Showing papers on "Spherical shell published in 1984"
TL;DR: In this paper, the static and dynamic axisymmetric buckling of elastic orthotropic thin shallow spherical shells with elastically restrained edge for inplane and rotational displacements was investigated.
Abstract: This investigation deals with the static and dynamic axisymmetric buckling of elastic orthotropic thin shallow spherical shells with elastically restrained edge for inplane and rotational displacements. Governing equations in terms of normal displacementw and stress function ψ have been employed. Orthogonal point collocation method is used for spatial discretisation and Newmark-β scheme is used for time-marching. The uniformly distributed static and step function conservative loadings normal to the underformed surface are considered. The present results are in good agreement with the available results. The influence of orthotropicity parameter β and the support stiffness parameters on the static and dynamic buckling loads has been investigated.
41 citations
TL;DR: In this paper, the problem of free, harmonic vibrations of thin, elastic, spherical shells is studied and the differential equations are derived in an invariant form together with the appropriate kinematic and static boundary conditions.
40 citations
TL;DR: In this paper, a theoretical analysis of the harmonic oscillation as well as the subharmonic oscillation of order 1/2 was conducted using a shallow spherical steel shell, and the experimental analysis confirmed the validity of the theoretical analysis.
Abstract: Axisymmetric forced oscillations of a shallow spherical shell subjected to harmonic excitation are investigated. Based on modal equations derived from the von Karman dynamic equations, a theoretical analysis is conducted of the harmonic oscillation as well as the subharmonic oscillation of order 1/2. The theoretical analysis reveals that in certain cases the response curve of the harmonic oscillation is of soft spring type, that the subharmonic oscillation of order 1/2 can occur, and that the characters of the subharmonic oscillation are greatly influenced by internal resonance. An experimental analysis is also conducted with use of a shallow spherical steel shell. The experimental analysis confirms the validity of the theoretical analysis.
35 citations
TL;DR: In this paper, the authors presented an analysis in which the zoned lens is approximated by an ideally thin spherical shell (phase transformer) in evaluating the phase aberrations in its aperture plane which are caused by off-axis scanning and deviations from the design frequency.
Abstract: Zoned dielectric lenses, designed for wide-angle scanning characteristics, are serious contenders to reflector systems for multiple-beam communications and radar applications at EHF frequencies. An analysis is presented in which the zoned lens is approximated by an ideally thin spherical shell (phase transformer) in evaluating the phase aberrations in its aperture plane which are caused by off-axis scanning and deviations from the design frequency. Those results are used to produce a set of universal curves which predict the decrease in directive gain of the lens as a function of scan angle and frequency. Gain and radiation pattern measurements on a 90 \lambda zoned dielectric lens show agreement with these predictions and with ray-tracing and geometric optics calculations. This study establishes the validity of the spherical shell analysis as a means for rapid estimation of lens parameters for specific system requirements.
26 citations
TL;DR: In this paper, the axisymmetric shell form which maximizes the fundamental frequency of vibration was obtained for thin, shallow, elastic shells with a given circular boundary, where the boundary conditions, material, surface area, and uniform thickness of the shell were specified.
Abstract: Thin, shallow, elastic shells with given circular boundary are considered. We seek the axisymmetric shell form which maximizes the fundamental frequency of vibration. The boundary conditions, material, surface area, and uniform thickness of the shell are specified. We employ a bimodal formulation and use an iterative procedure based on the optimality condition to obtain optimal forms. Results are presented for clamped and simply supported boundary conditions. For the clamped case, the optimal forms have zero slope at the boundary. The maximum fundamental frequency is significantly higher than that for the corresponding spherical shell if the boundary is clamped, but only slightly higher if it is simply supported.
26 citations
TL;DR: In this article, the frequency and modal shape of a spherical shell or dome is derived for a wide range of conical angle angles, and an approximate solution is proposed for dynamic response analysis and which easily provides natural frequencies and modality shapes which are accurate enough for engineering purposes.
25 citations
TL;DR: In this article, the photophoretic force of a spherical particle covered with a volatile concentric spherical shell was calculated for a single particle at the nucleation mode (0.022 μm radius) and the accumulation mode(0.16 μm diameter) of Eastern United States haze for conditions corresponding to the upper atmosphere.
