Ratio Of Mean Radius Research Articles

Analysis of free vibrations in transradially isotropic spherically symmetric thermoelastic spheres

PurposeThe purpose of this manuscript is to study the vibration characteristics of the spherically symmetric solid and hollow spheres poised of a homogeneous thermoelastic material, based on the three dimensional coupled thermoelasticity.Design/methodology/approachIn this paper, matrix Fröbenius series solution is used to derive the frequency equations, for the field functions. Results have been applied on rigidly fixed boundary conditions.FindingsThe main finding of this paper is that the frequency of vibration of spherically symmetric sphere (structure is independent of theta and phi) increases with the increase of radius, for solid spheres and for hollow spheres with thickness to mean radius ratio. Deformation in the given materials increases with thickness to mean radius ratio of the hollow sphere.Originality/valueA numerical simulation has been done with the help of functional iteration method for solid and hollow thermoelastic spheres made of zinc and poly methyl meth acrylate materials for different boundary conditions. The computer simulated results in contempt of frequency, damping of vibration modes and displacement have been obtained graphically and compared with the existed results.

Vibration analysis of a fluid conveying sandwich cylindrical shell with a soft core

The free vibrations of a circular cylindrical sandwich shell with a flexible core containing a flowing fluid are investigated. Within the framework of the higher-order sandwich panel theory which assumes a variable displacement through the thickness, the core flexibility is taken into account. Using Hamilton’s extended principle, for an inviscid, non-rotational, laminar and incompressible flow, via the potential flow theory, the governing equations of the coupled structure and fluid system are derived. The eigenvalue problem’s equations are found by implementing a modal expansion method which has been validated by the existing results and is found to be accurate. The effect of the axial flow velocity, circumferential wave number, core to total thickness ratio and total thickness to mean radius ratio on the natural frequencies are investigated. It is found that taking into account the core's flexibility results in lower frequency values. The study shows that, unlike in dry shells, increasing the ratio of core thickness to total thickness reduces the natural frequencies monotonically in wet shells. For a constant total shell thickness, the critical velocity of the fluid decreases with increases in core thickness.

Optimal Thickness of a Porous Micro‐Electrode Operating a Single Redox Reaction

AbstractThis article reports on a procedure to predict the optimal thickness of cylindrical porous electrodes operating a single redox reaction. This is obtained from a macroscopic model for the coupled diffusion‐reaction process that is first validated with voltammetry experiments of the H2O2/H2O reduction reaction carried out with a series of porous electrodes elaborated in this work. An analytical solution to this model is developed in the steady regime and for electrodes featuring a thickness to mean radius ratio small enough compared to unity. An analytical expression of the optimal electrode thickness is derived corresponding to the crossover value of two asymptotic regimes characterizing the dependence of the volume current density produced by the electrode upon its thickness. The predictive tool of the optimal thickness is general, regardless of the porous microstructure. The case of the electrodes used in the reported experiments illustrates that the optimal thickness is not intrinsic to the microsctructure characterized by the size of the representative volume, its specific area and effective diffusion coefficient. It also depends on the operating conditions reflected in the kinetic number, Ki, and the thickness of the diffusion layer surrounding the electrode. The dependence of the optimal thickness on these two parameters is quite significant in a range of very small values of Ki but remains quasi constant beyond a threshold value.

REMOVED: The Optimality Principle Decreases Hemodynamic Stresses for Aneurysm Initiation at Anterior Cerebral Artery Bifurcations

