Effect Of Radial Gradient Research Articles

A refined beam theory for bending and vibration of functionally graded tube-beams

This paper presents a novel approach for analyzing transverse bending and vibration of functionally graded circular cylindrical tubes with radial nonhomogeneity. Different from the Euler-Bernoulli and Timoshenko theories of beams, a refined beam theory or third-order shear deformation beam theory for radially graded tubes is proposed, where warping, shear deformation and rotational moment of inertia of cross-section are all considered. The shear correction coefficient is not needed. Coupled governing equations for the deflection and rotation about the neutral axis of cross-section are derived from equilibrium equations, and then converted to a single fourth-order partial differential governing equation. The deflection and stress distribution for cantilever and simply-supported tubes are derived explicitly. The frequency equations for free flexural vibration of radially graded hollow cylinders with clamped-clamped, pinned-pinned, and clamped-free ends are obtained and the natural frequencies are calculated for different power-law gradients and various length/thicknesses ratios. The effects of radial gradient on the stress distribution and the natural frequencies are analyzed in detail.

THE LINK BETWEEN LIGHT AND MASS IN LATE-TYPE SPIRAL GALAXY DISKS

We present the correlation between the extrapolated central disk surface brightness (mu) and extrapolated central surface mass density (Sigma) for galaxies in the DiskMass sample. This mu-Sigma-relation has a small scatter of 30% at the high-surface-brightness (HSB) end. At the low surface brightness (LSB) end, galaxies fall above the mu-Sigma-relation, which we attribute to their higher dark matter content. After correcting for the dark matter, as well as for the contribution of gas and the effects of radial gradients in the disk, the LSB end falls back on the linear mu-Sigma-relation. The resulting scatter about the corrected mu-Sigma-relation is 25% at the HSB end, and about 50% at the LSB end. The intrinsic scatter in the mu-Sigma-relation is estimated to be 10% to 20%. Thus, if the surface brightness is known, the stellar surface mass density is known to within 10-20% (random error). Assuming disks have an exponential vertical distribution of mass, the average (M_L)_K is 0.24 Msun/Lsun, with an intrinsic scatter around the mean of at most 0.05 Msun/Lsun. This value for (M/L)_K is 20% smaller than we found in Martinsson et al., mainly due to the correction for dark matter applied here. This small scatter means that among the galaxies in our sample variations in scale height, vertical density profile shape, and/or the ratio of vertical over radial velocity dispersion must be small.

Buckling of functionally graded circular columns including shear deformation

An analysis of the stability of circular cylindrical columns/beams composed of functionally graded materials is made where shear deformation is taken into account. In this study, a new approach is carried out. Different from the assumption of uniform shear stress at the cross-section adopted in the Timoshenko beam theory, proposed model provides a new approach for treating the problem. Based on the traction-free surface condition, two coupled governing equations for the deflection and rotation are derived, and a single governing equation is further obtained. A comparison of buckling loads derived from the proposed circular column model and the Timoshenko and Euler–Bernoulli theories of beams is made. Moreover, the effects of radial gradient on buckling loads of elastic columns with circular cross-section made of functionally graded materials are elucidated. Finally, the stability of double-walled carbon nanotubes is considered and critical stress is determined and compared with existing results. The results obtained by the proposed model show very good agreement with the results of the Timoshenko beam theory or Reddy–Bickford beam theory.

Rainbow refractrometry on particles with radial refractive index gradients

The rainbow refractrometry, under its different configurations (classical and global), is an attractive technique to extract information from droplets in evaporation such as diameter and temperature. Recently a new processing strategy has been developed which increases dramatically the size and refractive index measurements accuracy for homogeneous droplets. Nevertheless, for mono component as well as for multicomponent droplets, the presence of temperature and/or of concentration gradients induce the presence of a gradient of refractive index which affects the interpretation of the recorded signals. In this publication, the effect of radial gradient on rainbow measurements with a high accuracy never reached previously is quantified.

Rapid communication/Communication rapide: Effects of radial gradient of the Shafranov shift on the kinetic ballooning and drift-type modes in high-performance tokamaks

The radial derivative of the Shafranov shift { is shown to have a strong stabilizing influence on the long-wavelength kinetic ballooning mode and also the trapped electron drift mode. The internal transport barrier in a tokamak characterized by negative magnetic shear, large ballooning parameter Ek ; D ,a nd { 3 fappears to be free from long-wavelength pressure-gradient-driven instabilities, including the drift-type and kinetic-ballooning modes. R´ esum´ e : Nous montrons que la derivee radiale du decalage de Shafranov, { ,au ne forte influence stabilisatrice sur les modes de gonflement cinetique a grande longueur d'onde (KBM) et de derive des electrons captifs. Dans un Tokamak avec un cisaillement magnetique negatif et de larges parametres de gonflement Ek ; D, { 3f, la barriere de transport interne (ITB) semble libre des instabilites induites par les gradients de pression de grande longueur d'onde, incluant les modes de derive et de gonflement cinetique. (Traduit par la r ´ The ballooning mode in magnetically confined plasmas occurs when the interchange drive (a com- bination of the plasma pressure gradient and unfavorable magnetic curvature) exceeds the stabilizing magnetic field line bending associated with the shear Alfven wave and it is expected to impose an upper limit on the maximum plasma pressure that can be stably confined in a given magnetic con- figuration. Although the ballooning mode may not lead to a total loss of equilibrium, its detrimental effects, due to Alfvenic magnetic fluctuations (alpha particles, in particular) on the confinement of energetic ions are well recognized. The stability of an ideal MHD ballooning mode in tokamaks was investigated in detail in the past after the advent of the ballooning transformation (1 -3) with which rigorous stability analysis of the ideal MHD ballooning mode can be made. As is well known, in low- tokamak discharges, the ballooning parameter and the magnetic shear parameter v suffice to determine the stable-unstable boundary. Stabilization at a large plasma pressure gradient (the so-called

<I>Rapid communication/Communication rapide</I>: Effects of radial gradient of the Shafranov shift on the kinetic ballooning and drift-type modes in high-performance tokamaks

<I>Rapid communication/Communication rapide</I>: Effects of radial gradient of the Shafranov shift on the kinetic ballooning and drift-type modes in high-performance tokamaks

Methode des elements finis appliquee au calcul du regime etabli laminaire de convection naturelle dans les faisceaux tubulaires verticaux de dimension finie

This study concerns some physical aspects of fully developed natural convection in finite vertical rod bundles. The equations of the problem are solved by the finite element Galerkin method. Piecewise linear interpolation polynomials are used as shape functions for velocity and temperature with triangular elements. No restrictions are required on temperature boundary conditions except a constant axial gradient along the walls. Natural convection in closed hexagonal 7-rod and 91-rod bundles with triangular arrangement is computed. Effects of radial gradients in the power generation are studied. The results show that ascendant velocities can exist in the peripheral region for high Rayleigh numbers and that the use of the distance between the center of the bundle and the duct wall as a characteristic length is preferable to the hydraulic diameter.