Abstract: New calculations of the photophoretic force are presented for a spherical particle that may be coated with a volatile concentric spherical shell. The distribution of heat sources within the particle was obtained from an extension of the electromagnetic model of a concentric sphere of Aden and Kerker. The calculation for heat conduction within the sphere utilized a Monte Carlo technique. The nun momentum and energy transport at the particle surface was obtained in the “free molecule” regime. Computations were carried out mainly for particles at the nucleation mode (0.022 μm radius) and the accumulation mode (0.16 μm radius) of Eastern United States haze for conditions corresponding to the upper atmosphere. The photophoretic force was frequently much greater than the gravitational force and, in some cases, it was negative. Indeed, negative photophoresis for smoke, desert dust and soot coated with dirty ice might account for levitation of such particles with subsequent transport in the atmosphere ov...
24 citations
Patent•
03 Apr 1984
TL;DR: In this article, a spherical switching member for fluid cut-off elements, which consists of a spherical shell having through openings, and a guide pipe connecting the through openings in the interior of the shell, is described.
Abstract: 1. Process for the manufacture of a spherical switching member for fluid cut-off elements, which consists of a spherical shell having through openings, and a guide pipe (18) connecting the through openings in the interior of the shell, starting with a shell black (22) having a tubular end which is deformed spherically inwards to form one of the through openings (20), characterised in that the guide pipe (18) is inserted coaxially into the shell blank (22) before the inward deformation of the latter and during the deformation is clamped between the edges defining the through openings.
24 citations
TL;DR: In this paper, the role of increasing viscosity with depth, of two layers of convection, and of the coupling with lithospheric plates has been investigated, and it is shown that a planet with constant viscosities will have positive values for the admittance for all wavenumbers.
Abstract: Summary.
A formalism based on an analytical approximation for convection in a layered spherical shell leads to the computation of the Green kernels for topography and gravity, and to the admittance of gravity over topography for the harmonics of the Earth. We study the role of increasing viscosity with depth, of two layers of convection, and of the coupling with lithospheric plates. It is found that a planet with constant viscosity will have positive values for the admittance for all wavenumbers. However, when a step of viscosity between the lower and upper mantle is assumed, negative values for the first harmonics are achieved. This result explains some long-wave observations and provides evidence for an increase of viscosity in the lower mantle.
23 citations
TL;DR: In this paper, the interplay of shell structure and rotational motion in the nuclear level density is discussed and the result of a schematic calculation reveals a washing out of spherical shell effects at much lower excitation energies than expected if only the intrinsic level density in the independent particle model is considered.
Abstract: The interplay of shell structure and rotational motion in the nuclear level density is discussed. The result of a schematic calculation reveals a washing out of spherical shell effects at much lower excitation energies than expected if only the intrinsic level density in the independent particle model is considered.
23 citations
TL;DR: In this article, the use of a juxtaposition preequilibrium model is examined for a wide range of mechanisms, focusing on the effects of ionic strength both on equilibria and on electron transfe...
Abstract: The use of a juxtaposition preequilibrium model is examined for a wide range of mechanisms. Particular attention is given to the effects of ionic strength both on equilibria and on electron transfe...
Patent•
02 Apr 1984
TL;DR: In this article, the acoustic matching layer has been used to obtain an ultrasonic wave transmitter-receiver with fast sound velocity, matching layer and ease of manufacture by using an epoxy resin or a silicone resin as a base material and using a composite material mixed with a thermal expansion balloon as an acoustic matching member.
Abstract: PURPOSE:To obtain an ultrasonic wave transmitter-receiver with fast sound velocity, matching layer and ease of manufacture by using an epoxy resin or a silicone resin as a base material and using a composite material mixed with a thermal expansion balloon as an acoustic matching member. CONSTITUTION:The acoustic matching layer 2 is bonded to an ultrasonic wave irradiating plane 4 of a piezoelectric vibrator 11 transmitting and receiving an ultrasonic wave and a back load member 31 is bonded as required made of ferrite rubber is bonded to the back side 5. As the acoustic matching layer 2, a composite agent where the thermal expansion balloon as the 1st filler and glass balloon as the 2nd filler using silicone rubber as the base material are mixed is used. The elastic modulus of a high polymer constituting a spherical shell of the thermal expansion balloon is <=1/10 in comparison with the elastic modulus of the glass constituting the spherical shell of the glass balloon. Thus, the acoustic matching layer having fast sound velocity is obtained without reducing remarkably the sensitivity of wave transmission and reception.
TL;DR: Mollweide projections allow details on the surface of a sphere to be presented as a two-dimensional map as discussed by the authors, which allows details on a sphere surface to be represented as a map.
Abstract: Mollweide projections allows details on the surface of a sphere to be presented as a two-dimensional map.
TL;DR: In this article, the elastic dynamic deformations of an air-filled spherical shell upon explosion of a lumped high energy charge in its cavity were investigated, and the authors concluded that there is no connection between the build-up of vibrations and the disturbance in the central symmetry of the load.