To investigate hemodynamic stresses on anterior cerebral artery bifurcation apex and possible mechanism of the optimality principle in protecting bifurcation wall from supercharged hemodynamic stresses. Three-dimensional angiographic datasets of 122 patients with anterior communicating artery (Acom) aneurysms, 21 patients with non-Acom aneurysms, and 220 control subjects with no aneurysms were used. Radii of parent (r0) and daughter branches (r1 and r2) were measured, and bifurcations obeying the optimality principle required optimal caliber control of r0n= r1n+ r2n, with the junction exponent n approximating 3. Radius ratio= r03/(r13+ r23) and n were compared between aneurysmal and control bifurcations. Blood flow was simulated for analysis of hemodynamic stresses. Acom bifurcations in subjects without Acom aneurysms displayed optimal caliber radius, with mean radius ratio of 0.99 and n of 3.25, whereas Acom aneurysmal bifurcations had significantly lower radius ratio, 0.62 (P < 0.05), but higher n, 4.23 (P < 0.05). Peak wall shear stress and corresponding total pressure were significantly smaller for bifurcations obeying than disobeying the optimality principle (P < 0.001 and P < 0.05, respectively). Total pressures in the direct impinging center, peak wall shear stress distance, and anterior cerebral artery bifurcation angle all were significantly smaller for bifurcations obeying than disobeying the optimality principle (P < 0.05 and P < 0.001, respectively). Normal anterior cerebral artery bifurcations obey the optimality principle whereas bifurcations with Acom aneurysms do not. Disobeying the optimality principle presents significantly enhanced hemodynamic stresses to possibly damage the bifurcation wall for aneurysm initiation.

Deviation from optimal vascular caliber control at middle cerebral artery bifurcations harboring aneurysms

Cerebral aneurysms form preferentially at arterial bifurcations. The vascular optimality principle (VOP) decrees that minimal energy loss across bifurcations requires optimal caliber control between radii of parent (r0) and daughter branches (r1 and r2): r0n=r1n+r2n, with n approximating three. VOP entails constant wall shear stress (WSS), an endothelial phenotype regulator. We sought to determine if caliber control is maintained in aneurysmal intracranial bifurcations. Three-dimensional rotational angiographic volumes of 159 middle cerebral artery (MCA) bifurcations (62 aneurysmal) were processed using 3D gradient edge-detection filtering, enabling threshold-insensitive radius measurement. Radius ratio (RR)=r03/(r13+r23) and estimated junction exponent (n) were compared between aneurysmal and non-aneurysmal bifurcations using Student t-test and Wilcoxon rank-sum analysis. The results show that non-aneurysmal bifurcations display optimal caliber control with mean RR of 1.05 and median n of 2.84. In contrast, aneurysmal bifurcations had significantly lower RR (0.76, p<.0001) and higher n (4.28, p<.0001). Unexpectedly, 37% of aneurysmal bifurcations revealed a daughter branch larger than its parent vessel, an absolute violation of optimality, not witnessed in non-aneurysmal bifurcations. The aneurysms originated more often off the smaller daughter (52%) vs. larger daughter branch (16%). Aneurysm size was not statistically correlated to RR or n. Aneurysmal males showed higher deviation from VOP. Non-aneurysmal MCA bifurcations contralateral to aneurysmal ones showed optimal caliber control. Aneurysmal bifurcations, in contrast to non-aneurysmal counterparts, disobey the VOP and may exhibit dysregulation in WSS-mediated caliber control. The mechanism of this focal divergence from optimality may underlie aneurysm pathogenesis and requires further study.

Relationship between heterogeneity and seismic velocities of the Yudongzi Triassic oolitic reservoirs in the Erlangmiao area, northwest Sichuan Basin, China

