Outer Radius Ratio Research Articles

Comparative Theoretical Study of the Optical Properties of Silicon/Gold, Silica/Gold Core/Shell and Gold Spherical Nanoparticles

The scattering and absorption efficiencies of light by individual silicon/gold core/shell spherical nanoparticles in air are analysed theoretically in the framework of Lorenz-Mie formalism. We have addressed the influence of particle-diameter and gold-shell thickness on the scattering and absorption efficiencies of such nano-heterostructures. For comparison, we also considered the famous silica/gold core/shell nanoparticle and pure gold nanoparticle. Our simulation clearly shows that the optical response of the illuminated Si/Au core/shell nanoparticle differs markedly from that of the famous SiO2/Au heterostructure which in turn does not show a significant difference with that of the pure gold nanoparticle. This difference is clearly evident for shell thickness to outer particle radius ratio of less than 0.5. It manifests itself essentially by the occurrence of a strong and sharp absorption resonance beyond the wavelength of 600 nm where the silica/gold and the pure gold nanoparticles never absorb. The characteristics of this resonance are found to be sensitive to the particle diameter and the shell thickness. In particular, its spectral position can be adjusted over a wide spectral range from the visible to the mid-IR by varying the particle diameter and/or the shell thickness.

ALGORITHM OF WINDING TENSION FOR CYLINDER WITH THICK-WALLED LINER

As a key factor in winding process, reasonable design of winding tension directly affects the performance of productions. An algorithm to design winding tension is proposed for the design of winding tension. Considering the deformations of mandrel, radial and circumferential stresses of winding layers under external pressure are obtained through analyzing on the basis of anisotropic composite elastic theory and isotropic thick-walled cylinder elastic theory. Within the scope of the elastic limit and based on the stress superposition principle, the analytic algorithm between residual tension distribution and winding tension is established. By analyzing three typical tension models of filament winding, residual tension formulas are given. Furthermore, according to these formulas, different analytical formulas of winding tension are estibilished through analyzing the uniform residual tension. The influence of inner to outer radius ratio of mandrel and taper coefficient on isotropic material residual tension distribution is investigated. The results indicate that changes of radius ration and taper coefficient have remarkable effects on residual tension distribution, while the algorithm to calculate the residual tension distribution is simple, reasonable and reliable. By analyzing uniform residual tension of the anisotropic composite, the result is found consistent with the existing netting theory, and the winding tensions of up and down layers change gently and are easy to be implemented.

Stress analysis of rotating cylindrical shell composed of functionally graded incompressible hyperelastic materials

In this paper, rotating thick-walled hollow cylindrical shell composed of functionally graded material are analyzed by using the theory of hyperelasticity. Hyperelastic behavior is modeled by using proposed power law strain energy function with variable material parameters. Material is considered incompressible and material properties are assumed as a function of the radius of the cylinder to a power law function. Material inhomogeneity parameter (n) is a power in the mentioned power law function. Material constant of strain energy function is calculated from experimental data by using Levenberg–Marquardt nonlinear regression method. The analytical solution is obtained for the axisymmetric plane strain state. Following this, profiles of circumferential stretch, radial stress, circumferential stress and longitudinal stress as a function of radial direction are plotted for different values of n. The obtained results show that the material inhomogeneity parameter (n) and structure parameter (β: ratio of outer radius to inner radius) have a significant influence on the mechanical behavior of rotating thick-walled hollow cylindrical shell made of functionally graded materials with power law varying properties. Thus with selecting a proper n and structure parameter (β), engineers can design a specific FGM hollow cylinder that can meet some special requirements.

Theoretical analysis of hot electron injection from metallic nanotubes into a semiconductor interface.

