Showing papers on "Spherical shell published in 1978"

Resonant acoustic scattering by swimbladder‐bearing fisha)

Abstract: A new model of swimbladder‐bearing fish has been developed in order to provide improved predictions of the resonance frequency and acoustic cross section of such a fish. The model consists of a small spherical shell in water, enclosing an air cavity which supports a surface tension. The shell is a viscous, heat‐conducting Newtonian fluid, with the physical properties of fish flesh. A comparison of the results obtained with the new model to experimental data indicates that the new model constitutes a definite improvement over previous models. The new model can predict the high values of damping and elevated resonance frequencies that previous models could not. The model appears to be most accurate for fish in which tension in the swimbladder wall has a minor effect on resonant scattering. This includes the fish which are of interest in studies of volume reverberation, and the new model should therefore be of considerable value in such studies.

Micromechanical analysis of a model for particulate composite materials with composite particles—survey of craze initiation

Abstract: Particulate-filled materials consisting of a continuous matrix phase and a discontinuous filler phase made up of discrete heterogeneous particles are simulated by an elementary model consisting of a single spherical particle embedded in an infinite matrix, the particle being constituted by a spherical core within a concentric spherical shell. The specific case studied is one in which the particle core and matrix are of the same glassy polymer, and particle shell is a rubbery material. The distributions of six suggested craze initiation factors in the region surrounding the single particle are calculated when the material is subjected to a uniform uniaxial tension at infinity. Results indicate that the critical regions for craze formation are located either at the pole or at the equator of the particle (the polar axis being parallel to the applied tension), depending on the criterion considered and on the relative size of the glassy core in the particle.

Stokes Flow in Conical Trenches

Abstract: In this paper we develop a separation of variables theory, for solving problems of Stokes flow in cone-shaped trenches formed as the intersection of a cone of circular cross-section and a spherical shell centered at the vertex of the cone. The theory leads to a new set of Stokes flow eigenfunctions which describe axisymmetric motions in the vertex of a cone. Asymptotic formulas for the distribution of eigenvalues are derived; an adjoint system is defined and is used to develop an algorithm for the computation of the coefficients in an eigenfunction expansion of edge data prescribed on the spherical boundaries.

Closable sales kiosk

Abstract: A simple molded plastic sales kiosk design is described having a unique closure means. The kiosk has a fixed substantially spherical shell member mounted on a cylindrical base. This fixed shell member is truncated by a vertical chordal plane in the region of the central axis, extending between the top of the shell and a horizontal serving counter mounted in an intermediate region of the shell. This serving counter is annular and extends between the vertical truncated edges of the shell. For entry into the kiosk, a gap is provided in the serving counter adjacent one of the vertical truncated edges. An outer shell including a spherical segment portion merging into a chordal skirt portion is mounted for rotation on and surrounding the fixed shell. This outer shell is truncated by a vertical chordal plane located forward of its central axis and is arranged to rotate relative to the fixed shell such that in the normal open position the serving counter is exposed and the entry gap is covered by the outer shell, in the normal closed position the serving counter and entry gap are entirely covered by the outer shell and in the entry position, the entry gap is uncovered.

The relativistic dynamics of a thin spherically symmetric radiating shell in the presence of a central body

Abstract: We construct an idealized spherically symmetric relativistic model of an exploding object within the framework of the theory of surface layers in GR. A Vaidya solution for a radially radiating star is matched through a spherical shell of dust to a Schwarzschild solution. The (incomplete) equations for the motion of the spherical shell of dust and the radiation density of the Vaidya solution, as given by the matching conditions, are reduced to a first-order system and a general analysis of the characteristics of the motion is given. This system of differential equations is completed, adding a relation between the unknowns which represents the simplest way to avoid an unphysical singularity in the motion. The results of a numerical integration of the equations are presented in two cases which we think may have some relationship to stellar explosions. A comparative set of results for other solutions is also given, and some possible generalizations of the model are pointed out.

