Dynamic and Stability Analysis of the Rotating Nanobeam in a Nonuniform Magnetic Field Considering the Surface Energy

2016 ◽  
Vol 08 (04) ◽  
pp. 1650048 ◽  
Author(s):  
M. Baghani ◽  
M. Mohammadi ◽  
A. Farajpour

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.

2011 ◽  
Vol 71-78 ◽  
pp. 3760-3763
Author(s):  
Xing Wang

This paper carries out stability analysis on plate-cone reticulated shell considering geometrical nonlinearity of cooperating work between plates and members. In this paper, stability behavior of different kinds of plate-cone reticulated shell considering geometrical nonlinearity is analyzed by using the software ANSYS, tracking complete process balance path for load-displacement by using arc-length method, the several problems of plate-cone reticulated shell are studied, such as destruction mechanism, structural ductility, ultimate bearing capacity and strength reserve, some important conclusions are obtained. After analyzing the stability behavior of double-layer reticulated shell by ANSYS and comparing with plate-cone reticulated shell, it is proved that plate-cone reticulated shell is more advantageous than double-layer reticulated shell in the aspect of stability behavior.


1978 ◽  
Vol 33 (7) ◽  
pp. 792-798
Author(s):  
W. Kerner

The stability behavior with respect to internal modes is discussed for a class of tokamak equilibria with non-circular cross-sections and essentially flat current profiles. The stability analysis is done by computer both symbolically and numerically with the help of a normal mode code, which extremizes the Lagrangian of the system . It is found that the stability limit agrees well with that of the Mercier criterion. There are stable high-beta equilibria in this model.


Several recent investigations in geophysics and astrophysics have involved a consideration of the hydrodynamics of a fluid which is a good electrical conductor. In this paper one of the problems which seem likely to arise in such investigations is discussed. The fluid is assumed to be incompressible and in homogeneous turbulent motion, and externally imposed electric and magnetic fields are assumed to be absent. The equations governing the interaction of the electromagnetic field and the turbulent motion are set up with the same assumptions as are used to obtain the Maxwell and current flow equations for a metallic conductor. It is shown that the equation for the magnetic field is identical in form with that for the vorticity in a non-conducting fluid; immediate deductions are that lines of magnetic force move with the fluid when the conductivity is infinite, and that the small-scale components of the turbulence have the more powerful effect on the magnetic field. The first question considered is the stability of a purely hydrodynamical system to small disturbing magnetic fields, and it is shown that the magnetic energy of the disturbance will increase provided the conductivity is greater than a critical value determined by the viscosity of the fluid. The rate of growth of magnetic energy is approximately exponential, with a doubling time which can be simply related to the properties of the turbulence. General mechanical considerations suggest that a steady state is reached when the magnetic field has as much energy as is contained in the small-scale components of the turbulence. Estimates of this amount of energy and of the region of the spectrum in which it will lie are given in terms of observable properties of the turbulence.


2019 ◽  
Vol 30 (11) ◽  
pp. 4697-4710 ◽  
Author(s):  
Fadzilah Md Ali ◽  
Kohilavani Naganthran ◽  
Roslinda Nazar ◽  
Ioan Pop

Purpose This study aims to perform a stability analysis on a steady magnetohydrodynamic (MHD) mixed convection boundary-layer stagnation-point flow of an incompressible, viscous and electrically conducting fluid over a vertical flat plate. The effect of induced magnetic field is also considered. Design/methodology/approach The governing boundary layer equations are transformed into a system of ordinary differential equations using the similarity transformations. The system is then solved numerically using the “bvp4c” function in MATLAB. Findings Dual solutions are found to exist for a certain range of the buoyancy parameter for both the assisting and opposing flows. The results from the stability analysis showed that the first solution (upper branch) is stable and valid physically, while the second solution (lower branch) is unstable. Practical implications This problem is important in many metallurgical processes, namely, drawing, annealing and tinning of copper wires. The results obtained are very useful for researchers to determine which solution is physically stable, whereby mathematically more than one solution exists for the skin friction coefficient and the heat transfer characteristics. Originality/value The present results of the stability analysis are original and new for the problem of MHD mixed convection stagnation-point flow of viscous conducting fluid over a vertical flat plate, with the effect of induced magnetic field.