Metallic nanostructures under optical illumination can generate a non-equilibrium high-energy electron gas (also known as hot electrons) capable of being injected into neighbouring media over a potential barrier at particle boundaries. The nature of this process is highly nanoparticle shape and size dependent. Here, we have derived an analytical expression for the frequency dependent rate of injection of these energetic electrons from a metallic nanotube into a semiconductor layer in contact with its inner boundary. In our derivation, we have considered the quantum mechanical motion of the electron gas confined by the particle boundaries in determining the electron energy spectrum and wave functions. We present a comprehensive theoretical analysis of how different geometric parameters such as the outer to inner radius ratio, length and thickness of a nanotube and illumination frequency affect the hot electron injection and internal quantum efficiency of the nanotube. We reveal that longer nanotubes with thin shells and high inner to outer radius ratios show better performance at visible and infrared frequencies. Our derivations and results provide the much needed theoretical insight for optimization of thin nanotubes for different hot electron based applications.

STRESS ANALYSIS OF ECCENTRIC RINGS IN BIPOLAR COORDINATE SYSTEM

Stress analysis of eccentric ring is carried out in bipolar coordinate system under uniform internal and external pressure. Airy stress function is chosen in such a way that it satisfies the bi-harmonic equations and boundary conditions in bipolar coordinate system. Stresses are obtained for various parameters such as eccentricity, various inner radius to outer radius ratios. Effect of eccentricity is investigated on the stresses of the eccentric rings. Results are useful for the design of eccentric rings.

Analytical layerwise free vibration analysis of circular/annular composite sandwich plates with auxetic cores

In the present research, free vibration of circular and annular sandwich plates with auxetic (negative Poisson’s ratio) cores and isotropic/orthotropic face sheets is investigated for different combinations of the boundary conditions. To ensure that the results are accurate and reliable, a global–local layerwise plate theory is employed instead of the traditional equivalent single-layer theories. The governing equations are derived based on Hamilton’s principle and solved using a Taylor transform whose center is located at the outer radius of the plate. Due to this hint, the resulting semi-analytical solution can be employed for both circular and annular sandwich plates. After investigation of vibration behavior of a single-layer annular auxetic plate, a comprehensive parametric study including evaluation of effects of the auxeticity for sandwich plates with isotropic and orthotropic face sheets, symmetric and asymmetric layups, different core to sheet thickness, radius to thickness, and inner to outer radius ratios, and various boundary conditions, is carried out. Results show that unlike the single-layer auxetic plates that exhibit a transition state, the auxeticity may considerably increase the natural frequencies and rigidities of the circular/annular sandwich plates, especially when the boundary conditions induce higher rigidity in the plate or when the fibers are along the radial direction. Accuracy of results of the employed layerwise theory and the proposed semi-analytical solution is verified by comparing the results with those of the three-dimensional theory of elasticity extracted from the ABAQUS software.

A semi-analytical state-space approach for 3D transient analysis of functionally graded material cylindrical shells

A good understanding of the mechanical behavior of functionally graded material (FGM) cylindrical shells is necessary for designers and researchers. However, the 3D transient response of FGM cylindrical shells under various boundary conditions has not yet been analyzed. In this paper, the problem is addressed by proposing an approach integrating the state space method, differential quadrature method, and Durbina’s numerical inversion method of Laplace transform. The laminate model is used to obtain the transient solution in the radial direction. At the edges, four kinds of boundary conditions are considered: Clamped-Clamped, Clamped-Simply supported, Clamped-Free, and Simply supported-Simply supported. The results of the proposed method and finite element (FE) method agree with each other excellently. Convergence studies show that the proposed method has a fast convergence rate. The natural frequencies obtained by the proposed method, experiment, and other theoretical methods are in close agreement with each other. The effects of the load frequency and duration, length/outer radius ratio, and the (outer radius-inner radius)/outer radius ratio on the transient response of FGM shells are investigated. Two laws of variation of material properties along the radial direction are considered: the first has material properties varying according to an exponential law along the radial direction, while the second has material properties varying according to a power law. The effect of a functionally graded index on the transient response of FGM shells is investigated in both cases. The results obtained in this paper can serve as benchmark data for further research.

RETRACTED ARTICLE: A novel approach for free vibration of circular/annular sector plates using Reddy’s third order shear deformation theory

A new exact closed-form solution based on Reddy’ third-order shear deformation plate theory for free vibration of thick circular/annular sector plates is presented. Characteristic equations are given for sector plates having hard simply supported radial edges and all combinations of free, soft simply supported, hard simply supported and clamped boundary conditions along the circular edges. Based on the present solution, the governing equations of the vibrated thick circular/annular sector plates were exactly solved by introducing the new auxiliary and potential functions as well as using the separation method of variables. To clarify the efficiency and accuracy of the present solution, several comparison studies are examined with the available data in the literature. Also, natural frequencies of the circular/annular sector plates are presented for different thickness–radius ratios, inner–outer radius ratios, sector angle values and boundary conditions.

