Showing papers on "Spherical shell published in 1982"
TL;DR: In this article, the surface-enhanced Raman scattering with excitation profiles sharply depend upon the relative thickness of the spherical shell was studied, where the incident radiation can be tuned over a range of optical wavelengths to give a variation of ${10}^{6}$ in scattering cross section.
Abstract: Elastic scattering by a small inhomogeneous sphere, comprised of two concentric spherical regions, may be abnormally low if the dielectric constant of the external medium is intermediate between those of the two regions. When one of these regions is a metal with a real negative dielectric constant, there may also be very large enhancement of the scattering due to excitation of a dipolar surface plasmon. For a sphere in which the metallic region is silver, the incident radiation can be tuned over a range of optical wavelengths to give a variation of ${10}^{6}$ in scattering cross section. Such objects may exhibit very large surface-enhanced Raman scattering with excitation profiles sharply dependent upon the relative thickness of the spherical shell.
108 citations
TL;DR: In this article, a general methodology is developed and simple closed-form solutions are derived for the case of a conical shell, a spherical shell under point load and a spherical cap under external uniform pressure.
Abstract: The crushing analysis of rotationally symmetric plastic shells undergoing very large deflections is presented. A general methodology is developed and simple closed-form solutions are derived for the case of a conical shell, a spherical shell under point load, a spherical shell crushed between rigid plates and under boss loading, and a spherical cap under external uniform pressure.
82 citations
01 Jan 1982
TL;DR: In this paper, the dynamics of A-L-P electron models with rigid or flexible shell surfaces were studied, and a non-electromagnetic (mechanical) attractive force is present to keep the electron from puffing up like a balloon due to the mutual repulsion of its charged parts.
Abstract: An electron, in an Abraham-Lorentz-Poincare model, is a uniformly charged spherical shell (Abraham, 1903, 1904; Lorentz, 1952; Poincare, 1905, 1906) A non-electromagnetic (“mechanical”) attractive force is present to keep the electron from puffing up like a balloon due to the mutual repulsion of its charged parts In this chapter we will study the dynamics of A-L-P electron models* with rigid or flexible shell surfaces Hereafter, an A-L-P electron model will often be simply called “the electron”
73 citations
72 citations
TL;DR: In this paper, the singularity theory point of view was used to study certain bifurcation problems which commute with the five-dimensional irreducible representation of the orthogonal group O(3) and to give some implications of this study for the Benard problem in spherical geometry.
Abstract: This paper has two purposes: to study from the singularity theory point of view certain bifurcation problems which commute with the five-dimensional irreducible representation of the orthogonal group O(3) and to give some implications of this study for the Benard problem in spherical geometry. We shall now describe in general terms our results and compare them with the work of Chossat [3] whose paper motivated our own interest in the problem. The Benard problem is concerned with convection in a viscous fluid when it is heated from below. The fluid is assumed to be confined in a spherical shell of outer radius R, and inner radius qRo, where q is near 0.3. This choice of q is partially motivated by considering convection within the molten layer of the core of the earth (see Busse [l] for further discussion). We consider the Binard problem in the Boussinesq approximation. In this model there is a trivial solution representing pure heat conduction radially outward. As the temperature on the inner sphere (that is, the Rayleigh number R) is increased, this trivial solution loses stability, say at R = R'. The Benard problem is the study of the resulting bifurcation. Chossat studies this problem using the Lyapunov-Schmidt reduction. In the Boussinesq approximation the fluid is driven from the pure conduction state by a term in the momentum equation involving the gravity vector g(r) and a term in the temperature equation involving the gradient of the conduction temperature VT,. Assuming that the production of heat and the density are uniform throughout the shell, these vectors have the form
51 citations
TL;DR: In this paper, the dynamic axisymmetric behavior of clamped orthotropic shallow spherical shell subjected to instantaneously applied uniform step-pressure load of infinite duration, is investigated, and the resulting modal equations, two in number, are numerically integrated using Runge-Kutta method, and hence the load-deflection curves are plotted.
48 citations
TL;DR: In this paper, a simple analytic model is developed to describe the plasma parameters produced at peak compression when gas-filled spherical shell targets are imploded by the ablation pressure produced by irradiation with constant laser power.
