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At least 1,315 records · Page 73

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NASA NTRS1974

Computer extension and analytic continuation of Stokes' expansion for gravity waves

Stokes' infinitesimal-wave expansion for steady progressive free-surface waves has been extended to high order using a computer to perform the coefficient arithmetic. Stokes' expansion has been found to be incapable of yielding the highest wave for any value of the water depth since convergence is limited by a square-root branch-point some distance short of the maximum. By reformulating the problem using a different independent parameter, the highest waves are obtained correctly. Series summation and analytic continuation are facilitated by the use of Pade approximants. The method is valid in principle for any finite value of the wavelength and solutions of high accuracy can be obtained for most values of the wave height and water depth.

Schwartz, L. W.↗

NASA NTRS1975

Cold air study of the effect on turbine stator blade aerodynamic performance of coolant ejection from various trailing edge slot geometries. 2: Comparison of experimental and analytical results

Experimentally determined efficiencies of turbine stator blades having trailing-edge coolant ejection are compared with efficiencies predicted from two previously published approximate analytical methods. The experimental results were obtained from two-dimensional data with the temperature of the primary and coolant flows both being nearly ambient. Data from five stator blade configurations having different slotted trailing-edge geometries were included in the comparison. The two analytical methods gave results which agreed reasonably well with experimental results. An average of the absolute values of differences between experimental and predicted efficiencies for all five blade configurations showed that one method gave average efficiency differences which were about 1.3 percent different than experimental efficiencies, while the other method gave average efficiency differences that were about 0.7 percent different than experimental. However, in some instances, maximum differences of as much as 4 percent occurred. A comparison between experimental and analytical results indicated that the ratio of trailing-edge slot width to trailing-edge thickness influences the measured efficiencies to a greater extent than is accounted for by either analytical model.

Prust, H. W., Jr.↗

NASA NTRS1975

A new structural analysis/synthesis capability - ACCESS

The creation of an efficient automated capability for minimum weight design of structures is reported. The ACCESS 1 computer program combines finite element analysis techniques and mathematical programming algorithms using an innovative collection of approximation concepts. Design variable linking, constraint deletion techniques and approximate analysis methods are used to generate a sequence of small explicit mathematical programming problems which retain the essential features of the design problem. Organization of the finite element analysis is carefully matched to the design optimization task. The efficiency of the ACCESS 1 program is demonstrated by giving results for several example problems.

Schmit, L. A.↗

NASA NTRS1975

An analysis of the strong zonal circulation within the stratosphere of Venus

A dynamic model is presented for the strong zonal circulation within the stratosphere of Venus which was observed by Mariner 10 and Venera. Rotational effects are neglected, a compressible and radiating atmosphere is considered, and diurnal radiative heating is shown to be negligible in the lower stratosphere (below 85 km). Analysis of the model indicates that propagating internal gravity waves generated by solar heating of the upper stratosphere may induce mean zonal velocities within the upper and lower stratosphere which would have a retrograde direction. The nonlinear equations of motion and energy are solved by an approximate analytical method to determine the magnitude of the zonal velocity, which is found to increase from zero at the tropopause to about 200 m/sec at the 85-km level. The calculated velocity near the UV cloud level compares favorably with the observed value of 100 m/sec.

Ramanathan, V.↗

NASA NTRS1975

A Method for Calculating the Induced Pressure Distribution Associated with a Jet in a Crossflow

A model is presented which can be used to study the loss of lift during hovering and horizontal flight of the VTOL aircraft. The model numerically predicts the pressure distribution induced by a round, turbulent, unheated, subsonic jet exhausting normally through a flat plate into a subsonic crossflow. The complete model assumes that the predominant features of the flow are jet entrainment and a pair of contrarotating vortices which form downstream of the jet. Experimentally determined vortex properties and a reasonable assumption concerning jet entrainment were used. Potential flow considerations were used except in the wake region, where a simple method for approximating the pressure distribution was suggested. The calculated pressure distribution, lift, and pitching moments on the flat plate are presented for a jet to crossflow velocity ratio of 8 and were compared with experimental results. A computer program is given which was used to calculate the pressure distribution across the flat plate.

