL STRESS DIFFERENCES IN COUETTE FLOW OF GRANULAR MATERIALS
J. KUMAR, C. LAKSHMANA RAO
Department of Applied Mechanics
Indian Institute of Technology, Madras
Chennai  600036, INDIA
M. MASSOUDI
U.S. Department of Energy
National Energy Technology Laboratory
P.O. Box 10940, Pittsburgh, PA 15236, USA
email: massoudi@netl.doe.gov
Normal stress differences, a phenomenon which is exhibited by many nonNewtonian fluids or nonlinear elastic materials, also arises in the Couette flow of granular materials. This problem is studied using a continuum model proposed by Rajagopal and Massoudi (1990). For a steady, fully developed condition, the governing equations were reduced to a system of coupled nonlinear ordinary differential equations, and the resulting boundary value problem was solved numerically (Kumar et al., 2003). The expression for one of the normal stress differences is derived in this paper and from the values of volume fraction obtained in (Kumar et al., 2003), the normal stress difference is calculated. The effect of material parameters, i.e., dimensionless numbers on the normal stress difference is studied. It is observed that the distribution parameter, "B_{2}" and the density parameter "P" affect the normal stress differences most.

Key words: 
granular materials, normal stress effects, continuum mechanics. 
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2.
GENERATION OF WAVES IN A RUNNING STREAM
U. BASU
Department of Applied Mathematics, Calcutta University
92 A.P.C. Road, Calcutta  700 009, INDIA
email: umabasu@cucc.ernet.in
P. GHOSH
Physics and Applied Mathematics Unit, Indian Statistical Institute
203, B.T. Road, Calcutta  700 035, INDIA
In this paper, a problem of the twodimensional wave generation due to an initial disturbance at the free surface in an ocean of finite depth in the presence of surface tension and a uniform running stream is investigated. Using linear theory, the problem is formulated as an initial value problem for the velocity potential describing the ensuing motion in the fluid. In the mathematical analysis the Laplace and Hankel transform techniques have been utilized to obtain the elevation of the free surface in the form of an infinite integral. This is then evaluated asymptotically for large time and distance by applying the method of stationary phase. The form of the free surface is depicted graphically for two types of initial disturbances. The effect of the surface tension and the presence of the running stream on the wave motion are discussed.

Key words: 
wave generation, surface tension, running stream, stationary phase, free surface elevation. 
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3.
NONLINEAR VISCOELASTIC BEHAVIOR OF FLEXIBLE CELLULAR PLASTICS: REFINED ROD MODEL
D.A. CHERNOUS, S.V. SHILKO, D.A. KONYOK
and Yu.M. PLESKACHEVSKY
V.A. Belyi MetalPolymer Research Institute, Belarussian Academy of Sciences
32A Kirov Str., 246050 Gomel, BELARUS
email: depa10@tut.by
A new technique of modelling nonlinear viscoelastic behavior of lowdensity flexible foams including cellular plastics used in advanced implants, namely, artificial analogs of periodont of the dental system and trabecular bones of the skeletal system has been developed. The material microstructure is modeled by a rod structure with chaotically oriented cubic cells. Young's modulus and critical strain (i.e., the case of stability loosing) dependence on the solid state phase fraction of flexible cellular plastics has been investigated. The dependences of tangential stress on shear strain, hydrostatic pressure on volume strain and axial stress on longitudinal deformation with taking into account solid phase viscosity at a given strain rate have been obtained for the simulated materials. The numerical results led to the conclusion that at a certain compression rate the transversal strain factor of a material becomes negative.

Key words: 
flexible foams, cellular structures, implants, large rod deflections, viscoelastic behavior, structural unit. 
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4.
HALL EFFECTS ON UNSTEADY HYDROMAGNETIC FLOW IN A ROTATING SYSTEM WITH OSCILLATING PRESSURE GRADIENT
S.K. GHOSH
Department of Mathematics, Narajole Raj College
P.O. Narajole, Dist.  Midnapore, West Bengal, INDIA
email: g_swapan@rediffmail.com
I. POP
Faculty of Mathematics, University of Cluj
R3400 Cluj, CP 253, ROMANIA
email: popi@math.ubbcluj.ro
The Hall effects on unsteady MHD plasma behaviour of a rotating environment with oscillating pressure gradient in the presence of a transverse magnetic field have been studied. The solution in a dimensionless form contains five pertinent flow parameters, viz., 'alpha'_{m}, E, P, 'omega' and m are, respectively, the magnetic interaction parameter, the Ekman number, the magnetic Prandtl number, the inertial frequency and the Hall current parameter. A new approach is based on the plasma behaviour in the electromagnetic field in a rotating environment which corresponds to inertial frequency over the oscillating pressure gradient. Eventually, the dominance of inertial frequency is experienced by the mechanism; the whole system stops due to the absence of inertial frequency of a rotating environment.

