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NASA NTRS1946

Numerical procedures for the calculation of the stresses in monocoques III : calculation of the bending moments in fuselage frames

This report deals with the calculation of the bending moments in and the distortions of fuselage rings upon which known concentrated and distributed loads are acting. In the procedure suggested, the ring is divided into a number of beams each having a constant radius of curvature. The forces and moments caused in the end sections of the beams by individual unit displacements of the end sections are listed in a table designated as the operations table in conformity with Southwell's nomenclature. The operations table and the external loads are equivalent to a set of linear equations. For their solution the following three procedures are presented: 1) Southwell's method of systematic relaxations. This is a step-by-step approximation procedure guided by the physical interpretation of the changes in the values of the unknown. 2) The growing unit procedure in which the individual beams are combined successively into beams of increasing length until finally the entire ring becomes a single beam. In each step of the procedure a set of not more than three simultaneous linear equations is solved. 3) Solution of the entire set of simultaneous equations by the methods of the matrix calculus. In order to demonstrate the manner in which the calculations may be carried out, the following numerical examples are worked out: 1) Curved beam with both its end sections rigidly fixed. The load is a concentrated force. 2) Egg-shape ring with symmetric concentrated loads. 3) Circular ring with antisymmetric concentrated loads and shear flow (torsion of the fuselage). 4) Same with V-braces incorporated in the ring. 5) Egg-shape ring with antisymmetric concentrated loads and shear flow (torsion of the fuselage). 6) Same with V-braces incorporated in the ring. The results of these calculations are checked, whenever possible, by calculations carried out according to known methods of analysis. The agreement is found to be good. The amount of work necessary for the solution of ring problems by the methods described in the present report is practically independent of the degree of redundancy of the structure. For this reason the methods are recommended for use particularly in problems of rings having one or more internal bracing elements.

LOADS - FUSELAGES↗
NASA NTRS1980

The narrow rings of Jupiter, Saturn and Uranus

The origin of the newly discovered narrow ring systems around Jupiter, Saturn and Uranus is considered. It is pointed out that both the Uranian and Jovian ring systems have mean orbital radii of 1.8 planetary radii and lie within the Roche zones of their respective planets, and it is suggested that the Jovian ring is the product of the disintegration of a satellite that entered the Roche zone, and that large numbers of small particles are now in horseshoe orbits about the Lagrangian equilibrium points of the remnant chunks. Analysis of the path of a ring particle in a horseshoe orbit is shown to result in ring structures in agreement with those observed for the circular rings of Jupiter and the highly eccentric ring of Uranus. The stability of these ring systems is then considered, and it is suggested that the F ring of Saturn, which lies outside the Roche zone, represents primordial matter not yet accreted by small satellites just inside the Mimas first-order resonances.

Dermott, S. F.↗
NASA NTRS1970

Stability of structural rings under uniformly distributed radial loads

Energy method analysis establishes parameters governing stability of circular rings acted upon by constant, uniformly distributed loads. Energy method is used so that nonlinear behavior of structure before buckling can be accounted for. Method affords conceptually superior basis for analyzing the axisymmetric deviation mode.

Williams, H. E.↗
NASA NTRS1983

Precession of inclined rings

It is proposed that node alignment across an inclined ring is maintained by the self-gravity of the ring, which cancels the tendency for differential node precession due to the planet's multiple moments. The analysis is confined to circular rings, which is a self-consistent approximation because the interactions among circular and inclined ringlets do not generate secular perturbations of eccentricity.

Borderies, N.↗
NASA NTRS1987

Observational studies of Saturn's rings

Several noteworthy phenomena in Saturn's rings were investigated which have until now received an inadequate amount of attention. Among these are the periodic variation of the spokes in the B ring and eccentric features throughout the rings. One of the major discoveries by Voyager was the existence of eccentric features within the predominantly circular rings of Saturn. Several of these nonaxisymmetric features are narrow elliptical rings which share many characteristics with the rings of Uranus. In recent work, two narrow ringlets were added to the list of eccentric features in the rings of Saturn. Voyager imaging and occultation data are now in hand, as well as image-processing software which allows accurate absolute positional measurements to be made in Voyager imaging data. Work is in progress to re-examine this region of Saturn's rings and to study the possibility of a dynamical interaction between the outer B ring edge, the Huygens ringlet and the nearby Mimas 2:1 resonance. An understanding of the kinematics and dynamics of this region promises to yield important clues to a matter of great interest in both theoretical and observation ring studies.