Abstract: A simple analytic model is developed to describe the plasma parameters produced at peak compression when gas‐filled spherical shell targets are imploded by the ablation pressure produced by irradiation with constant laser power. The range of validity of the model is discussed and, in particular, the constraints due to preheating by hot electrons. Comparison with numerical simulation verifies the accuracy of the model. The implications of the scaling of compressed plasma parameters with target and laser parameters are discussed.
38 citations
TL;DR: In this article, the electromagnetic scattering problem for a thin optically isotropic spherical shell of arbitrary size and refractive index has been solved exactly in closed form, which is the only closed form solution in Mie scattering known to the authors.
Abstract: The electromagnetic scattering problem for a thin optically isotropic spherical shell of arbitrary size and refractive index has been solved exactly in closed form. This is the only closed form solution in Mie scattering known to the authors. The standard series solution to the layered sphere problem is shown to be summable and simple exact expressions are obtained for the scattering amplitudes. The Rayleigh–Debye approximation results are also obtained by direct summation of the infinite series. The horizontal depolarization ratio, given a zero value for isotropic shells in the Rayleigh–Debye theory, is given considerable attention and is compared to the Rayleigh–Debye calculation for anisotropic radially oriented segments in the shell. Some comparisons with the Mie scattering from solid spheres are also included. In addition, the deviations of Rayleigh–Debye theory from the exact Mie theory of thin shell scattering are examined in detail as a function of various parameters.
29 citations
TL;DR: In this paper, the Brans-Dicke field equations for singular hypersurfaces are derived and an exact solution of the field equations is presented which represents a static spherical shell of perfect fluid.
Abstract: Junction conditions are formulated in an invariant manner for the jumps in the gravitational and scalar fields across a singular time-like hypersurface in the Brans-Dicke theory of gravity. The equations of motion for singular hypersurfaces are also derived, and an exact solution of the Brans-Dicke field equations is presented which represents a static spherical shell of perfect fluid.
20 citations
Patent•
26 Mar 1982TL;DR: In this paper, a spherical lens of graded refractive index distribution comprises a core of uneven refractive indices of the shape of a sphere or hemisphere and a clad of the shapes of a spherical shell and a rod, with the two clads disposed on the periphery of the core.
Abstract: A spherical lens of graded refractive index distribution comprises a core of uneven refractive index of the shape of a sphere or hemisphere and a clad of the shape of a spherical shell and a rod clad, with the two clads disposed on the periphery of the core. By the combination of the core showing negative aberration characteristic and the spherical-shell type clad and the rod clad both showing positive aberration characteristic, there can be formed a lens of corrected aberration. This lens suits combination or integration with other elements and permits easy manufacture of clads. It also provides effective convergence of beams of light desirable for use in an optical pickup, for example.
18 citations
TL;DR: In this article, the minimum weight design of a spherical shell under a concentrated load at the apex is presented and the usual restrictions of statical equilibrium and various yield criteria have been utilized.
Abstract: The minimum weight design of a spherical shell under a concentrated load at the apex is presented in this paper. The usual restrictions of statical equilibrium and various yield criteria have been utilized. The finite element method is used to discretize the design parameters and the resulting nonlinear minimization problems are solved using the modified Rosenbrock's optimization method.
TL;DR: In this article, a finite element model for symmetrically loaded shells of revolution is described, where nonlinear geometric effects are accounted for by incrementing loads and iterating for equilibrium.
Abstract: A finite element model for symmetrically loaded shells of revolution is described. The nonlinear geometric effects are accounted for by incrementing loads and iterating for equilibrium. The iteration process also allows for nonlinear materials. The shell model accounts for large strains, large rotations and shear deformation. Three example problems demonstrate the ability of this model to solve linear problems. Also, three example problems demonstrate the versatility and accuracy of this model for nonlinear problems. These nonlinear example problems are an axially loaded cylinder and an internally pressurized spherical shell that have large membrane strains, and a cylinder that deforms into a spherical shape, having large rotations.
TL;DR: In this paper, a comparison between the resonant frequencies of two dry human skulls and corresponding spherical shell models was made, and the elastic modulus of the model was adjusted to bring its resonances into closer agreement with those of the skull.
TL;DR: In this paper, the transmission of a spherical electromagnetic wave through a dielectric shell is considered and the field solution determined by the geometrical optics (GO) theory is given in a simple closed form.