In this paper, we use a range of parameters to quantitatively analyze the heterogeneity of oolitic reservoirs aiming to establish a predictive relationship between the reservoir heterogeneity and seismic velocities. The Yudongzi Oolitic shoals on the Triassic carbonate platform margin in the Erlangmiao area, NW Sichuan Basin, contain two facies elements: a stabilized sand flat and a mobile fringe. The stabilized sand flat consists mainly of oolitic limestones with moderately sorted grains of 0.1–6mm diameter that account for 40–65% of the rock components. The mobile fringe is characterized by residual oolitic dolostones in which the grains are extremely sorted with a diameter of 0.1–0.5mm and account for 70–80% of the rock components. These oolitic shoals occurred in the lower part of the Feixianguan Formation in each of the four sequence sets (i.e., Pss1–Pss4), and they were continuously progradational from Pss1 to Pss4. Diagenesis and reservoir properties of the oolitic shoals are closely related to their depositional environments, with the mobile fringe tending to contain potential reservoirs. Predictive relationships between the geological properties and seismic velocities of the oolitic reservoirs show that the content, mean diameter, mean radius ratio, and standard deviation of grains and dolomite content are linearly related to seismic velocities, while the porosity has a logistical correlation with seismic velocities. The seismic velocities decrease either with an increase of grain content or dolomite content, or with a decrease of mean grain diameter, mean radius ratio or standard deviation, and they decrease rapidly at first, and then slowly with an increase of porosity. With these correlations, impedance data from seismic exploration could be used to predict depositional environments, mineral composition, and porosity distribution of the oolitic reservoirs.

On the interaction of a single-walled carbon nanotube with a moving nanoparticle using nonlocal Rayleigh, Timoshenko, and higher-order beam theories

Interaction of a moving nanoparticle with a single-walled carbon nanotube (SWCNT) is of concern. The SWCNT is simulated by an equivalent continuum structure (ECS) under simply supported boundary conditions. The moving nanoparticle is modeled by a moving point load by considering its full inertial effects and Coulomb friction with the inner surface of the ECS. The ECS under the moving nanoparticle is modeled based on the Rayleigh, Timoshenko, and higher-order beam theories in the context of the nonlocal continuum theory of Eringen. The dimensionless discrete equations of motion associated with the nonlocal beam models are then obtained by using Galerkin method. The effects of slenderness ratio of the ECS, ratio of mean radius to thickness of the ECS, mass weight and velocity of the moving nanoparticle, and small scale parameter on the dynamic response of the SWCNT are explored. The capabilities of various nonlocal beam theories in capturing the longitudinal and transverse displacements as well as the nonlocal axial force and bending moment are also scrutinized in some detail. The possibility of moving nanoparticle separation from the inner surface of the SWCNT is examined by monitoring the sign of the contact force. Subsequently, the role of important parameters on the possibility of this phenomenon is explored using various nonlocal beam theories.

Modified Expression for Critical Reynolds Number in Eccentric Taylor-Couette Flow

d = mean gap width between two cylinders e = displacement of the centers of the outer and inner cylinders H = height of fluid column Re = Ri d= Rec = critical Reynolds number Reco = critical Reynolds number at zero eccentricity Ri = outer radius of the inner cylinder Ro = inner radius of the outer cylinder Tac = critical Taylor number = aspect ratio (H=d) = clearance ratio Ro Ri =Ri = eccentricity (e=d) = mean radius ratio (Ri=Ro) c = critical axial wavelength = kinematic viscosity = angular velocity, rad=s

Shakedown limit loads for elbows under internal pressure and cyclic in-plane bending

This paper presents elastic, shakedown and plastic limit loads for 90° elbows under constant internal pressure and cyclic in-plane bending, via finite element (FE) analysis. Effects of the elbow geometry (the bend radius to mean radius ratio and the mean radius-to-thickness ratio) and of the large geometry change are systematically investigated. By normalizing the in-plane bending moment by the plastic limit load solution of Calladine, the shakedown diagram is found to be close to unity up to a certain value of normalized pressure (normalized with respect to the limit pressure) and then to decrease almost linearly with increasing normalized pressure. The value up to which shakedown limit loads remain constant depends on the elbow geometry and the large geometry change effect. Effects of the elbow geometry and the large geometry change on shakedown diagrams are discussed.