Porco, Carolyn C.↗
NASA NTRS1993

The morphology of and locations of star formation in impact induced ring galaxies

Observed ring galaxies appear to fall into two major types. The first tends to consist of isolated galaxies which display a smooth, apparently circular ring and a central nucleus. These have been variously classified as R(S) by de Vaucouleurs (1959) and as type O by Few and Madore (1986). The second class of ring galaxy nearly always has a close companion of comparable size (no less than about one tenth that of the ring galaxy). In these objects the ring is knotty in appearance, is usually elliptical, even when deprojected on the sky, and is often open on one side, having a 'horse shoe' or 'banana' shape. The nucleus does not usually appear at the center of the ring and is sometimes apparently absent, giving rise to an 'empty ring' galaxy. deVaucouleurs et al. (1976) designated this second type as RING, while Few and Madore (1986) have classified similar galaxies as P type. These galaxies have elevated far IR emission, bright HII regions, and blue spectral colors. The different environments of the two types or ring galaxy, together with their overall morphological and spectral differences suggest that the R(S)/O type are most probably the result of an instability that occurs in isolated galaxies, whereas the RING/P type appears to be the result of a recent collision between two roughly equal mass objects, at least one of which is a disk galaxy. Theys and Spiegel (1976) studied a sample of this latter type and identified three subclasses: RE: galaxies with crisp, empty rings; RN: galaxies like those of RE but with off-center nuclei; RK: galaxies having single dominant knots or condensations in the rings. A presentation of a preliminary understanding of the connections between these different observed forms in terms of parameters which are intrinsic to the galaxy system, such as time since collision and impact parameter, and in terms of our line of sight view is the purpose of this paper. Here we report results we have obtained from three dimensional computer simulations of collisions between equal mass galaxies, one of which is a rotating, disk galaxy containing both gas and stars and the other is an elliptical containing stars only. We have used a combined n-body/SPH program (see Balsara, 1990) to model fully self consistent models in which the halo mass is 2.5 times that of the disk and gas comprises ten percent of the disk mass.

Lamb, Susan A.↗
NASA NTRS1992

Line fluorescence from the ring around supernova 1987A

Observations in lambda 5007 which reveal an ellipse of line emission around SN 1987A are reviewed. A simple expression for the rate at which the kinematically accessible paraboloid sweeps over the length of a thin uniform circular ring is derived, and a simple integral expression for the light curve F(t) of a fluorescent line in terms of epsilon(t), the local line emissivity, is presented. Many simple examples of the relationship between epsilon(t) and F(t) are graphed, and the results are used to deduce the characteristics of the local emissivity functions which produce the best fit to the observed semiforbidden N III 1750 and N V 1240 light curves. The N III and N V light curves are inverted to find the functions epsilon(t) which give best fits to the observations.

Dwek, Eli↗
NASA NTRS1973

The nature of circular maria based on gravity studies.

Current thinking on the evolution of major lunar morphological features, i.e., large lunar circular basins, and on the nature and origin of surface structures observed in the fill deposits is summarized. The great lunar circular basins must result from high-velocity impact of large bodies with the moon. A hydrostatic mechanism is outlined, and a working hypothesis is presented for the evolution of lunar circular basins subsequent to their origin by impact. In the main appeal is made to Doppler gravity data to support the hypothesis, although photographic and altimetric information is also used. It is considered that all large ringed circular basins follow a common evolutionary path of superisostatic volcanic flooding followed by partial and variable isostatic adjustment. The difference between basins is the amount of flooding, which in turn may be related to the center of figure-center of mass offset of the moon.

Phillips, R. J.↗
NASA NTRS1985

A granular flow model for dense planetary rings

In the present study of the viscosity of a differentially rotating particle disk, in the limiting case where the particles are densely packed and their collective behavior resembles that of a liquid, the pressure tensor is derived from both the equations of hydrodynamics and a simple kinetic model of collisions due to Haff (1983). Density waves and narrow circular rings are unstable if the liquid approximation applies, and the consequent nonlinear perturbations may generate 'splashing' of the ring material in the vertical direction. These results are pertinent to the origin of the ellipticities of ringlets, the nonaxisymmetric features near the outer edge of the Saturn B ring, and unexplained residuals in kinematic models of the Saturn and Uranus rings.

Borderies, N.↗
NASA NTRS1972

Mascons - Progress toward a unique solution for mass distribution.

Through a series of analyses with high-altitude Lunar Orbiter and low-altitude Apollo 15 Doppler gravity data, it is shown that the Serenity mascon is a thin body whose horizontal dimensions are well determined and show a strong correlation with circular wrinkle ridge structure. Analysis to date has not uniquely determined the depth of the anomalous mass. However, geological evidence strongly suggests that the mass excess is near the surface, because (1) the surface solution has a geometry highly suggestive of the partial filling of a ringed circular basin, and (2) the boundaries of the anomalous mass separate regions of shallow and deep mare flooding.

Phillips, R. J.↗
NASA NTRS1991

Properties of the SN 1987A circumstellar ring and the distance to the Large Magellanic Cloud

The distance to SN 1987A was determined by comparing the angular size of its circumstellar ring, measured from an HST image obtained in a narrow forbidden O III 5007 A filter, with its absolute size derived from an analysis of the light curves of narrow UV lines measured with the IUE. The analysis confirms that the observed elliptical structure is a circular ring seen at a mean inclination of i = 42.8 + or - 2.6 deg and provides a determination of its absolute diameter of (1.27 + or - 0.07) x 10 to the 18th cm. Its ratio to the angular diameter of 1.66 + or - 0.03 arcsec gives an accurate determination of the distance to SN 1987A, i.e., d(1987A) = 51.2 + or - 3.1 kpc.