Abstract: The transmission of a spherical electromagnetic wave through a dielectric shell is considered. The two surfaces of the shell are spherical (either concave or convex), and their centers are arbitrarily located in relation to the source point. The field solution determined by the geometrical optics (GO) theory is given in a simple closed form. Special attention is given to the lens effect of the dielectric shell which converts the incoming spherical pencil into a focusing pencil.
TL;DR: In this paper, the authors studied the Yang-Mills equations for spherically symmetric situations and found the same types of solutions as for purely electric sources: besides the Abelian (Coulomb-Biot-Savart) solution there are two non-Abelian types, one of which requires minimal source strengths and comes in two branches.
Abstract: Classical, time-independent solutions of the Yang-Mills equations are studied for spherically symmetric situations. In the presence of charge and current distributions the same types of solutions are found as for purely electric sources: Besides the Abelian (Coulomb-Biot-Savart) solution there are two non-Abelian types, one of which requires minimal source strengths and comes in two branches. The solution pattern is investigated by rough numerical calculations for a simple source model corresponding to spherical shell distributions. In the absence of charge distributions an additional type is found, which has zero electric field and a magnetic field corresponding to a monopole of fixed strength. This type of solution exists for a large class of reasonable source currents. Some analytical examples are given in addition to numerical results for the shell model. Stability problems are not touched.
TL;DR: A mathematical model for the motion of a large, flexible shallow spherical shell in a circular orbit is presented in this paper, where a rigid dumbbell connected to the shell at its apex by a spring-loaded double-gimball joint is proposed to stabilize the structure gravitationally.
Abstract: A mathematical model for the motion of a large, flexible shallow spherical shell in a circular orbit is presented. For small elastic displacements and attitude angles the linearized equations for the roll and yaw (out-of-plane) motions completely separate from the pitch (in-plane) and elastic motions. However, the pitch and only the axisymmetric elastic modes are seen to be coupled in the linear range. With the shell's symmetry axis following the local vertical, the structure undergoes a static deformation under the influence of gravity and inertia. Further, the pitch and roll motions are unstable due to the unfavorable moment of inertia distribution. A rigid dumbbell connected to the shell at its apex by a spring-loaded double-gimball joint is proposed to stabilize the structure gravitationally. A sensitivity study of the system response characteristics to the key system parameters is carried out.
Patent•
10 Jul 1982
TL;DR: In this paper, the adjustment of a pressure plate to the inclination of the pressure surface of the test piece is performed first and then, on loading, a relative movement between the spherical cup and spherical shell is prevented by frictional connection or respectively static friction.
Abstract: 1. Method for the mounting and adjustment of pressure plates in materials testing machines, which have a pressure plate with a spherical cup, a spherical shell which is connectable with the testing machine for receiving the spherical cup, and connecting elements for connecting the spherical cup and the spherical shell, the adjustment of the pressure plate to the inclination of the pressure surface of the test piece being effected first and thereafter, on loading, a relative movement between the spherical cup and spherical shell being prevented, characterised in that - for the almost force-free adjustment of the pressure plate to the inclination of the pressure surface of the test piece which is brought against it whilst maintaining a centering of the spherical cup to the spherical shell, a first pair of contact surfaces is brought into effect, which pair consists of spherical shell ans spherical cup elements which can be supported against each other and which are arranged concentrically to the spherical shell axis, and which pair forms a contact surface with slight friction, - and that thereafter, on loading, a second pair of contact surfaces, consisting of a spherical cup and spherical shell, is brought into effect, the second contact surfaces having a high coefficient of friction, so that on resting the spherical cup against the spherical shell, a relative movement between the spherical cup and the spherical shell is prevented by frictional connection or respectively static friction.
01 Jan 1982
TL;DR: The buckling behavior of complete spherical shells and spherical caps is explained and test results are extensively reviewed in this paper, where the development of the theory up to the point where theoretical and experimental results agree is presented.
Abstract: The buckling behaviour of complete spherical shells and spherical caps is explained and test results are extensively reviewed. The development of the theory up to the point where theoretical and experimental results agree is presented. The treatment is confined to completely elastic material.
TL;DR: Using a circumscribing yield surface, the limit pressure was obtained for a spherical shell with a circumferential partial penetration defect in this article, which indicates the importance of the transverse shear stress for deep defects and is in good agreement with experiments on four vessels that were also described.