Key words: 
Hall current, electric field, magnetic interaction parameter, Ekman number, magnetic Prandtl number, inertial frequency, boundary layer. 
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5.
RELIABLE HIGH SPEED SPINDLES BY OPTIMUM BEARINGS PRELOAD
G. HAGIU
"Gh. Asachi" Technical University of Iasi
Department of Machine Design
63 D. Mangeron Blvd., 6000 Iasi, ROMANIA
To design a high speed spindle with enhanced qualitative performances  high accuracy and service life together with a stable dynamic and thermal regime  two main conditions have to be secured: an optimum internal load distribution on the bearings and an efficient and safe lubrication regime. The preload force, by the significant changes produced on the bearings functioning parameters, i.e., kinematics, both load internal distribution and amount, appears as one of the most important factors affecting the main reliability parameters of high speed spindles. A theoretical research assisted by an experimental validation on grinding machine spindles was developed to determine the bearings preload influence on the spindles main reliability parameters, i.e., service life, dynamic and thermal stability. From the analysis of the results obtained, the optimum bearings preloads able to secure, in given operating conditions, the imposed reliability parameters for the high speed spindles were determined.

Key words: 
bearing, high speed spindle, reliability, optimum preload bearings. 
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6.
EXACT SOLUTIONS TO AN INCOMPRESSIBLE SECONDGRADE FLUID FLOW EQUATIONS
R.K. NAEEM and S.S. ZIA
Department of Mathematics, University of Karachi, Karachi  75270, PAKISTAN
email: ss.sadia@yahoo.com, s_sadiazia@yahoo.co.in
Employing complex variables and complex functions the exact solutions to equations governing the motion of an incompressible secondgrade fluid are determined.

Key words: 
exact solutions, fluid flow equations, incompressible fluid, complex variable technique, secondgrade fluid. 
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7.
SOME ASPECTS OF RIKITAKE SYSTEM OF DYNAMICAL EQUATIONS
S. PORIA
Department of Mathematics, Midnapur College
Midnapur, West Bengal, INDIA
B.K. CHAKRABORTY
Sodepur Deshbandhu Vidyapith For Boys
Sodepur, 24 Parganas (North), West Bengal, INDIA
H.P. MAZUMDAR
Physics and Applied Mathematics Unit
Indian Statistical Institute, Calcutta  700035, INDIA
email: hpm@isical.ac.in
In this paper, some characteristic features of a dynamical system proposed by Rikitake (1958), as a model for the selfgeneration of the Earth's magnetic field by large current carrying eddies in the core are examined. First, a linear stability analysis of a fixed point of the Rikitake system of three dynamical equations is made. Next, utilizing the conjecture that an integral of motion must assume constant value when evaluated at a singularity, a few integrals of motion of the Rikitake system are worked out. Finally, the effects of a linear feedback control on the linearized versions of the Rikitake system in terms of state perturbation variables, are investigated. The dynamical equations are solved numerically by the fourth order RungeKutta method. The results are presented graphically and discussed.

Key words: 
dynamical system, stability analysis, integrals of motion, feedback control. 
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8.
PARAMETER INVESTIGATION AND MULTICRITERIA DESIGN OPTIMISATION OF PLANETARY GEAR TRAIN
B.B. ROSIC
Department of Mechanical Engineering, University of Belgrade
27. marta 80, Belgrade, YUGOSLAVIA
email: boza.r@eunet.yu
This paper presents an analytical and computer aided procedure for the multicriteria design optimisation of planetary gear trains. Geometric and operating constraints for internal and external gears and whole planetary gear trains are defined. For the defined multicriteria optimisation model of the planetary gear train, a computer program based on an interactive dialogue is developed. The results of the program are presented on an appropriate tables with Paretooptimal solutions. A graphical illustration of the above problem is presented in terms of objective functions.

Key words: 
planetary gear train, gear ratio, efficiency, internal and external gears, optimization. 
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9.
INERTIA EFFECTS IN A CURVILINEAR SQUEEZE FILM BEARING WITH ONE POROUS WALL LUBRICATED BY A POWERLAW FLUID
A. WALICKA, E. WALICKI, P. JURCZAK and D. MICHALSKI
University of Zielona Góra, Department of Mechanics
ul. Szafrana 2, P.O. Box 47, 65516 Zielona Góra, POLAND
email: e.walicki@ijame.uz.zgora.pl
The flow of a powerlaw lubricant in a squeeze film bearing with one porous wall is considered. The bearing is modelled by two curvilinear surfaces and the porous wall is adhered to the curved nonporous surface. The flow in the bearing clearance is considered with inertia and the NavierStokes and Poisson equations are uncoupled by using the MorganCameron approximation. Using the averaged inertia method the closedform solution is obtained. A step bearing is discussed as an example.

