Finite deformations and incremental axisymmetric motions of a magnetoelastic tube

2017 ◽  
Vol 23 (6) ◽  
pp. 950-983 ◽  
Author(s):  
Prashant Saxena
Keyword(s):  
Magnetic Field ◽  
Internal Pressure ◽  
Applied Magnetic Field ◽  
Axial Magnetic Field ◽  
Cylindrical Tube ◽  
Axial Stretch ◽  
Mechanical Waves ◽  
Wave Guides ◽  
The Stability ◽  
Circular Cylindrical Tube

A thick-walled circular cylindrical tube made of an incompressible magnetoelastic material is subjected to a finite static deformation in the presence of an internal pressure, an axial stretch and an azimuthal or an axial magnetic field. The dependence of the static magnetoelastic deformation on the intensity of the applied magnetic field is analysed for two different magnetoelastic energy density functions. Then, superimposed on this static configuration, incremental axisymmetric motions of the tube and their dependence on the applied magnetic field and deformation parameters are studied. In particular, we show that magnetoelastic coupled waves exist only for particle motions in the azimuthal direction. For particle motion in radial and axial directions, only purely mechanical waves are able to propagate when a magnetic field is absent. The wave speeds as well as the stability of the tube can be controlled by changing the internal pressure, axial stretch and applied magnetic field that demonstrates the applicability of magneto-elastomers as wave guides and vibration absorbers.

Nonlinear magnetoelastic deformations of porous solids

2021 ◽  
pp. 108128652198896
Author(s):  
Pei Zheng ◽  
Xiong Tang ◽  
Ding Ding
Keyword(s):  
Magnetic Field ◽  
Polymer Matrix ◽  
Mechanical Response ◽  
Axial Magnetic Field ◽  
Cylindrical Tube ◽  
Porous Solid ◽  
Porous Polymer ◽  
Porous Solids ◽  
Porous Space ◽  
Circular Cylindrical Tube

A magnetoactive porous solid comprises a porous polymer matrix with embedded magnetizable particles. The connected porous space of the polymer matrix is filled with a fluid. Under externally applied magnetic fields, the magnetoactive porous solid can undergo large deformations in the elastic regime, triggering diffusive flow in the interconnected pores. The coupled hydromagnetomechanical behavior of such materials has recently received considerable attention. In this paper, the effective stress principle is applied to the constitutive modeling of the material at finite strains. In contrast to previous works, the Lagrangian porosity is no longer treated as an independent constitutive variable in the proposed formulation. To investigate the effect of the magnetic field on the mechanical response of the material, as well as to illustrate the theory, the problem of inflation of a circular cylindrical tube in the presence of a uniform axial magnetic field is formulated and solved. Computational results are presented graphically.

scholarly journals Stability of nonaxisymmetric ferrofluid flow in rotating cylinders with magnetic field

2005 ◽  
Vol 2005 (23) ◽  
pp. 3727-3737 ◽  
Author(s):  
Jitender Singh ◽  
Renu Bajaj
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Critical Value ◽  
Annular Space ◽  
Rotating Cylinders ◽  
The Stability

Effect of an axially applied magnetic field on the stability of a ferrofluid flow in an annular space between two coaxially rotating cylinders with nonaxisymmetric disturbances has been investigated numerically. The critical value of the ratioΩ∗of angular speeds of the two cylinders, at the onset of the first nonaxisymmetric mode of disturbance, has been observed to be affected by the applied magnetic field.

Stability of the Base Flow to Axisymmetric and Plane-Polar Disturbances in an Electrically Driven Flow Between Infinitely-Long, Concentric Cylinders

2000 ◽  
Vol 123 (1) ◽  
pp. 31-42
Author(s):  
J. Liu ◽  
G. Talmage ◽  
J. S. Walker
Keyword(s):  
Magnetic Field ◽  
Electric Current ◽  
Axial Magnetic Field ◽  
Normal Modes ◽  
Azimuthal Velocity ◽  
Base Flow ◽  
Transition To Turbulence ◽  
Electrically Conducting ◽  
Concentric Cylinders ◽  
The Stability

The method of normal modes is used to examine the stability of an azimuthal base flow to both axisymmetric and plane-polar disturbances for an electrically conducting fluid confined between stationary, concentric, infinitely-long cylinders. An electric potential difference exists between the two cylinder walls and drives a radial electric current. Without a magnetic field, this flow remains stationary. However, if an axial magnetic field is applied, then the interaction between the radial electric current and the magnetic field gives rise to an azimuthal electromagnetic body force which drives an azimuthal velocity. Infinitesimal axisymmetric disturbances lead to an instability in the base flow. Infinitesimal plane-polar disturbances do not appear to destabilize the base flow until shear-flow transition to turbulence.

THE STAEILITY OF COUETTE FLOW IN AN AXIAL MAGNETIC FIELD

1958 ◽  
Vol 36 (11) ◽  
pp. 1509-1525 ◽  
Author(s):  
E. R. Niblett
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Theoretical Prediction ◽  
Viscous Flow ◽  
Rotation Speed ◽  
Axial Magnetic Field ◽  
Radioactive Isotopes ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
The Stability

Chandrasekhar's theory of the stability of viscous flow of an electrically conducting fluid between coaxial rotating cylinders with perfectly conducting walls is extended to include the case of non-conducting walls, and it is found that their effect is to reduce the critical Taylor numbers and increase the wavelength of the instability patterns by considerable amounts. An experiment designed to measure the values of magnetic field and rotation speed at the onset of instability in mercury between perspex cylinders is described. The radioactive isotopes Hg197 and Hg203 were used to trace the flow. The results support the theoretical prediction that the boundary conditions can have a large effect on the motion.

An exact solution in the stability of m. h. d. Couette flow

1972 ◽  
Vol 327 (1569) ◽  
pp. 269-278 ◽  
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Couette Flow ◽  
Stability Problem ◽  
Axial Magnetic Field ◽  
Narrow Gap ◽  
Mhd Stability ◽  
Arbitrary Magnetic Field ◽  
The Stability ◽  
Conducting Cylinders

The MHD stability problem for dissipative Couette flow in a narrow gap between corotating, conducting cylinders with an axial magnetic field is solved exactly. Results are presented for an arbitrary magnetic field; in particular, previous results on the zero and infinite magnetic field limits are verified.

ONSET OF INSTABILITY IN HYDROMAGNETIC COUETTE FLOW

2004 ◽  
Vol 02 (02) ◽  
pp. 145-159 ◽  
Author(s):  
ISOM H. HERRON
Keyword(s):  
Magnetic Field ◽  
Prandtl Number ◽  
Boundary Conditions ◽  
Viscous Flow ◽  
Couette Flow ◽  
Axial Magnetic Field ◽  
Narrow Gap ◽  
Rotating Cylinders ◽  
Magnetic Prandtl Number ◽  
The Stability

The stability of viscous flow between rotating cylinders in the presence of a constant axial magnetic field is considered. The boundary conditions for general conductivities are examined. It is proved that the Principle of Exchange of Stabilities holds at zero magnetic Prandtl number, for all Chandrasekhar numbers, when the cylinders rotate in the same direction, the circulation decreases outwards, and the cylinders have insulating walls. The result holds for both the finite gap and the narrow gap approximation.

Vibration Behavior of Gravity-Loaded Whirling Micro-Scale Shafts Influenced by an Axial Magnetic Field

2017 ◽  
Vol 17 (09) ◽  
pp. 1750110 ◽  
Author(s):  
K. B. Mustapha ◽  
Z. W. Zhong ◽  
S. B. A. Kashem
Keyword(s):  
Magnetic Field ◽  
High Speed ◽  
Axial Magnetic Field ◽  
Torsional Rigidity ◽  
Transformation Method ◽  
Theoretical Treatment ◽  
Micro Scale ◽  
Gravity And Magnetic ◽  
The Stability ◽  
Micro Vibration

Some high-speed rotating micro-machines and micro-vibration devices rely on the use of whirling micro-shafts subject to the effect of gravity and magnetic fields. At present, the consequences of the interaction between the elastic deformation of such shafts and the magnetic/gravitational field effects remain unresolved. Focusing on micro-scale whirling shafts with very high torsional rigidity, this study presents a theoretical treatment grounded in the theory of micro-continuum elasticity to examine the ramification of this interaction. The differential transformation method (DTM) is used to obtain extensive numerical results for qualitative assessments of the magnetic-gravitational effects interaction on standing, hanging and horizontally positioned spinning micro-scale shafts. The influence of bearing-support flexibility on the response of the whirling micro-shaft is also considered with rotational and translational springs. The gravitational sag reduces the stability of whirling standing micro-shafts and increases that of the hanging micro-shafts. Further, for all the micro-shafts configurations investigated, the magnetic field is observed to stiffen the response of the shaft and favorably shifts the critical points of vibration of the whirling shafts forward.

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