Rotatable lamp fixture

Abstract: A rotating lamp fixture including a spherical shell member rotatably supported on a vertically extending support member, a platform disposed in the shell member, a drive motor mounted on the platform, a stationary gear secured to a vertical support member, the shell member being rotatably mounted on the support member, the motor being drivingly connected to the stationary gear and being effective when energized to rotate the platform and the shell in which it is supported about the vertical support member, and a light bulb socket suspended within the shell member.

Protective shell for nuclear reactor and method for assembling the shell

Abstract: A method for assembling a large massive steel shell is disclosed for housing a nuclear reactor while having sufficient strength to contain an explosion of such nuclear reactor. The shell is formed of large heavy gauge metal plates which are welded to each other to form a large sphere. Locating and supporting rings are mounted concentrically on a base. The rings increase in height from the center of the sphere to support and locate correspondingly higher annular segments of the sphere. The rings are erected and positioned with precisely adjustable tie rods so that the annular upper edge of the rings have a correspondingly accurately known position with respect to the annular sphere segments to be supported by the rings. The large heavy plate segments are then mounted on the rings and welded together to form a lower spherical portion whose spherical shape closely conforms to that desired for the sphere. The spherical structure is horizontally encircled with a long heavy gauge cable mounted at a midsection of the spherical shell. The cable encircles the sphere with a multiple number of wraps and is tensioned to provide a sufficient inwardly directed force for inhibiting an equatorial bulge.

Acoustic amplification in imploding spherical shells

Abstract: A potentially disruptive new phenomenon in imploding targets is described. Initially weak standing sound waves (vibrations) in an imploding spherical shell can become comparable in amplitude with the shell thickness if the effective adiabatic index satisfies ..gamma.. < ..gamma..*, where ..gamma..* depends on how the aspect-ratio changes during compression. Detailed calculations for a model of self-similar implosions with ..gamma..* = 5/3, show that the relative amplification is strongest for long-wavelength modes in thin shells with small ..gamma.., and is insensitive to the density profile.

Free oscillations of submerged spherical shells

Abstract: Free vibrations of a spherical shell submerged in a fluid medium are investigated. It is found that no undamped natural frequency of the submerged shell can exist even if the surrounding fluid is assumed inviscid. In this case the damping is solely due to the compressibility of the fluid. However, for the intermediate modes, the damping components of the complex frequencies are extremely small; thus, an almost steady‐state, undamped free oscillation is possible for these modes and a pronounced resonance may be observed for the forced vibrations. When the shell is submerged in an ideal fluid, it is shown that there exist two real natural frequencies for each mode. These frequencies are lower than the corresponding in vacuo natural frequencies. The effect of fluid viscosity on the complex natural frequencies has also been examined. It is found that for small viscosities, the viscosity has essentially no effect on the real component of the natural frequencies.

Rotational speed reduction and reversing mechanisms

Abstract: A rotational speed reduction and reversing mechanism wherein power is input thru a hollow spherical shell and taken out thru relative small rollers mounted in a perpendicular fashion on the circumference of an output rotor. The axis of the output rotor is rotated relative to the axis of the input spherical shell to vary the rotational speed reduction ratio.

Structural strength of glued permanent joint in spherical shell of brittle material. I

Abstract: 1. Numerical investigation of spherical sectional shells with permanent glued joint fully characterizes their real state of stress as a whole and in the zones of stress concentration. 2. To achieve the most favorable stress state in the zone of the joint, it is recommended to use a uniform glued seam 0.06 to 0.04 mm thick which does not induce stress concentrations in the shell in the zone of the joint. 3. Application of the recommended solutions concerning design and technology will help considerably to reduce stress concentration in the zone of the permanent glued joint, and this, in turn, will increase the load-bearing capacity of the sectional structure in one-time short-term loading up to failure; it is also bound to increase the durability of such structures under cyclic loading. 4. Glued permanent joints in strong sectional spherical glass shells are a promising kind of joint. 5. Accurate calculation of the zone of the joint makes it possible to find the length of the lateral surface along the meridian which requires accurate machining to obtain a section of equal thickness in the zone of the joint.