Free vibration analysis of non-local annular sector Mindlin plates

The free vibration analysis of non-local annular sector Mindlin plates has been investigated. Mindlin plates at the micro/nano-scale are modeled using Eringen׳s nonlocal elasticity theory, where the small scale effect is taken into consideration. The governing equations are derived using the nonlocal differential constitutive relations of Eringen. For this purpose, the resulted eigenvalue problem is solved numerically by applying the Chebyshev collocation method. The effects of the inner to outer radius ratio, the thickness to outer radius ratio, the nonlocal scale effect, and the boundary conditions on the natural frequencies have been studied.

Axisymmetric Free Vibration Analysis of Annular and Circular Mindlin Plates Using the Nonlocal Continuum Theory

This study aims to investigate and analyze the axisymmetric free vibration of non-local annular and circular Mindlin plates at the micro/nano scale which are modeled using Eringen’s nonlocal elasticity theory, taking into consideration the small scale effect. The governing equations are derived using the nonlocal differential constitutive relations of Eringen. For this purpose, the resulted eigenvalue problem is solved numerically by applying the Chebyshev collocation method. The effects of the inner to outer radius ratio, the thickness to outer radius ratio, the nonlocal scale effect and the boundary conditions on the natural frequencies are studied.

Thermal Behavior of Multidisk Friction Pairs in Hydroviscous Drive Considering Inertia Item

Considering the influence of the inertia item on temperature distribution of multidisk friction pairs in hydroviscous drive (HVD), transient temperature models are derived with the aim of revealing the effect of engagement pressure, lubricant viscosity, viscosity–temperature correlation, surface roughness and the ratio of inner and outer radius of disks on temperature distribution. The results indicate that unsteady temperature gradient can be avoided by matching the suitable materials for multidisk friction pairs. The average temperature for the case of neglecting the inertia item is lower than that of the case of including the inertia item. It is shown that during the soft-start, the temperature along the radial direction achieves its peak value near the outlet and keeps decreasing along the axial direction; while after the engaging process, the temperature distribution tends to be uniform. It is also shown that the decrease of engagement pressure, surface roughness and the ratio of inner and outer radius of disks can reduce temperature gradient effectively as well as the increase of lubricant viscosity. The average temperature for the case of including the viscosity–temperature correlation is much higher than that for other cases.

Nonaxisymmetric instabilities in self-gravitating disks. II. Linear and quasi-linear analyses

We studied global nonaxisymmetric hydrodynamic instabilities in an extensive collection of hot, self-gravitating polytropic disk systems, systems that covered a wide expanse of the parameter space relevant to protostellar and protoplanetary systems. We examined equilibrium disk models varying three parameters: the ratio of the inner to outer equatorial radii, the ratio of star mass to disk mass, and the rotation law exponent q. We took the polytropic index n=1.5 and examined the exponents q=1.5 and 2, and the transitional one q=1.75. For each of these sets of parameters, we examined models with inner to outer radius ratios from 0.1 to 0.75, and star mass to disk mass ratios from 0 to 103. We numerically calculated the growth rates and oscillation frequencies of low-order nonaxisymmetric disk modes, modes with azimuthal dependence ∝e imϕ . Low-m modes are found to dominate with the character and strength of instability strongly dependent on disk self-gravity. Representatives of each mode type are examined in detail, and torques and mass transport rates are calculated.