2003 ◽  
Vol 21 (8) ◽  
pp. 1691-1707 ◽  
Author(s):  
S. W. H. Cowley ◽  
E. J. Bunce

Abstract. We calculate the latitude profile of the equatorward-directed ionospheric Pedersen currents that are driven in Saturn’s ionosphere by partial corotation of the magnetospheric plasma. The calculation incorporates the flattened figure of the planet, a model of Saturn’s magnetic field derived from spacecraft flyby data, and angular velocity models derived from Voyager plasma data. We also employ an effective height-integrated ionospheric Pedersen conductivity of 1 mho, suggested by a related analysis of Voyager magnetic field data. The Voyager plasma data suggest that on the largest spatial scales, the plasma angular velocity declines from near-rigid corotation with the planet in the inner magnetosphere, to values of about half of rigid corotation at the outer boundary of the region considered. The latter extends to ~ 15–20 Saturn radii (RS) in the equatorial plane, mapping along magnetic field lines to ~ 15° co-latitude in the ionosphere. We find in this case that the ionospheric Pedersen current peaks near the poleward (outer) boundary of this region, and falls toward zero over ~ 5°–10° equator-ward of the boundary as the plasma approaches rigid corotation. The peak current near the poleward boundary, integrated in azimuth, is ~ 6 MA. The field-aligned current required for continuity is directed out of the ionosphere into the magnetosphere essentially throughout the region, with the current density peaking at ~ 10 nA m-2 at ~ 20° co-latitude. We estimate that such current densities are well below the limit requiring field-aligned acceleration of magnetospheric electrons in Saturn’s environment ( ~ 70 nAm-2), so that no significant auroral features associated with this ring of upward current is anticipated. The observed ultraviolet auroras at Saturn are also found to occur significantly closer to the pole (at ~ 10°–15° co-latitude), and show considerable temporal and local time variability, contrary to expectations for corotation-related currents. We thus conclude that Saturn’s ‘main oval’ auroras are not associated with corotation-enforcing currents as they are at Jupiter, but instead are most probably associated with coupling to the solar wind as at Earth. At the same time, the Voyager flow observations also suggest the presence of radially localized ‘dips’ in the plasma angular velocity associated with the moons Dione and Rhea, which are ~ 1–2 RS in radial extent in the equatorial plane. The presence of such small-scale flow features, assumed to be azimuthally extended, results in localized several-MA enhancements in the ionospheric Pedersen current, and narrow bi-polar signatures in the field-aligned currents which peak at values an order of magnitude larger than those associated with the large-scale currents. Narrow auroral rings (or partial rings) ~ 0.25° co-latitude wide with intensities ~ 1 kiloRayleigh may be formed in the regions of upward field-aligned current under favourable circumstances, located at co-latitudes between ~ 17° and ~ 20° in the north, and ~ 19° and ~22° in the south.Key words. Magnetospheric physics (current systems; magnetosphere-ionosphere interactions; planetary magnetospheres)


1993 ◽  
Vol 157 ◽  
pp. 45-48
Author(s):  
A. Ferriz-Mas ◽  
M. Schüssler

We consider the linear stability of a toroidal flux tube lying in the equatorial plane of a differentially rotating star and investigate its dependence on superadiabaticity, magnetic field strength, and gradient of angular velocity.


2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Keivan Kiani

To study the size and surface effects on characteristics of in-plane shear waves in magnetically affected nanofilms, a novel model is developed. Using nonlocal and surface continuum theories, the governing equations are established and appropriate boundary conditions are imposed at the bottom and top surfaces of the nanofilm. The dispersion relations associated with symmetric and asymmetric modes are obtained. The effects of the surface energy, small-scale parameter, nanofilm's thickness, and magnetic field strength on dispersion curves are addressed. The limitations of the classical theory of elasticity are discussed. The obtained results show that the phase velocity of the propagated in-plane shear waves magnifies by an increase of the thickness as well as magnetic field strength. However, the phase velocity commonly decreases as the effect of the surface energy or nonlocality increases. Such a fact is more obvious for higher modes of vibration. Generally, the cutoff frequency reaches a lower value as the nanofilm's thickness reduces or the small-scale parameter increases. Additionally, variation of the magnetic field strength has fairly no influence on the cutoff frequency.