Buckling of a Complete Spherical Shell Under Uniform External Pressure

Abstract: : Non-linear axisymmetric bucking of a complete spherical elastic shell under uniform external pressure is treated numerically. Particular attention is given to the lower critical load, which is the theoretical least failure load. Among the new results are the evaluation of this load for thinner shells than those treated in the existing literature; in particular, the values 6.73% and 4.9% of the classical linear buckling loads are obtained for the radius-to-thickness ratios 100 and 200, respectively. The shapes of the buckled shells are computed for the first time in an unexpected hint that there is an asymptotic (ratios-to-thickness ration-independent) buckled shape. Numerical solution is by means of spectral (Galerkin) expansions of up to 60 modes in associated Legendre functions of order one applied to the quadratically non-linear version of E. Reissner's equations. (Author)

Solar reactor for chemical processes - with concentric spherical shells located in focus of solar rays

Abstract: A solar reactor for the use of focussed sunlight for water gas or methane processes or for coal gasification is located in the focus of a parabolic mirror. The rays enter through an opening in a spherical shell, permeable to radiation, which is surrounded by a concentric shell, impermeable to radiation. The space between them which contains baffles to enforce a swirling flow, receives the feedstock gas, if the rays enter from the 7 o'clock position, from a pipe in the 12 o'clock position, two cracked gas outlets, one with a dust taphole, are in the 9 and 3 o'clock position. This facilitates the assembly of the solar reactor in a parabolic mirror or in heliostat towers.

Flux variations in relativistically expanding spherical radio sources.

Abstract: The conclusion reached by Terrell regarding relativistic expansion of a spherical light source, namely, that such expansion does not lead to observed pulses which are short compared with the light travel time across the apparent source, is shown to be a model-dependent result which does not apply in general. This is illustrated in the case of synchrotron radiation sources with a thin spherical shell which evolves according to the standard model. It is also suggested, on the basis of this example, that some observed effects in compact radio sources could be attributed to relativistic expansion of the source.

Analytical solutions for open nonshallow spherical shell vibrations

Abstract: This paper is concerned with axisymmetric as well as nonsymmetric vibrations of open nonshallow thin elastic spherical shells. Without employing the usual auxiliary variables for reduction of shell motion equations introduced by Van der Neut and Berry, independent analytical solutions for middle‐surface displacements are obtained and explicitly expressed in terms of associated Legendre functions. In order to gain physical insights into the free‐vibration characteristics of an open nonshallow shell, theoretical calculations together with asymptotic descriptions are made of natural frequencies and mode shapes of a hemispherical shell with a free edge. The numerical predictions obtained herein compare excellently against the experimental results obtained previously by Hwang and recently in the David W. Taylor Naval Ship R & D Center, Bethesda, Maryland. Essential features of shell dynamics are ultimately displayed by normalized frequency (Ω) and nondimensional shell thickness parameter (β). Five families of natural frequencies, i.e., low Rayleigh bending, mixed bending‐membrane, torsional, bending, and membrane frequencies, are found. The corresponding mode shapes exhibit distinctive displacement patterns. [Work supported by Naval Sea Systems Command.]

Dynamic response of a submerged hemispherical shell to earthquake motions

Abstract: The dynamic response to ground motion of hemispherical shells in a fluid, medium is studied numerically. In the analysis, linear thin shell theory is used and the fluid is assumed to be compressible and inviscid. The effect of the duration of the ground motion on the dynamic response is studied using two forcing functions, one with a very short duration and the other in the form of a Heaviside function. As special cases, dynamic responses of the shell in vacuo and of a rigid hemisphere in the fluid medium are investigated. The results are valid also for a ring-stiffened complete spherical shell accelerating in an acoustic medium.

An Analysis of the Free Vibration of a Shallow Spherical Membrane Shell.

Abstract: : The free vibration of a shallow spherical membrane shell is analyzed using the thin-shell theory developed by Kraus. The secular equation giving the lowest resonant frequencies of such a shell is derived. The normal and tangential modal displacement functions corresponding to these resonant frequencies are found for the case when the shallow spherical shell has a free edge. In addition, an approximate secular equation is derived for the shallow spherical membrane shell with a free edge by using the Rayleigh-Ritz method. Suitable approximate modal displacement functions, corresponding to the resonant frequencies that are determined using this approximate secular equation and satisfying the free-edge boundary condition, are found. (Author)