Numerical experiments on neutron yield and soft x-ray study of a ∼100 kJ plasma focus using the current profile fitting technique

Numerical experiments using the Lee model were performed to study the neutron yield and soft x-ray emission from the IR-MPF-100 plasma focus using the current fitting technique. The mass sweeping factor and the current factor for the axial and radial phase were used to represent the imperfections encountered in experiments. All gross properties including the yields were realistically simulated once the computed and measured current profiles were well fitted. The computed neutron yield Yn was in agreement with the experimentally measured Yn at 20 kV (E0 ∼ 30 kJ) charging voltage. The optimum computed neutron yield of Yn = 1.238 × 109 neutrons per shot was obtained at optimum physics parameters of the plasma focus operated with deuterium gas. It was also observed that no soft x-rays were emitted from the IR-MPF-100 plasma focus operated with argon gas due to the absence of helium-like and hydrogen-like ions at a low plasma temperature (∼0.094 keV) and axial speed (8.12 cm µs−1). However, the soft x-ray yield can be achieved by increasing the charging voltage, using a higher ratio of outer anode radius to inner anode radius c or shorter anode length z0, or using neon as the operating gas.

Flexural behavior of composite curved beams on an elastic foundation

The effects of the inner outer radius ratio on the through-thickness tensile stress and the in-plane tension stress are discussed with a focus on the curved beam based on an elastic foundation. The curved beam composed of two different materials was analyzed,and the location of the neutral axis for the in-plane tension stress was determined. Combining the boundary conditions of the zero internal and external surface stress,interlaminar normal stress,and continuous displacement in the thickness direction,the analytical solutions of the through-thickness tensile stress of the composite curved beam and in-plane normal stress were obtained under pure bending. Furthermore,the effects of volume fraction,material parameters and the placed position of the two kinds of materials on the stress of the composite curved beam were investigated. As a convenient and effective calculation strategy,the method could be extended to the application of curved beams with multiple layers of different materials for solving the strength of rectangular composite curved beams,especially the interlaminar strength in practical engineering.

BUCKLING DEFORMATION OF ANNULAR PLATES DESCRIBING NATURAL FORMS

It has been observed that undulating periodic patterns formed on an initial flat annular plate that model the leaves of plants are a physical response to the expansion of the surface under a lateral restraint. They are not visible at the beginning but become apparent only when the plants continue to grow. The behavior can be explained via the inhomogeneous deformation of gel materials that behave in a similar manner to hyperelastic materials in solid mechanics.This paper compares the stability of thin annular plates clamped along the inner edge and free along the outer periphery using numerical simulations of the swelling of thin gel annular plate held along the inner edge as well as analysis of a similar class of structures by solid mechanics concept via energy principle. The trends of results from both approaches compare favorably. The buckling patterns of annular plates with various values of inner radius to outer radius ratio illustrate the relationship between the geometry of the annular plate and the inhomogeneous deformation of gels or buckling patterns of solid mechanics materials. The undulating patterns on leaves such as those of flowering cabbage can thus be explained via the buckling behavior of annular plates, which can be regarded as thin soft materials adhered to a stiffer core. The study can also be extended to cover other stimuli under different environmental conditions and the outcome may bring further insights into the evolution of plants.

Accurate approach implementation in vibration analysis of thick sector plates

An exact closed-form solution based on Reddy’s third-order shear deformation plate theory for the free vibration of thick circular/annular sector plates is presented. Characteristic equations are given for sector plates having hard simply supported radial edges and all combinations of free, soft simply supported, hard simply supported and clamped boundary conditions along the circular edges. To clarify the efficiency and accuracy of the present solution, several comparison studies are examined with the available data in the literature. Also, natural frequencies of the circular/annular sector plates are presented for different thickness–radius ratios, inner–outer radius ratios, sector angle values and boundary conditions.

Size of discs formed by wind accretion in binaries can be underestimated if the role of wind-driving force is ignored

Binary systems consisting of a secondary accreting form a wind-emitting primary are ubiquitous in astrophysics. The phenomenology of such Bondi-Hoyle-Lyttleton (BHL) accretors is particularly rich when an accretion disc forms around the secondary. The outer radius of such discs is commonly estimated from the net angular momentum produced by a density variation of material across the BHL or Bondi accretion cylinder, as the latter is tilted with respect to the direction to the primary due to orbital motion. But this approach has ignored the fact that the wind experiences an outward driving force that the secondary does not. In actuality, the accretion stream falls toward a retarded point in the secondary's orbit as the secondary is pulled toward the primary relative to the stream. The result is a finite separation or "accretion stream impact parameter" (ASIP) separating the secondary and stream. When the orbital radius a_o exceeds the BHL radius r_b, the ratio of outer disc radius estimated as the ASIP to the conventional estimate a_o^{1/2}/r_b^{1/2}>1. We therefore predict that discs will form at larger radii from the secondary than traditional estimates. This agrees with the importance of the ASIP emphasized by Huarte-Espinosa et al. (2013) and the practical consequence that resolving the initial outer radius of such an accretion disc in numerical simulations can be less demanding than what earlier estimates would suggest.