TL;DR: In this paper, the dispersion relation obtained has the form of the Rossby-Haurwitz formula when the shell is spherical, and is asymptotically equivalent to that found by Longuet-Higgins (1965) for the free surface problem on a sphere.
TL;DR: In this article, the simple von Karman model of a clamped shallow elastic cap subjected to external pressure is reformulated as an elementary catastrophe, and three distinct modes of deflection behavior are identified.
Abstract: The simple von Karman model of a clamped shallow elastic cap subjected to external pressure is reformulated as an elementary catastrophe. Conceptual understanding of load deflection behavior is substantially improved as a result. Three distinct modes of deflection behavior are identified. One snap-through type behavior is substabtiated by comparison to experimental data.
Patent•
13 Jan 1982
TL;DR: In this article, a high liquid tight embankment which the upper portion is cylindrical in closed type to the ground is installed under good attitude against earth quakes, and prescribed maintenance is carried out by derrick 20, chain hoist 19 and deck 17 for upper diameter of spherical shell 4.
Abstract: PURPOSE:To install under good attitude against earth quake, building high liquid tight embankment which the upper portion is cylindrical in closed type to the ground. CONSTITUTION:Liquid accumulating load weight of spherical shell are transmitted to high liquid tight embankment 6 by support 8 through bracket 12, total weight including the weight of high liquid tight embankment 6 is transmitted to the ground 1 surely through wide floor space of its lower semispherical portion 6''. Thermal behavior under running is absored sufficiently through relative slide between bracket 12 and steel plate 9. When checking maintenance, prescribed maintenance is carried out by derrick 20, chain hoist 19 and deck 17 for upper diameter of spherical shell 4. In case of earth quake, embankment 6 is maintained sufficiently through its stiffness and strength, and spherical shell 4 is restricted for displacement to maintain through doweling of bracket 12 and ring plate 9, while, maintenance step 7, 7... is installed annularly inside of lower spherical shell 4 and concentrical semispherical portion.
TL;DR: In this paper, the authors proposed a method by which the elasto-plastic behavior of the axisymmetric shell can be exactly expressed by using the membrane forces and bending moments, and moreover investigates effects of the imperfections on the collapse pressure of the spherical shell.
Abstract: It is very important to predict the collapse strength of externally pressurized spherical shell which have imperfections such as welding deformation and residual stresses.Many experimental studies on this problem have been made by M. Krenzke et al., but few theoretical researches have been reported.To exactly obtain a numerical solution of the collapse pressure of the spherical shell, it is necessary to consider the strain hardening in the elasto-plastic analysis of the axisymmetric shell.This paper introduces a newly developed method by which the elasto-plastic behavior of the axisymmetric shell can be exactly expressed by using the membrane forces and bending moments, and moreover investigates effects of the imperfections on the collapse pressure of the spherical shell.Main conclusions obtained from this study are as follows ;(1) The usefullness and accuracy of the new method are confirmed by comparison with the experimental results.(2) The more plastically the spherical shell collapses, the smaller the effects of the imperfections on the collapse pressure becomes.(3) In the case that a penetrator or a partial sphere is welded circumferentially to the spherical shell, according as the diameter of the penetrator or partial sphere increases, the collapse pressure of the spherical shell will increase if both have same value imperfection by welding.(4) If the spherical shell has the residual stress, its collapse pressure will reduce.
Patent•
11 Dec 1982
TL;DR: In this paper, the authors proposed a method to improve the energy saving effect by a method wherein the heat of solidification liberated at the phase change from liquid to solid and the fusion absorbed at the phases change from solid to liquid of straight-chain alpha olefin sealed as medium within a spherical shell are put to good use.
Abstract: PURPOSE:To improve the energy-saving effect by a method wherein the heat of solidification liberated at the phase change from liquid to solid and the heat of fusion absorbed at the phase change from solid to liquid of straight-chain alpha olefin sealed as medium within a spherical shell are put to good use. CONSTITUTION:The heat accumulating body A consists of the spherical shell 1 and straight-chain alpha olefin with its melting point lying between -24-80 deg.C sealed within the spherical shell 1 as heat transfer medium. If the body A is intended to be used, for example, as building material parts, a large number of the bodies A are packed tightly between concrete walls 5 and formed as one body product together with the concrete walls 5 at the excecution of the concrete walls 5. As a result, the heat insulating effect, heat accumulating effect and heat shock absorbing effect of the concrete walls 5 is remarkably increased, resulting in enabling to sharply economize energy consumption at air-condition or the like.