Abstract: These authors conduct experimental investigations of the elastic dynamic deformations of an air-filled spherical shell upon explosion of a lumped high energy charge in its cavity. A sketch illustrates the arrangement of the steel shell with ball charge and strain gauges; oscillograms show the pressure measurements on the outer and inner surfaces; and a table records shell strain as a function of eccentricity. The authors conclude that there is no connection between the build-up of vibrations and the disturbance in the central symmetry of the load.
TL;DR: In this article, the solution of viscoplastic buckling of a complete thin spherical shell subjected to impulse pressure is given, where the nonlinear flow law is assumed and the influence of elevated temperature on the magnitude of displacements, buckling mode and threshold impulse is discussed.
01 Jan 1984
TL;DR: In this paper, it has been shown that polar dimpling is possible when a spherical shell is subject to an axisymmetric normal pressure distribution which is directed inward near a pole and outward in an adjacent region.
Abstract: Under favourable loading conditions, dome-shaped thin elastic shells of revolution are known to exhibit a predominantly inextensional bending deformation in the form of a finite axisymmetric dimple centered at the pole. For example, it has been shown in [1,2] that polar dimpling is possible when a spherical shell is subject to an axisymmetric normal pressure distribution which is directed inward near a pole and outward in an adjacent region(3). To a good approximation, the dimple base radius, which characterizes the location of the dimple base and therefore the dimple size, was shown to depend on the external loading in a simple way. To bring out the essential idea behind the asymptotic method for constructing the simple solution, results for a spherical cap with a clamped edge were first presented in [1] for a quadratically varying pressure distribution along the shell meridian. Analogous and more general results were reported for a complete spherical shell in [2] for a meridionally sinusoidal pressure distribution.
TL;DR: Theorems based on earlier work that simplify difficult ligand π-and δ-group orbital combinations and their irreducible symmetries are presented in this paper.
Abstract: Theorems based on earlier work that simplify difficult ligand π- and δ-group orbital combinations and their irreducible symmetries.
TL;DR: In this paper, the buckling of spherical shells is investigated with the aid of finite element calculations by introducing not only geometrical imperfections but also displacements of the clamped boundary of the spherical cap.
TL;DR: In this article, the authors constructed a solution of the field equations with a possible astrophysical interest by matching a Vaidya solution with another Vidal solution through a thin spherical shell of radially radiating matter.
Abstract: We construct a solution of Einstein's field equations with a possible astrophysical interest by matching a Vaidya solution with another Vaidya solution through a thin spherical shell of radially radiating matter. We study the system of equations for the motion of the shell and the radiation fields in two simple cases. In one of them we consider a dust shell of constant proper mass radiating at constant rate. In the other case we restrict the motion of the shell to a stationary configuration and assume it to be totally opaque. We find that this later solution is unstable under small perturbations in the radius of the shell but there exist stable stationary solutions if the pressure within the shell is different from zero.
TL;DR: In this paper, the authors used the ray method to study slow hydromagnetic waves in an incompressible, inviscid, perfectly conducting fluid of constant density in the presence of a constant toroidal magnetic field.
Abstract: The ray method is used to study slow hydromagnetic waves in an incompressible, inviscid, perfectly conducting fluid of constant density in the presence of a constant toroidal magnetic field. The fluid is bounded below by a rigid sphere and above by a rigid spheroidal surface, and the mean fluid layer thickness is assumed to be small. Both the general time-dependent and time-harmonic (free oscillation) problems are studied and dispersion relations and conservation laws are derived. These results are applied to free oscillations with constant azimuthal wave number in a spherical shell and then compared to those of previous authors. Such oscillations propagate to the east and are trapped between circles of constant latitude. Wave propagation in axisymmetric shells is then studied with emphasis on the relationship between shell shape and direction of propagation, and it is found that such shells can sustain westward propagating modes wherever the shell thickness decreases sufficiently rapidly from a ...
01 Jul 1984
TL;DR: In this paper, the transient thermal stress problems of a spherical region under the condition that the continuum medium possesses spherically isotropic thermoelastic properties were analyzed for both solid and hollow spheres.
Abstract: In this paper, we deal with transient thermal stress problems of a spherical region under the condition that the continuum medium possesses spherically isotropic thermoelastic properties. For illustrative purposes, we have analyzed the transient thermal stress problems of solid and hollow spheres. From the numerical calculations it is shown that the thermal stress distributions vary considerably in accordance with the variation of the thermoelastic compliance constants.