An analytical global–local Taylor transformation-based vibration solution for annular FGM sandwich plates supported by nonuniform elastic foundations

Free vibration of functionally graded annular sandwich plates resting on Winkler-type elastic foundations is investigated based on a zigzag global–local plate theory and a finite Taylor's transform whose center is located at the outer edge. Material properties of each layer may be graded in the transverse direction according to a power law. It is the first time that a global–local theory is combined with a layerwise analytical solution for analysis of the annular functionally graded sandwich plates. Various edge conditions are considered for the inner and outer edges. A parametric study including evaluating effects of the material properties distributions of the core and face sheets, symmetric and asymmetric layups, thickness to radius ratio of the plate, inner to outer radius ratio, coefficient of the elastic foundation, and the edge conditions on vibration behavior of the annular plate is carried out. Accuracy of the employed sandwich plate theory and the presented analytical solution are verified by comparing present results with those of the three-dimensional theory of elasticity extracted from ABAQUS software.

Buckling of circular/annular Mindlin nanoplates via nonlocal elasticity

The present study proposes an analytical solution for the axisymmetric/asymmetric buckling analysis of moderately thick circular/annular Mindlin nanoplates under uniform radial compressive in-plane load. In order to consider small-scale effects, nonlocal elasticity theory of Eringen is employed. To ensure the efficiency and stability of the present methodology, the results are compared with other ones presented in the literature. Further the exact closed-form solution is obtained using three potential functions. In addition, the effect of small scales on buckling loads for different parameters such as geometry of the nanoplate, boundary conditions, and axisymmetric/asymmetric mode numbers, is investigated. It is observed that the buckling mode shape for annular nanoplates, which corresponds to the lowest critical buckling load, may be axisymmetric or asymmetric depending on boundary conditions, inner to outer radius ratios, and thickness of the nanoplate. In other words, for stiffer boundary conditions and smaller inner to outer radius ratios, the mode shape corresponding to the lowest critical buckling load is an asymmetric mode. Also, the difference between axisymmetric and asymmetric buckling loads for higher mode numbers, greater thickness to outer radius ratios and smaller outer radii decreases by increasing the nonlocal parameter.

Fabrication and Characterisation of the Graphene Ring Micro Electrode (GRiME) with an Integrated, Concentric Ag/AgCl Reference Electrode

We report the fabrication and characterisation of the first graphene ring micro electrodes with the addition of a miniature concentric Ag/AgCl reference electrode. The graphene ring electrode is formed by dip coating fibre optics with graphene produced by a modified Hummers method. The reference electrode is formed using an established photocatalytically initiated electroless deposition (PIED) plating method. The performance of the so-formed graphene ring micro electrodes (GRiMEs) and associated reference electrode is studied using the probe redox system ferricyanide and electrode thicknesses assessed using established electrochemical methods. Using 220 μm diameter fibre optics, a ∼15 nm thick graphene ring electrode is obtained corresponding to an inner to outer radius ratio of >0.999, so allowing for use of extant analytical descriptions of very thin ring microelectrodes in data analysis. GRiMEs are highly reliable (current response invariant over >3,000 scans), with the concentric reference electrode showing comparable stability (current response invariant over >300 scans). Furthermore the micro-ring design allows for efficient use of electrochemically active graphene edge sites and the associated nA scale currents obtained neatly obviate issues relating to the high resistivity of undoped graphene. Thus, the use of graphene in ring microelectrodes improves the reliability of existing micro-electrode designs and expands the range of use of graphene-based electrochemical devices.