2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Pascalin Tiam Kapen ◽  
Cédric Gervais Njingang Ketchate ◽  
Didier Fokwa ◽  
Ghislain Tchuen

Purpose For this purpose, a linear stability analysis based on the Navier–Stokes and Maxwell equations is made leading to an eigenvalue differential equation of the modified Orr–Sommerfeld type which is solved numerically by the spectral collocation method based on Chebyshev polynomials. Unlike previous studies, blood is considered as a non-Newtonian fluid. The effects of various parameters such as volume fraction of nanoparticles, Casson parameter, Darcy number, Hartmann number on flow stability were examined and presented. This paper aims to investigate a linear stability analysis of non-Newtonian blood flow with magnetic nanoparticles with an application to controlled drug delivery. Design/methodology/approach Targeted delivery of therapeutic agents such as stem cells and drugs using magnetic nanoparticles with the help of external magnetic fields is an emerging treatment modality for many diseases. To this end, controlling the movement of nanoparticles in the human body is of great importance. This study investigates controlled drug delivery by using magnetic nanoparticles in a porous artery under the influence of a magnetic field. Findings It was found the following: the Casson parameter affects the stability of the flow by amplifying the amplitude of the disturbance which reflects its destabilizing effect. It emerges from this study that the taking into account of the non-Newtonian character is essential in the modeling of such a system, and that the results can be very different from those obtained by supposing that the blood is a Newtonian fluid. The presence of iron oxide nanoparticles in the blood increases the inertia of the fluid, which dampens the disturbances. The Strouhal number has a stabilizing effect on the flow which makes it possible to say that the oscillating circulation mechanisms dampen the disturbances. The Darcy number affects the stability of the flow and has a stabilizing effect, which makes it possible to increase the contact surface between the nanoparticles and the fluid allowing very high heat transfer rates to be obtained. It also emerges from this study that the presence of the porosity prevents the sedimentation of the nanoparticles. By studying the effect of the magnetic field on the stability of the flow, it is observed that the Hartmann number keeps the flow completely stable. This allows saying that the magnetic field makes the dissipations very important because the kinetic energy of the electrically conductive ferrofluid is absorbed by the Lorentz force. Originality/value The originality of this paper resides on the application of the linear stability analysis for controlled drug delivery.


2014 ◽  
Vol 5 ◽  
pp. 1725-1731 ◽  
Author(s):  
Carmine Putignano ◽  
Luciano Afferrante ◽  
Luigi Mangialardi ◽  
Giuseppe Carbone

In the present paper we propose a generalization of the model developed in Afferrante, L.; Carbone, G.; Demelio, G.; Pugno, N. Tribol. Lett. 2013, 52, 439–447 to take into account the effect of the pre-tension in the tape. A detailed analysis of the peeling process shows the existence of two possible detachment regimes: one being stable and the other being unstable, depending on the initial configuration of the tape. In the stability region, as the peeling process advances, the peeling angle reaches a limiting value, which only depends on the geometry, on the elastic modulus of the tape and on the surface energy of adhesion. Vice versa, in the unstable region, depending on the initial conditions of the system, the tape can evolve towards a state of complete detachment or fail before reaching a state of equilibrium with complete adhesion. We find that the presence of pre-tension in the tape does not modify the stability behavior of the system, but significantly affects the pull-off force which can be sustained by the tape before complete detachment. Moreover, above a critical value of the pre-tension, which depends on the surface energy of adhesion, the tape will tend to spontaneously detach from the substrate. In this case, an external force is necessary to avoid spontaneous detachment and make the tape adhering to the substrate.


Sign in / Sign up

Export Citation Format

Share Document