Dietz, W. E., Jr.↗

NASA NTRS1975

Effects of particle shape on volume and mass estimates of interstellar grains

Mass estimates of interstellar grain materials based on visual extinction characteristics are shown to be insensitive to shape and, so long as the wavelength dependence of extinction is defined well into the infrared, they are also insensitive to size distribution. Spheroidal particles are treated by an approximate analytical method. Spheres and cylinders (core mantle as well as homogeneous) are treated by exact methods.

Greenberg, J. M.↗

NASA NTRS1976

Dynamics of spin stabilized spacecraft during deployment of telescoping appendages

The dynamics of a spin stabilized spacecraft with telescoping appendages are treated both analytically and numerically. Two types of telescoping appendages are considered: (a) where an end mass is mounted at the end of an (assumed) massless boom; and (b) where the appendage is assumed to consist of a uniformly distributed homogeneous mass throughout its length. For the telescoping system Eulerian equations of motion are developed. During all deployment sequences it is assumed that the transverse component of angular momentum is much smaller than the component along the major spin axis. Closed form analytical solutions for the time response of the transverse components of angular velocities are obtained when the spacecraft hub has a nearly spherical mass distribution. For the more general case, a series solution is obtained and this solution is limited by its radius of convergence. The comparison of the different approximate analytical methods with numerical integration results are studied and it is observed that the oscillatory nature of the responses of the transverse angular velocity components reduces rapidly with faster extension rates.

Sellappan, R.↗

NASA NTRS1976

A numerical solution of the flow field over a transonic airfoil including strong-shock-induced flow separation

An approximate numerical method has been developed for computing the entire transonic flow field over an airfoil, including the boundary layer, the shock-wave/boundary-layer interaction, and the shock-induced-separation. The inviscid flow, the turbulent boundary layer in the weak interaction zone, and the strong interaction elliptic region are solved separately. The inviscid flow is represented by the solution of the transonic small-disturbance equation, while the boundary layer is solved by the generalized Galerkin method, and the strong interaction region (including the wake) is computed from the time-averaged Navier-Stokes equations. A second-order interaction is computed iteratively using the inviscid pressure distribution as a boundary condition for the boundary layer and Navier-Stokes codes, and the viscous displacement thickness to modify the airfoil geometry for the inviscid computation. The computed pressure distributions and shock-wave profiles are compared with experimental data. Agreement is very good except that the pressure recovery on the trailing edge is greater than the experimental data.

Seginer, A.↗

NASA NTRS1976

A study on the forced vibration of a Timoshenko beam

By using Galerkin's variational method an approximate solution is developed for a system of two differential equations with linear partial derivatives of the second order. This system of differential equations corresponds to the physical model, known in the literature as the Timoshenko Beam. The results obtained are applied to two particular cases representing respectively: the case of a beam with a rectangular section, with a constant height and a basis with a linear variation; and the case of a beam with a constant basis and a height with cubic variation.

Zainea, B.↗

NASA NTRS1976

Surface crack growth in fiber composites

The results of an experimental study of damage extension and failure in glass and graphite/epoxy laminates containing partially through-thickness surface cracks are presented. The laminates studied are divided between those containing four plies, 90/0/0/90, 15/-15/-15/15, and 45/-45/-45/45, and those containing 12-16 plies of the general configurations 0/90, + or - 45, and 0/+ or - 60. Most of the results are for surface cracks of various lengths and several depths. Stable damage extension in laminates containing surface cracks is predominantly delamination between plies, and tends to be much more extensive prior to failure than is the case with through-thickness cracks, resulting in approximately notch-insensitive behavior in most cases. A greater tendency for notch-sensitive behavior is found for 0/90 graphite/epoxy laminates for which stable damage extension is more limited. The rate of damage extension with increasing applied stress depends upon the composite system and ply configuration as well as the crack length and depth. An approximate semiempirical method is presented for estimating the growth rate of large damage-regions.

Im, J.↗

NASA NTRS1977

Constraints on the gravitational constant at large distances

D. R. Long (1976) and others have speculated that the gravitational force between point masses in the Newtonian regime might not be exactly proportional to 1/r squared. Distance-dependent deviations from the 1/r squared law can be represented by a distance-dependent gravitational 'constant', G(r). Long has summarized the experimental evidence which constrains G(r) to be very nearly constant for 5 cm less than r less than 1 m. This paper presents observational evidence for constancy in the range 1000 km less than r less than 10 to the eighth km, and points out that the value of G(r) identical to Gc in this range has not been experimentally determined. Constraints on G(r) in the intermediate distance range 10 m less than r less than 1 km are so poor that one cannot rule out the possibility that Gc differs greatly from the laboratory value Go. Models of the earth and sun are used to argue that Gc differs from Go by not more than approximately 40%. Methods of improving the determination of Gc are suggested.

Mikkelsen, D. R.↗

NASA NTRS1977

Numerical determination of the fundamental eigenvalue for the Laplace operator on a spherical domain

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (i.e., the membrane eignevalue problem for the vibration equation) on the unit spherical surface are developed. Two types of spherical surface domains are considered: the interior of a spherical triangle, and the exterior of a great circle arc extending for less than pi radians (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is employed. The fundamental eigenvalue is approximated by iteration utilizing the power method and point successive overrelaxation. Some numerical results are given and compared, in certain special cases, with analytical solutions to the eigenvalue problem. The significance of the numerical eigenvalue results is discussed in terms of the singularities in the solution of three-dimensional boundary-value problems near a polyhedral corner of the domain.

Walden, H.↗

NASA NTRS1978

A review and assessment of the stress-intensity factors for surface cracks

The stress-intensity factor solutions proposed for a surface crack in a finite plate subjected to uniform tension are reviewed. Fourteen different solutions for the stress-intensity factors are compared. These solutions were obtained over the past 16 years using approximate analytical methods, experimental methods, and engineering estimates. The accuracy is assessed of the various solutions by correlating fracture data on surface-cracked tension specimens made of a brittle epoxy material. Fracture of the epoxy material was characterized by a constant value of stress-intensity factor at failure. Thus, the correctness of the various solutions is judged by the variations in the stress-intensity factors at failure. The solutions were ranked in order of minimum standard deviation. The highest ranking solutions correlated 95 percent of data analyzed within + or - 10 percent, whereas the lowest ranking solutions correlated 95 percent of data analyzed within + or - 20 percent. However, some solutions could be applied to all data considered, whereas others are limited with respect to crack shapes and crack sizes that could be analyzed.

Newman, J. C., Jr.↗

NASA NTRS1979

Effect of parasitic plasma currents on solar-array power output

Solar-array voltage-current curves are calculated by assuming the existence of parasitic loads that consist of local currents of charged particles collected by the array. Three cases of interest are calculated to demonstrate how the distribution and magnitude of parasitic currents affect output. Solar array performance degradation became significant when the total parasitic current plus the load current exceeded the short-circuit current. Approximate graphical methods were useful for many applications. Power loss, which was calculated by summing the product of parasitic current and the local potential, underestimated the loss in maximum power.

Domitz, S.↗

NASA NTRS1979

Aperture amplitude and phase control of offset dual reflectors

An approximate synthesis method is presented for solving the problem of offset dual-shaped reflectors. It is shown that the equations obtained by this method are partial differential equations that can be integrated numerically, except that these equations are generally not total and therefore do not have a 'smooth' solution. However, it is demonstrated that these equations form a nearly total differential that enables one to generate a smooth subreflector by integrating the differential equations and then synthesizing a main reflector which gives an exact solution for the specified aperture phase distribution. Several important illustrative examples are treated, which validate the adequacy of the proposed method.

Galindo-Israel, V.↗

NASA NTRS1979

Failure of underground concrete structures subjected to blast loadings

The response and failure of two edges of free reinforced concrete slabs subjected to intermediate blast loadings are examined. The failure of the reinforced concrete structures is defined as a condition where actual separation or fracture of the reinforcing elements has occurred. Approximate theoretical methods using stationary and moving plastic hinge mechanisms with linearly varying and time dependent loadings are developed. Equations developed to predict deflection and failure of reinforced concrete beams are presented and compared with the experimental results.

Ross, C. A.↗

NASA NTRS1980

The dynamics and control of large flexible space structures, 3. Part A: Shape and orientation control of a platform in orbit using point actuators

The dynamics, attitude, and shape control of a large thin flexible square platform in orbit are studied. Attitude and shape control are assumed to result from actuators placed perpendicular to the main surface and one edge and their effect on the rigid body and elastic modes is modelled to first order. The equations of motion are linearized about three different nominal orientations: (1) the platform following the local vertical with its major surface perpendicular to the orbital plane; (2) the platform following the local horizontal with its major surface normal to the local vertical; and (3) the platform following the local vertical with its major surface perpendicular to the orbit normal. The stability of the uncontrolled system is investigated analytically. