Stability Analysis of CNT Based Nano-Actuator Under Magnetic Field and Rippling Deformation

It is well-known that rotating nanobeams can have different dynamic and stability responses to various types of loadings. In this research, attention is focused on studying the effects of magnetic field, surface energy and compressive axial load on the dynamic and the stability behavior of the nanobeam. For this purpose, it is assumed that the rotating nanobeam is located in the nonuniform magnetic field and subjected to compressive axial load. The nonlocal elasticity theory and the Gurtin–Murdoch model are applied to consider the effects of inter atomic forces and surface energy effect on the vibration behavior of rotating nanobeam. The vibration frequencies and critical buckling loads of the nanobeam are computed by the differential quadrature method (DQM). Then, the numerical results are testified with those results are presented in the published works and a good correlation is obtained. Finally, the effects of angular velocity, magnetic field, boundary conditions, compressive axial load, small scale parameter and surface elastic constants on the dynamic and the stability behavior of the nanobeam are studied. The results show that the magnetic field, surface energy and the angular velocity have important roles in the dynamic and stability analysis of the nanobeams.

Download Full-text

Stability analysis of a cylindrical surface current plasma confined by a force-free magnetic field with perfectly conducting tenuous plasma

Plasma Physics and Controlled Fusion ◽

10.1088/0741-3335/28/5/007 ◽

1986 ◽

Vol 28 (5) ◽

pp. 813-821

Author(s):

M Seki ◽

M Kito ◽

I Kaji

Keyword(s):

Magnetic Field ◽

Stability Analysis ◽

Cylindrical Surface ◽

Surface Current

Download Full-text

Rayleigh–Bénard instability in a vertical cylinder with a vertical magnetic field

Journal of Fluid Mechanics ◽

10.1017/s0022112002001623 ◽

2002 ◽

Vol 469 ◽

pp. 189-207 ◽

Cited By ~ 12

Author(s):

B. C. HOUCHENS ◽

L. MARTIN WITKOWSKI ◽

J. S. WALKER

Keyword(s):

Magnetic Field ◽

Stability Analysis ◽

Numerical Solution ◽

Linear Stability ◽

Linear Stability Analysis ◽

Hartmann Number ◽

Critical Rayleigh Number ◽

Vertical Wall ◽

Vertical Cylinder ◽

Vertical Magnetic Field

This paper presents two linear stability analyses for an electrically conducting liquid contained in a vertical cylinder with a thermally insulated vertical wall and with isothermal top and bottom walls. There is a steady uniform vertical magnetic field. The first linear stability analysis involves a hybrid approach which combines an analytical solution for the Hartmann layers adjacent to the top and bottom walls with a numerical solution for the rest of the liquid domain. The second linear stability analysis involves an asymptotic solution for large values of the Hartmann number. Numerically accurate predictions of the critical Rayleigh number can be obtained for Hartmann numbers from zero to infinity with the two solutions presented here and a previous numerical solution which gives accurate results for small values of the Hartmann number.

Download Full-text

Linear Stability Analysis of Liquid Metal Flow in an Insulating Rectangular Duct under External Uniform Magnetic Field

Fluids ◽

10.3390/fluids4040177 ◽

2019 ◽

Vol 4 (4) ◽

pp. 177 ◽

Cited By ~ 3

Author(s):

Tagawa

Keyword(s):

Magnetic Field ◽

Stability Analysis ◽

Liquid Metal ◽

Linear Stability ◽

Linear Stability Analysis ◽

Uniform Magnetic Field ◽

Metal Flow ◽

Rectangular Duct ◽

Liquid Metal Flow ◽

External Uniform Magnetic Field

Linear stability analysis of liquid metal flow driven by a constant pressure gradient in an insulating rectangular duct under an external uniform magnetic field was carried out. In the present analysis, since the Joule heating and induced magnetic field were neglected, the governing equations consisted of the continuity of mass, momentum equation, Ohm’s law, and conservation of electric charge. A set of linearized disturbance equations for the complex amplitude was decomposed into real and imaginary parts and solved numerically with a finite difference method using the highly simplified marker and cell (HSMAC) algorithm on a two-dimensional staggered mesh system. The difficulty of the complex eigenvalue problem was circumvented with a Newton—Raphson method during which its corresponding eigenfunction was simultaneously obtained by using an iterative procedure. The relation among the Reynolds number, the wavenumber, the growth rate, and the angular frequency was successfully obtained for a given value of the Hartmann number as well as for a direction of external uniform magnetic field.

Download Full-text