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1

Inertial elastic instability of rotating nano disks

Güven Uğur

Journal of Theoretical and Applied Mechanics

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2019

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Vol. 57 nr 4

853--858

EN

In this work, the static inertial-elastic instability of rotating nano disks is investigated with the centrifugal force formulation considering the radial displacement. Thus, Brunelle’s previous local solution is generalized by using Eringen’s nonlocal elasticity theory. The variations of critical rotation speeds with the nonlocal scale parameter are illustrated under different boundary conditions. It is seen that the critical rotation speeds decrease as the nonlocal scale parameters increase for all cases. Also, it is remarkable that the presented results are affected significantly from the boundary conditions.

2

Ferrofluid flow due to a rotating disk in the presence of a non-uniform magnetic field

Bhandari A., Kumar V.

International Journal of Applied Mechanics and Engineering

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2016

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Vol. 21, no. 2

273--283

EN

The flow of a ferrofluid due to a rotating disk in the presence of a non-uniform magnetic field in the axial direction is studied through mathematical modeling of the problem. Contour and surface plots in the presence of 10 kilo-ampere/meter, 100 kilo-ampere/meter magnetization force are presented here for radial, tangential and axial velocity profiles, and results are also drawn for the magnetic field intensity. These results are compared with the ordinary case where magnetization force is absent.

3

Analysis of the liquid flow in a vessel with a rotating disk at the liquid surface

Suchecki W.

Chemical and Process Engineering

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2014

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Vol. 35, nr 1

3--18

EN

This study is concerned with liquid flow induced by a disk which rotates steadily around its axis and touches the free surface of liquid contained in a cylindrical vessel. It is a simplified model of the flow in the inlet part of a vertical cooling crystallizer where a rotary distributor of inflowing solution is situated above the free surface of solution contained in the crystalliser. Numerical simulations of flow phenomena were conducted and the simulation results were interpreted assuming an analogy with Kármán’s theoretical equations. In a cylindrical coordinate system, the components of flow velocity were identified as functions of distance from the surface of the rotating disk. The experimental setup was developed to measure velocity fields, using digital particle velocimetry and optical flow. Conclusions concerning the influence of disc rotation on liquid velocity fields were presented and the experimental results were found to confirm the results of numerical simulation. On the basis of simulation data, an approximation function was determined to describe the relationship between the circumferential component of flow velocity and the distance from the disk.

4

The effect of suction on magnetohydrodynamic forced flow of a viscous electrically conducting fluid through a porous medium induced by a rotating disk

Sharma B. K., Jha A. K., Chaudhary R. C.

International Journal of Applied Mechanics and Engineering

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2012

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Vol. 17, no. 4

1297-1308

EN

The present paper investigates the steady MHD forced flow of an incompressible viscous electrically conducting fluid, due to an infinite rotating disk bounded by a porous medium. A uniform suction is applied on the upper disk. It is assumed that the flow between the disk and the porous medium is governed by Navier-Stokes equations and that in the porous medium by Brinkman equations. Flows in the two regions are matched at the interface by assuming that the velocity and stress components are continuous at it. At the interface (porous medium-clear fluid boundary), a modified set of boundary conditions suggested by Ochao-Tapia and Whittaker is applied. Assuming constant suction at the disk surface, analytical expressions for the velocity and shearing stress are calculated and effects of various parameters upon them are examined.

5

Modelling of rotating disk vibration with fixed blades

Zeman V., Sasek J., Byrtus M

Modelling and Optimization of Physical Systems

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2009

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z. 8

125--130

EN

The paper presents the method for the mathematical modelling of bladed disk vibrations. The blades are considered as one dimensional continuum fixed with three-dimensional elastic disk centrally clamped into turbine rotor rotating with constant speed. A dynamic analysis and optimization of the bladed disk Vibration with damping elements requires a development of the efficient method pointing to the bladed disk model with relatively small DOF number. In the future, such model will enable simulations of the whole system nonlinear Vibration influenced by slip contact interactions in inner couplings between blades.

CS

Příspěvek uvádí metodu matematického modelování kmitání rotujících olopatkovaných disků. Lopatky jsou uvažovány jako jednodimenzionální kontinua vetknutá do třídimenzionálního poddajného disku středově upevněného k rotoru turbíny, který rotuje konstantní úhlovou rychlostí. Dynamická analýza a optimalizace olopatkovaných disků s tlumícími elementy vyžaduje vyvinout efektivní metodu směřující k modelu olopatkovaného disku s relativně malým počtem stupňů volnosti. Takový model v budoucnu umožní simulovat nelineární kmitání celého systému ovlivněné interakcí kluzných kontaktních ploch ve vnitřních vazbách mezi lopatkami.

6

Próba optymalizacji tarcz wirujących ze względu na nośność rozdzielczą

Szuwalski K.

Czasopismo Techniczne. Mechanika

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2008

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R. 105, z. 4-M

135-142

PL

Przeprowadzona analiza wykazała, że dla zagadnienia nośności rozdzielczej nie da się sformułować problemu optymalizacji. Kresem górnym, a zarazem najlepszym możliwym rozwiązaniem jest zawsze dojście do układu, w którym nośność rozdzielcza nie wystąpi. Przedstawione w artykule propozycje to próba melioracji, ulepszenia układu. Jedynie dołożenie dodatkowego obciążenia w formie ciśnienia zewnętrznego stwarza szansę całkowitego wyeliminowania nośności rozdzielczej.

EN

Analysis pointed out, that formulation of the optimization problem of decohesive carrying capacity is impossible. The upper bound and simultaneously the best possible solution is to avoid decohesive carrying capacity. Presented in paper proposals in fact are attempts of structure improvements. Only additional loading in form of extermal pressure makes it possible to eliminate the effect of decohesion.

7

Flow through porous media induced by an impervious rotating disk in the presence of magnetic field

Sharma P. K., Chaudhary R. C.

Engineering Transactions

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2005

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Vol. 53, iss. 1

43-53

EN

The flow of an electrically conducting viscous incompressible fluid, due to an infinite impervious rotating disk bounded by porous medium is discussed. It is assumed that the flow between the disk and the porous medium is governed by Navier-Stokes equations and that in the porous medium - by Brinkman equations. A uniform magnetic field is applied in the direction normal to flow. At the interface (porous medium - clear fluid boundary), a modified set of boundary conditions is applied. Analytical expressions for the velocity and shearing stress are calculated and effects of various parameters upon them are examined.

8

The flow of viscous incompressible fluid confined between a rotating disk and a porous medium

Chaudhary R. C., Sharma P. K.

International Journal of Applied Mechanics and Engineering

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2004

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Vol. 9, no 3

607-612

EN

The flow of a viscous fluid induced by the rotation of a disk bounded by a porous medium fully saturated with the liquid is discussed. It is assumed that the flow between the disk and the porous medium is governed by Navier-Stokes equations and that in the porous medium by Brinkman (1947) equations. Flows in the two regions are matched at the interface by the conditions suggested by Ochao-Tapia and Whittaker (1995a; b). Analytical expressions for velocity and skin-friction are obtained and discussed.