Panagia, N.↗
NASA NTRS2013

Spatially-resolved Spectroscopy of the IC443 Pulsar Wind Nebula and Environs

Deep Chandra ACIS observations of the region around the putative pulsar, CXOU J061705.3+222117, in the supernova remnant IC443 reveal, for the first time, a ring-like morphology surrounding the pulsar and a jet-like structure oriented roughly north-south across the ring and through the pulsar location. The observations further confirm that (1) the spectrum and flux of the central object are consistent with a rotation-powered pulsar interpretation, (2) the non-thermal surrounding nebula is likely powered by the pulsar wind, and (3) the thermal-dominated spectrum at greater distances is consistent with emission from the supernova remnant. The cometary shape of the nebula, suggesting motion towards the southwest (or, equivalently, flow of ambient medium to the northeast), appears to be subsonic; there is no evidence for a strong bow shock, and the circular ring is not distorted by motion through the ambient medium.

Swartz, D. A.↗
NASA NTRS1973

Lunar thermal measurements in conjunction with Project Apollo

Problems related to the feasibility of measuring lunar heat flow at the lunar surface are analyzed, and the findings which required that a drill be developed for lunar use are discussed. Numerical simulations were made of the in situ measurement of lunar thermal conductivity using a circular ring source of heat. The results of these simulations formed the basis for the criteria used in designing a subsurface thermal probe for ALSEP. Preliminary analyses are presented on the data obtained from the Apollo 15 and 17 missions.

Clark, S. P., Jr.↗
NASA NTRS1975

Preload Torque Limiting Shaft Coupling

A torque limiting spring for a rotating shaft system which acts bidirectionally and is preloaded is examined. The spring is a split circular ring compressed into cavities on facing surfaces of matching shafts. The spring is preloaded by varying the width of a tang in the shaft cavity relative to the split in the spring.

Harmening, W. A.↗
NASA NTRS1981

Application of the line-spring model to a cylindrical shell containing a circumferential or axial part-through crack

An approximate solution was obtained for a cylindrical shell containing a part-through surface crack. It was assumed that the shell contains a circumferential or axial semi-elliptic internal or external surface crack and was subjected to a uniform membrane loading or a uniform bending moment away from the crack region. A Reissner type theory was used to account for the effects of the transverse shear deformations. The stress intensity factor at the deepest penetration point of the crack was tabulated for bending and membrane loading by varying three dimensionless length parameters of the problem formed from the shell radius, the shell thickness, the crack length, and the crack depth. The upper bounds of the stress intensity factors are provided by the results of the elasticity solution obtained from the axisymmetric crack problem for the circumferential crack, and that found from the plane strain problem for a circular ring having a radial crack for the axial crack. The line-spring model gives the expected results in comparison with the elasticity solutions. Results also compare well with the existing finite element solution of the pressurized cylinder containing an internal semi-elliptic surface crack.

Delale, F.↗
NASA NTRS1989

Mixed finite element formulation for frictionless contact problems

Simple mixed finite element models and a computational procedure are presented for the solution of frictionless contact problems. The analytical formulation is based on a form of Reissner's large-rotation theory of the structure with the effect of transverse shear deformation included. The contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the internal forces (or stress resultants), the generalized displacements, and the Lagrange multipliers associated with the contact conditions. Numerical examples of axisymmetric deformations of a hemispherical shell and planar deformations of a circular ring are presented. Both structures are pressed against a rigid plate. Detailed information about the response of the structures is presented. The numerical studies demonstrate the high accuracy of the mixed models and the effectiveness of the computational procedure based on combining the geometrically nonlinear terms and the contact conditions in one iteration loop.

Noor, Ahmed K.↗
NASA NTRS1991

Nonlinear response of infinitely long circular cylindrical shells to subharmonic radial loads

The nonlinear response of infinitely long circular cylindrical shells (thin circular rings) in the presence of a two-to-one internal (autoparametric) resonance to a subharmonic excitation of order one-half of the higher mode is analyzed with the multiple-scale method. Four autonomous first-order ordinary differential equations are derived for the modulation of the amplitudes and phases of the interacting models. These modulation equations are used to determine the fixed points and their stability. The fixed points correspond to periodic oscillations of the shell, whereas the limit-cycle solutions of the modulation equations correspond to amplitude and phase-modulated oscillations of the shell. The force response curves exhibit saturation, jumps, and Hopf bifurcation. As excitation frequency changes, all limit cycles deform and lose stability through either pitchfork or cyclic-fold (saddle-node) bifurcations. Some of these saddle-node bifurcations cause a transition to chaos. The pitchfork bifurcations break the symmetry of the limit cycles.

Nayfeh, Ali H.↗