TL;DR: In this paper, a dielectric fluid, contained in a spherical shell, with rigid boundaries is subjected to a simultaneous radial temperature gradient and radial a.c. electric field, and the dependence of each critical number is presented as a function of the gap size and temperature gradient.
Abstract: This paper is concerned with the dielectrophoretic instability of a spherical shell of fluid. A dielectric fluid, contained in a spherical shell, with rigid boundaries is subjected to a simultaneous radial temperature gradient and radial a.c. electric field. Through the dependence of the dielectric constant on temperature, the fluid experiences a body force somewhat analogous to that of gravity acting on a fluid with density variations. Linear perturbation theory and the assumption of exchange of stabilities lead to an eighth order differential equation in radial dependence of the perturbation temperature. The solution to this equation, satisfying appropriate boundary conditions, yields a critical value of the electrical Rayleigh number and corresponding critical wave number at which convective motion begins. The dependence of each critical number is presented as a function of the gap size and temperature gradient. In the limit of zero shell thickness both the critical Rayleigh number and critica...
TL;DR: In this paper, the frequency equations for free, axisymmetric vibrations of an elastic spherical shell submerged in a compressible viscous fluid are reduced to a simple polynomial expression.
09 Jul 1982
TL;DR: In this article, the dynamics of orbiting shallow flexible spherical shell structures under the influence of control actuators was studied and control laws were developed to provide both attitude and shape control of the structure.
Abstract: The dynamics of orbiting shallow flexible spherical shell structures under the influence of control actuators was studied. Control laws are developed to provide both attitude and shape control of the structure. The elastic modal frequencies for the fundamental and lower modes are closely grouped due to the effect of the shell curvature. The shell is gravity stabilized by a spring loaded dumbbell type damper attached at its apex. Control laws are developed based on the pole clustering techniques. Savings in fuel consumption can be realized by using the hybrid shell dumbbell system together with point actuators. It is indicated that instability may result by not including the orbital and first order gravity gradient effects in the plant prior to control law design.
TL;DR: In this article, a model for large axisymmetric deformations of a linearly elastic spherical shell compressed between two rigid plates is described, where the deformation of the free region may be determined from a two-point boundary value problem.
TL;DR: In this paper, it was shown that if this mean value property holds for all such spheres, then the law of force is given by for some constants A and B Furthermore, in certain cases, by use of the theory of mean periodic functions, it is shown that this law of forces holds when the attraction due to a uniform spherical shell with centre 0 is the same as the attraction caused by the mass of the shell concentrated at 0.
Abstract: In real Euclidean n Rn where r denotes the distance of a given point in Rn to the origin 0, it is well known that if the law of gravitational attration is proportional to 4n-1, then the attraction due to a uniform spherical shell with centre 0 is the same as the attraction due to the mass of the shell concentrated at 0 In this paper, it is shown that if this mean value property holds for all such spheres, then the law of force is given by for some constants A and B Furthermore, in certain cases, by use of the theory of mean periodic functions, it is shown that this law of force holds when this mean value property holds for just two spheres
Patent•
14 Jan 1982
TL;DR: In this article, the T-shaped steel pieces are arranged in such a manner that their web 2B is situated within a plane including the center O of a spherical body to form an enclosure S, and the enclosure S is enclosed by welding a metal plate 4 overhung inward of the spherical shell.
Abstract: PURPOSE:To obtain a diving spherical body easy to manufacture with large strength against pressure, by building up many T-shaped steel pieces to frame-shape in such a manner that their flange part faces outward further their web inward, welding the pieces and forming a spherical shell. CONSTITUTION:Flanges 2A of many T-shaped steel pieces 2 are faced outward and webs 2B of them are faced inward to build up respectively to frame shape, perform welding to one another and form a spherical shell 3. The T-shaped steel pieces 2 are arranged in such a manner that their web 2B is situated within a plane including the center O of a spherical body to form an enclosure S, and the enclosure S is enclosed by welding a metal plate 4 overhung inward of the spherical shell 3. The metal plate 4 is previously formed to such curved shape as durable with expansion force for pressure exceeding water pressure applied in the depths of the sea.