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Reconsideration of the problem of a complete semiinfinite circular cylindrical shell with a square cage investigated earlier by Reissner and Simmonds (1966). It is shown that the solution can be found in closed form rather than in the form of Fourier series, provided that the boundary data on the end of the shell are 'slowly varying.'
An algorithm is suggested to obtain the Luenberger canonical form for multivariable systems. The method computes the canonical form directly without having to compute the transformation matrix. In addition, there is a large reduction in the number of calculations. The reduced computations along with Gaussian techniques lend to greater inherent accuracy and the ability to refine the solution with additional computations.
Jordan canonical forms are used extensively in the literature on control systems. However, very few methods are available to compute them numerically. Most numerical methods compute a set of basis vectors in terms of which the given matrix is diagonalized when such a change of basis is possible. Here, a simple and efficient method is suggested for computing the Jordan canonical form and the corresponding transformation matrix. The method is based on the definition of a generalized eigenvector, and a natural extension of Gauss elimination techniques.
A new algorithm is presented to obtain the Luenberger canonical form for multivariable systems. A distinct feature of the method is that the canonical form is obtained directly and, if necessary, the similarity transformation can be computed. There is a substantial reduction in the amount of computation compared to Luenberger's method. The reduced computations along with Gaussian techniques lend greater inherent accuracy and the ability to refine the solution with additional computations. An example is presented to illustrate the technique.
Information is presented concerning cutting, shaping, and forming of materials, and the equipment and techniques required for utilizing these materials. The use of molds, electrical fields, and mechanical devices are related to forming materials. Material cutting methods by devices including borers and slicers are presented along with chemical techniques. Shaping and fabrication techniques are described for tubing, honeycomb panels, and ceramic structures. The characteristics of the materials are described. Patent information is included.
The process for manufacturing external tank dome gores is discussed. The test fixture and test procedure are described. The characteristics of the draw forming die are analyzed. The specific subjects included are: (1) forming, (2) trimming, (3) cleaning, and (4) heat treatment.
An account of activities and data gathered in the Room Temperature Stretch Forming of One-third Scale External Tank Bulkhead Gores for space shuttle study, and a tooling design and production cost study are reported. The following study phases are described: (1) the stretch forming of three approximately one-third scale external tank dome gores from single sheets of 2219-T37 aluminum alloy; (2) the designing of a full scale production die, including a determination of tooling requirements; and (3) the determination of cost per gore at the required production rates, including manufacturing, packaging, and shipping.
Matrix effects related to the chemical form of analyzed materials were studied. An arc in argon was used which was buffered with silver chloride. The effect of chemical form was minimal for a variety of metals, oxides, and carbides representing the most refractory compounds and thermally stable metal-containing molecules. Only four of the most refractory materials known showed significant emission depressions due to incomplete volatilization in the arc system. These results are discussed in terms of vapor pressures of the solid materials placed on the anodes and dissociation reactions of the molecules in the gaseous environment.
A method of forming a tubular wick for a heat pipe is presented. The method is characterized by the steps of forming a wick blank of a predetermined thickness comprising a plurality of superimposed layers of stainless steel mesh screen, wet rolling the blank for reducing the thickness, wrapping the blank about an inner mandrel, compressing the blank into a rigid tubular structure, removing the tubular structure from the mandrel and sintering the tubular structure.
Microcraters were formed in heated soda-lime glass by the normal incidence of spheres of plastic or fused silica with diameters between 0.8 and 4.5 microns and velocities between 2.5 and 10 km/s. The morphology of the craters in targets at temperatures up to 800 C is little different from those formed in unheated glass. Spallation still occurs to the same extent and above the same velocity threshold, but the spalls sag and sharp edges become dull in a few seconds at temperatures above the softening point. There is a small increase in the flow of glass from the central pit into a narrow lip at the higher temperatures, but this lip is often removed by spallation, especially at the higher velocities of impact. There is no evidence of a splashed lip with strings of melt overlying the spalled area. The results in conjunction with other evidence suggest that most lunar craters of micrometer size with a smooth central pit, splashed lip, and a spallation zone are the result of primary impacts.
This paper describes a study of matrix effects related to the chemical form of materials analyzed. The study was made using an arc in argon buffered with silver chloride. The effect of chemical form was minimal for a variety of metals, oxides, and carbides representing the most refractory compounds and thermally stable metal-containing molecules. Among these, only four of the most refractory materials known showed significant emission depressions due to incomplete volatilization in the arc system. These results are discussed in terms of vapor pressure of the solid materials placed on the anodes and dissociation reactions of the molecules in the gaseous environment.