Key words: 
curvilinear bearing, inertia effect, porous wall, squeeze film, nonNewtonian fluid. 
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10.
VIBRATION CONTROL OF A BUILDING WITH ATMD UNDER EARTHQUAKE EXCITATION
N. YAGIZ
Istanbul University, Faculty of Engineering
Department of Mechanical Engineering
34850 Avcilar, Istanbul, TURKEY
email: nurkany@istanbul.edu.tr
In this paper, the application of an active tuned mass damper (ATMD) is studied for controlling the earthquake induced vibration of buildings using a sliding mode control (SMC). Since the structural system may have uncertainties and/or parameter changes, the sliding mode control has been preferred because of its robust character. Additionally, this control method can easily be applied to nonlinear systems. The time history of the base and top floor displacements, control force input and frequency responses of both the uncontrolled and sliding mode of a realistic 9storey building model controlled by the ATMD are presented at the end of the study. The earthquake ground motion used is obtained using the seismic data of the Marmara Earthquake (M_{w} = 7.4) in Turkey in August 17th, 1999.

Key words: 
active tuned mass damper, sliding mode control, earthquake induced vibration, 9storey building model. 
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11. Brief note
RADIATION EFFECTS ON FLOW PAST AN IMPULSIVELY STARTED INFINITE VERTICAL PLATE WITH VARIABLE TEMPERATURE
R. MUTHUCUMARASWAMY
Department of Information Technology
Sri Venkateswara College of Engineering
Sriperumbudur 602 105, INDIA
email: msamy@svce.ac.in
P. GANESAN
Department of Mathematics, Anna University
Chennai 600 025, INDIA
email: ganesan@annauniv.edu
The effects of thermal radiation on flow past an impulsively started infinite vertical plate in the presence of variable temperature is considered. The temperature near the plate is made to rise linearly with time. The fluid considered is a gray, absorbingemitting radiation but a nonscattering medium. The dimensionless governing equations are solved using the Laplacetransform technique. The velocity and temperature are studied for different parameters like the Prandtl number, time and radiation parameter. It is observed that the velocity slightly decreases with increasing the value of the radiation parameter.

Key words: 
free convection, radiation. 
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12. Brief note
THERMAL RADIATION OF AN OPTICALLY THIN GRAY GAS
A. RAPTIS and C. PERDIKIS
University of Ioannina, Department of Mathematics
Ioannina 451 10, GREECE
email: araptis@cc.uoi.gr
In this paper, we study the effects of thermal radiation on the unsteady free convection and mass transfer boundary layer over a vertical moving plate of an optically thin gray gas.

Key words: 
free convection, radiation. 
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13. Laboratory report
MACHINERY HEALTH MONITORING AND MAINTENANCE TRIBOLOGY RESEARCH AT KING MONGKUT'S INSTITUTE OF TECHNOLOGY NORTH BANGKOK
S. RAADNUI
Machinery Health Monitoring and Tribology Laboratory
Department of Production Engineering, Faculty of Engineering
King Mongkut's Institute of Technology North Bangkok
1518 Pibulsongkram Road, Dusit, Bangkok, 10800, THAILAND
email: srr@kmitnb.ac.th
The King Mongkut's Institute of Technology North Bangkok (KMITNB), founded in 1959 with the support of the government of the Federal Republic of Germany, is one of the premier higher education institutions in Thailand with a strong base in applied sciences, technology and engineering. The faculty of engineering, the largest of the four faculties of the institute, was founded with an aim to provide a range of professional engineering education service to meet the community and industry at the early phase of industrialization in Thailand. The degrees were established to fill a need for bettereducated engineers in the practice of engineering as well as in research and development.
The Machinery Health Monitoring and Tribology Laboratory (MHM and Tribo. Lab.) forms part of the Production Engineering Department, Faculty of Engineering. Currently, machinery health monitoring research is combined with tribology studies. In general terms, the current activities of the condition monitoring and tribology research group include:
condition monitoring studies relating to oil and wear debris analysis,
hydraulic failure studies as related to contaminants,
routine oil, wear debris and contamination analysis for industry,
developments of new and improved condition monitoring techniques, especially used oil, wear debris and contamination analysis,
fundamental of friction, lubrication and wear studies,
maintenance strategy studies for productivity improvement.

Key words: 
health monitoring, machinery, tribology. 
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