TL;DR: In this article, a nonlinear convection with spherically symmetric basic state is investigated in a thin spherical shell with rigid and nearly insulating boundaries. And the preferred mode of convection is determined by a stability analysis.
Abstract: Nonlinear convection with spherically symmetric basic state is investigated in a thin spherical shell with rigid and nearly insulating boundaries. The nonlinear problem of steady three-dimensional convection is solved by a perturbation technique. Six physically distinct solutions are determined for the case where l =5 ( l is the degree of spherical harmonics) is preferred. The preferred mode of convection is determined by a stability analysis. The axisymmetric solution is found to be unstable, while a non-axisymmetric solution which transports the maximum amount of heat appears to be preferred.
TL;DR: In this paper, exact inextensional bending solutions of shell surfaces of explicit cubic representation are derived for exact and approximate inextension bending solutions for shell surfaces with the same shape as a uniformly loaded soap bubble.
01 Jan 1984
TL;DR: For the axisymmetric buckling problem of a complete spherical shell, the authors gave a complete imperfection sensitivity analysis for the most complicated case to occur, namely that of a double eigenvalue, if we restrict our analysis to nonlinear terms of quadratic order.
Abstract: For the axisymmetric buckling problem of a complete spherical shell we are able to give a complete imperfection sensitivity analysis for the most complicated case to occur, namely that of a double eigenvalue, if we restrict our analysis to nonlinear terms of quadratic order, which is correct mathematically as the bifurcation system turns out to be two determinate As we make a classical bifurcation analysis our results are strictly local and therefore are of restricted practical importance in two respects Firstly we do not take care of the fact that we have closely spaced eigenvalues We comment on this in chapter 7 Secondly we are not able to show that the experimentally observed single dimple solution (Fig 8) is one of the stable solutions found from our bifurcation equations up to terms of third order
Patent•
13 Jun 1984
TL;DR: In this paper, a spacer on the spherical top of a rest is provided to fit a spherical part of a curvature radius different from that of a spherical shell, so that spherical shells different in radius of curvature can be machined by using the single rest.
Abstract: PURPOSE:To enable economic machining and reduce the area of an occupied floor, by providing a spacer on the spherical top of a rest to fit a spherical part of a curvature radius different from that of a spherical shell, so that spherical shells different in radius of curvature can be machined by using the single rest. CONSTITUTION:A rest 1 is used to perform machining such as the edge preparation of the plate of a pressed spherical aluminum shell for a spherical tank. A spherical part A with a radius of curvature A is secured on the top of the rest 1 supported by pedestals 3 on an installation surface 2. A spacer 4 with a saw-tooth form is provided on the spherical part 1A of the rest 1. An attachment 5 having a spherical part 5A with a radius of curvature B is removably assembled on the spacer 4 to machine a spherical shell with the radius of curvature B. According to this constitution, spherical shells different in radius of curvature can be machined by using the single rest.
TL;DR: In this paper, a model system consisting of a thin spherical shell with radiusR and massM and a point massm at a distances>R from the center of the sphere, held fixed by an appropriate strut, is solved to ordermM.
Abstract: A model system, consisting of a thin spherical shell with radiusR and massM and a point massm at a distances>R from the center of the sphere, held fixed by an appropriate strut, is solved to ordermM. The stresses in the shell are not of the canonical Weyl type, and it is argued that the same is true for more realistic situations, e.g., rotating matter. Owing to the nonlinearity of Einstein's field equations, the field of the point mass is shielded from the interior of the shell by a factor η lying between 1–3M/R and 1–2M/R, and the field outside the shell explicitly depends onR.
TL;DR: In this article, an analysis of the free vibration of an elastically or rigidly point-supported circular cylindrical shell is presented, where the dynamical energies of the shell are evaluated, and the frequency equation is derived by the Ritz method.
Abstract: An analysis is presented for the free vibration of an elastically or rigidly point‐supported circular cylindrical shell. For this purpose, the deflection displacements of the shell are written in a series of the deflection functions of beam. The dynamical energies of the shell are evaluated, and the frequency equation is derived by the Ritz method. For a rigidly point‐supported shell, the Lagrangian multiplier method is conveniently employed. The method is applied to a cylindrical shell supported at symmetrically located four points; the natural frequencies and the mode shapes are calculated numerically, and the effects of the point supports on the vibration are studied.
TL;DR: In this paper, the combined Damkohler technique was applied to spherical shell geometry to predict facilitated mass transfer in the presence of non-equilibrium chemical reaction, which is a simple analytical method to accurately predict facilitated flux.