An implicit finite-difference scheme is developed for the efficient numerical solution of nonlinear hyperbolic systems in conservation-law form. The algorithm is second-order time-accurate, noniterative, and in a spatially factored form. Second- or fourth-order central and second-order one-sided spatial differencing are accommodated within the solution of a block tridiagonal system of equations. Significant conceptual and computational simplifications are made for systems whose flux vectors are homogeneous functions (of degree one), e.g., the Eulerian gasdynamic equations. Conservative hybrid schemes, which switch from central to one-sided spatial differencing whenever the local characteristic speeds are of the same sign, are constructed to improve the resolution of weak solutions. Numerical solutions are presented for a nonlinear scalar model equation and the two-dimensional Eulerian gasdynamic equations.
A limited capability form of NASTRAN level 16 is presented to meet the needs of universities and small consulting firms. The input cards, the programming language of the direct matrix abstraction program, the plotting, the problem definition, and the modules' diagnostic messages are described. Sample problems relating to the analysis of linear static, vibration, and buckling are included. This guide can serve as a handbook for instructional courses in the use of NASTRAN or for users who need only the capability provided by the condensed form.
A Lagrangian computer program is used to study the effects of large impacts on planetary surfaces. More specifically, the global seismic effects for cratering energies of 10 to the 24th and 10 to the 25th J between the Copernicus and Imbrium lunar events are investigated. The phenomenologies for assumed solid and molten planetary interiors are compared. The main results of this investigation are: (1) far-field effects are found to be largely independent of cratering mechanisms, (2) antipodal seismic effects, which are of substantial magnitude, are greatly enhanced by focusing, (3) the most violent activity takes place at significant depth, (4) seismic effects are more pronounced for a molten planet than for a solid one, and (5) tensile failure may occur at depths of tens of kilometers beneath the antipode, or over the entire surface at shallower depths. These results suggest that the unusual terrains antipodal to large planetary basins may have been greatly modified by seismicity generated by the basin-forming impacts, and that the impacts may have brecciated the entire lithospheres of the terrestrial planets as the lithospheres formed and thickened
The role of protogalaxy interactions in galactic evolution is studied during the formation of galaxy clusters. In the early stages of the collapse, coalescent encounters of protogalaxies lead to the development of a galactic luminosity function. Once galaxies acquire appreciable random motions, mutual collisions between galaxies in rich clusters will trigger the collapse of interstellar clouds to form stars. This provides both a source for enriched intracluster gas and an interpretation of the correlation between luminosity and color for cluster elliptical galaxies. Other observational consequences that are considered include optical, X-ray, and diffuse nonthermal radio emission from newly formed clusters of galaxies.
The paper discusses recent measurements pertaining to the relationship between high-latitude particle (electron) precipitation and auroras. The discussion covers three topics: the large-scale relationships between auroral forms and the particle populations of the magnetosphere as determined from satellite measurements; (2) the relationship between satellite and sounding-rocket observations, particularly field-aligned pitch-angle distributions and upward field-aligned currents measured in the vicinity of auroral forms; and (3) recent results on the interaction of auroral electrons with the atmosphere.
An antenna array is described which comprises three interferometer pairs of antenna elements with selected spacings made to form a single beam which is readily scannable. All spatial frequencies generated by a signal and intercepted by the array are derived from a signal processing technique applied to the array. The array samples space in the spatial frequency domain while the signal processing technique utilizes real time convolution of functions in the spectral frequency domain. Summation of the appropriate spatial frequencies is equilvalent to a Fourier transform operation, yielding the location of the signal source in space. Resolution and freedom from interference of the interferometer system is equal to that of a fully filled array of the same aperture size containing element spacings of one half wavelength. An antenna array system comprising four antenna elements forming six interferometer pairs with a resolution equal to that of a sixteen element array with spacings of one half wavelength is described, as well as other multiples of one quarter wavelength of partial multiples of a wave length.
The equilibrium equations of a uniformly rotating and tidally distorted star are reduced to the same form as for a spherical star except for the inclusion of two form factors. One factor, expressing the buoyancy effects of centrifugal force, is determined directly from the integrated structure variables. The other factor, expressing the deviation from spherical shape, is shown to be relatively insensitive to errors in the assumed shape, so that accurate solutions are obtained in spite of the use of an a priori shape. The method is employed by adding computations for the factors to an existing spherical model program. Upper Main Sequence models determined by this method compare closely with results from the double approximation method even for critical rotation and tidal distortion.