Derivation of twelve-by-twelve staffness matrix for shear panel undergoing parabolic deformation
Equations for stiffness matrix for 12-node shear panel undergoing parabolic deformation
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Equations for stiffness matrix for 12-node shear panel undergoing parabolic deformation
Satellite mounted mm wave parabolic dish antenna for tracking communication satellite in synchronous orbit
Thermal analysis of deployable parabolic antenna for Outer Planetary Explorer program, discussing spacecraft spin and radioisotope thermoelectric generators effect
Incompressible laminar boundary layer, vortex and axisymmetric wake/jet flow parabolic equations solution by weighted residuals method, describing use of exponentials
Beam equalization in large Cassegrain antennas with parabolic horn reflector feeds
Antenna was produced in segments. Parabole sections were built up as aluminum foil sandwich with core bonded by film adhesive; whole structure was oven-cured after assembly. Structure was assembled with special tool for splice-bonding segments into complete dish, and inflatable bladder to apply pressure at joints during cure.
The parabolic partial differential equation considered is u sub t = u sub xx + f(u), where minus infinity x plus infinity and o t plus infinity. Under suitable hypotheses pertaining to f, a class of initial data is exhibited: phi(x), minus infinity x plus infinity, for which the corresponding solutions u(x,t) appraoch zero as t approaches the limit of plus infinity. This convergence is uniform with respect to x on any compact subinterval of the real axis.
Theorems are developed to support bifurcation and stability of nonlinear parabolic partial differential equations in the solution of the asymptotic behavior of functions with certain specified properties.
A thermal distortion analysis of the ATS-6 Satellite parabolic reflector was performed using NASTRAN level 15.1. The same NASTRAN finite element method was used to conduct a one g static load analysis and a dynamic analysis of the reflector. In addition, a parametric study was made to determine which parameters had the greatest effect on the thermal distortions. The method used to model the construction of the reflector is described and the results of the analyses are presented.
Tests in which persons were subjected to a negative acceleration in an automobile are reported. The acceleration was obtained by stopping a moving car on the runway of an airport. The acceleration was found to produce a rotational movement of the subject's eyeball proportional to the degree of acceleration. Other investigations were conducted with a jet aircraft and a sports aircraft. G forces of up to 3 G were obtained during pull up of the aircraft, while values in the range from 0 to 1 G could be produced with the aid of a parabolic flight path. The effects of the flight conditions on the subject's direction of sight are discussed.
The Du Fort-Frankel difference scheme is generalized to difference operators of arbitrary high order accuracy in space and to arbitrary order of the parabolic differential operator. Spectral methods can also be used to approximate the spatial part of the differential operator. The scheme is explicit, and it is unconditionally stable for the initial value problem. Stable boundary conditions are given for two different fourth order accurate space approximations.
Extensive antenna-noise temperature measurements at 1.6 GHz (L-band) were made using a 1.2 m (4 ft. diameter) parabolic dish antenna mounted on the flying bridge of a modern 15,690-ton, commercial-container ship. Both in-harbor and at-sea radiometer measurements were made that indicated a steady background, antenna-noise temperature value slightly less than 70 degrees Kelvin (K) at elevation angles of 5 percent, and greater, at 1.6 GHz. A comparison of theoretical and measured values indicate excellent agreement within about 5K for at-sea data. These measurements are helpful to RF equipment designers of maritime, L-band shipboard terminals for operation with the two, geostationary, maritime satellites, Marisat-A and -B.
NASTRAN solution techniques are shown for a numerical analysis of a class of coupled vector flow processes described by simultaneous parabolic differential equations. To define one physical problem type where equations of this form arise, the differential equations describing the coupled transfers of heat and mass in mechanical equilibrium with negligible mass average velocity are presented and discussed. Also shown are the equations describing seepage when both electrokinetic and hydrodynamic forces occur. Based on a variational statement of the general problem type, the concepts of scalar transfer elements and parallel element systems are introduced. It is shown that adoptation of these concepts allows the direct use of NASTRAN's existing Laplace type elements for uncoupled flow (the heat transfer elements) for treating multicomponent coupled transfer. Sample problems are included which demonstrate the application of these techniques for both steady-state and transient problems.
A computer algorithm has been developed to determine the blunt-body flowfields supporting symmetric parabolic and paraboloidal shock waves at infinite free-stream Mach number. Solutions are expressed in an analytic form as high-order power series, in the coordinate normal to the shock, whose coefficients can be determined exactly. Analytic continuation is provided by the use of Pade approximations. Test cases provide solutions of very high accuracy. In the axisymmetric case for gamma equals 715 the solution has been found far downstream, where it agrees with the modified blast-wave results. For plane flow, on the other hand, a limit line appears within the shock layer, a short distance past the sonic line, suggesting the presence of an imbedded shock. Local solutions in the downstream limit are discussed.
A numerical method is presented which is valid for integration of the parabolic-elliptic Navier-Stokes equations. The solution procedure is applied to the three-dimensional supersonic flow of a jet issuing into a supersonic free stream. Difficulties associated with the imposition of free-stream boundary conditions are noted, and a coordinate transformation, which maps the point at infinity onto a finite value, is introduced to alleviate these difficulties. Results are presented for calculations of a square jet and varying-aspect-ratio rectangular jets. The solution behavior varies from axisymmetry for the square jet to nearly two-dimensional for the high-aspect-ratio rectangle, although the computation always calculates the flow as though it were truly three-dimensional.
The Du Fort-Frankel difference scheme is generalized to difference operators of arbitrary high order accuracy in space and to arbitrary order of the parabolic differential operator. Spectral methods can also be used to approximate the spatial part of the differential operator. The scheme is explicit, and it is unconditionally stable for the initial value problem. Stable boundary conditions are given for two different fourth order accurate space approximations.
A prototype apparatus for exposing persons to rotation about their Z-axis in parabolic flight is described. Although it resembles earth-horizontal axis devices, added features are its strength and portability, and the fiber glass 'couch' with adjustable elements providing support and restraint. Even under ground-based conditions, this device provides unique opportunities for investigations involving not only canalicular and macular mechanoreceptors, but also touch, pressure, and kinesthetic receptor systems.
A numerical method is presented for solving the parabolic-elliptic Navier-Stokes equations. The solution procedure is applied to three-dimensional supersonic laminar jet flow issuing parallel with a supersonic free stream. A coordinate transformation is introduced which maps the boundaries at infinity into a finite computational domain in order to eliminate difficulties associated with the imposition of free-stream boundary conditions. Results are presented for an approximate circular jet, a square jet, varying aspect ratio rectangular jets, and interacting square jets. The solution behavior varies from axisymmetric to nearly two-dimensional in character. For cases where comparisons of the present results with those obtained from shear layer calculations could be made, agreement was good.