Contact Analysis of a Nanocomposite Surface with Two Particle Size Distributions for Magnetic Particulate Tapes

The coating layer of magnetic particulate tapes consists of magnetic and nonmagnetic particles of different sizes on a polymeric matrix, which makes the tape surface have a bimodal or trimodal roughness distribution. In this study, an algorithm is developed to generate composite surfaces with two size distributions of particles. The composite surface is generated by superimposing large and small particles with radii following a Gaussian distribution on a random Gaussian surface, with the centers of the large particles sitting on the mean plane of a rough surface and the centers of the small particles sitting on the superimposed surface of large particles and a rough surface. Statistical analysis is carried out for the generated composite surfaces to study the effects of the particle distribution on the surface's probability density functions (PDFs) and roughness parameters. Also, contact analysis is conducted to identify particle distribution for low friction and wear. Variation of the fractional contact area, the maximum contact pressure, and the relative meniscus force with four design variables as well as the mean radius ratio, the standard deviation ratio, and two particle densities are studied. It is found that a higher mean radius ratio and standard deviation ratio and lower particle densities give a lower contact area, which is desirable for low friction; for low wear, the converse is true. It is recommended that a composite surface with a higher mean radius ratio is most desirable for low friction. On the other hand, for low wear, a lower mean radius ratio is recommended.

An Experimental and Computational Study of the Crushing of Metallic Hemispherical Shells Between Two Rigid Flat Platens

The axial compression of aluminium spherical shells with a ratio of mean radius to wall thickness ranging from 15 to 50 was carried out between two rigid flat parallel platens. Quasi-static tests were conducted on an Instron machine (model 1197) of 50 t capacity. Spherical shells of different radius and thickness were tested in order to identify their collapse modes and to study the associated energy absorption capacity. In experiments, all shells were found to collapse owing to the formation of inward dimpling associated with a rolling plastic hinge. The deformation of the shells was also studied and analysed with the help of the finite element code FORGE2. Predicted variations in different components of strain and stress are presented. Experimental and computed results are compared. Some of the obtained results are also compared with the solutions proposed in earlier studies. On the basis of the findings of the experiments and computational model, the basic mechanism of deformation of shells is presented and discussed.

Study of wave motion on tubulars using broad-band laser ultrasound

We investigate the transition characteristics of laser-generated ultrasonic waves propagating along the axial and circumferential directions in tubulars. The thermoacousto-photonic non-destructive evaluation technique is employed to initiate broad-band surface and guided waves in tubulars of several different outer diameters and wall thicknesses. A non-contact broad-band optical sensor known as fiber-tip interferometry is used for wave acquisition. Wave dispersion as a function of thickness to mean radius ratio is resolved using a Gabor wavelet transform based algorithm. The algorithm enables dispersion to be established through the deployment of just one sensing interferometer. This is in contrast to techniques which require multiple detection locations for the determination of wave dispersion.

Free vibration of a laminated composite circular cylindrical shell partially filled with fluid

Free vibrations of partially fluid-filled laminated composite circular cylindrical shells including transverse shear deformation are investigated using a semi-analytical procedure. In this approach, displacements and rotations of the shell and the dynamic pressure of the fluid are modelled by Fourier series and finite elements in the circumferential and axial directions, respectively, whereas the dynamic pressure of the fluid is expanded as a power series in the radial direction. The coupling between symmetric and antisymmetric modes is taken into account in the formulation. Numerical examples are given for free vibrations of partially fluid-filled laminated composite circular cylindrical shells with various boundary conditions. Parametric studies including circumferential wave number, fluid depth, thickness to mean radius ratio, length to mean radius ratio and boundary condition are carried out.

Non-axisymmetric bifurcation analysis of elastic-plastic thin circular tubes subjected to forming with axisymmetric die.

Non-axisymmetric buckling phenomenon seen during the nosing, sinking, and drawing of elastic-plastic thin circular tubes is investigated theoretically based upon Hill's bifurcation theory in conjunction with finite element approximation. The influence of the thickness of the tube to the initial mean radius ratio, the die semi-angle, the sinking zone and the exit radius, and the material properties including the transversely anisotropy of the tube on the buckling limit is investigated. It is revealed that the buckling limit is postponed when the thickness and the die semi-angle increase but conversely decreases as the yield stress σy, the hardening exponent n, and the average γ-value γ-<aν> increase Further, the existence of the sinking zone and the exit radius is found to have a suppressive effect on the critical drawing ratio.

純アルミニウム円筒の縦および円周方向の機械的性質の差

Effects of four factors on five mechanical properties of aluminum tubes were statistically investigated using the design of experiments (L27 containing dummy level). The four factors were direction of uniaxial tension Ai (longitudinal one Az, and circumferential one under internal pressure Aθ), length of reduced section (at three levels) of cylindrical specimen ki, inner diameter as recived Di, and ratio of mean radius of specimen to thickness Si. The mechanical properties were proof stress σS, tensile strength σB, F and n values (approximated on the stress-strain curve by the expression σ=Fεn), and stress ratio σ_??_/σB (σB being reduced from the F and n values). Ki is only a factor having no effect on the mechanical properties mentioned above. σB is independent of the position of wire strain gauge, and is the most reliable when assessing various factorial effects. The stress ratio σB/σB is significantly affected (significant at 5%) only by interaction of Ai × Si. The aluminum tube has the statistical average proof stress and tensile strength 5 to 7% higher in circumferential direction than in longitudinal one.

Existence of axisymmetric modes of thin cylindrical shells with axial displacement restraint

A necessary and sufficient condition is derived for the existence of the axisymmetric mode of cylindrical shells with a radial displacement having one half wave along the axis and axial displacement restrained at both ends. The condition is purely geometric and consists of an upper bound on the mean radius to thickness ratio for a given fixed value of the length to mean radius ratio, above which the mode with one half wave in radial displacement along the axis ceases to exist. The proof is based on enforcing two basic lemmas concerned with the simplicity of the eigenvalues of the shell and the uniform ordering of these eigenvalues with the number of nodes of their corresponding radial displacement eigenfunctions.

Shell Theory Solution for Asymmetric Balanced Radial Loads on Long Cylinders

The elastic behavior of a long cylinder subjected to equilibrated radial loads is considered. The problem is formulated by the use of shell theory equations. Although numerical results are available for simply supported cylinders, these results do not apply to long cylinders. The simply supported results were calculated, by Bijlaard, on the basis of equations formulated by Timoshenko and the use of a double Fourier series. The Bijlaard work uses some assumptions which limit the length of the cylinder. In the current work, the more complete equations derived by Flu¨gge and by Biezeno and Grammel are used as transformed by Kempner with the added simplification that the square of the thickness to mean radius ratio is negligible as compared to unity. Solutions for equal and opposite balanced uniformly distributed radial line loads of an any angle are obtained. The solution is carried out by means of a Fourier integral, Fourier series product. All the results are given by a single expression with tabulated coefficients. The infinite cylinder stress and deflection results are presented in graphical form for the parameters of axial position, circumferential position, angle of loading, and mean radius to thickness ratio of the cylinder. The results were checked with axisymmetric thin shell theory.

Radiation effects on large fire plumes

Recent attempts to model the flow in very hot fire plumes where radiative transport of heat may significantly modify both the dynamics of the flow and the processes of combustion have met with only partial success. This paper gives an account of a model for the flow in a turbulent fire plume at the levels above which combustion is not appreciable but where strong buoyancy and radiation effects are still important. The model includes an analysis of the radiation field in which some strong approximations are made, but the main features are retained. In the treatment, the radiative flux is divided into lateral and vertical components which are considered separately. An opacity is defined for the plume as the ratio of mean radius to mean free path of radiation, and the intermediate case in which this ratio is of order unity is discussed in detail. The role of large eddies which carry very hot gas to the edge of the smoke plume is emphasized, and an estimate is made of their substantial contributions to the radiative heat loss to the surroundings.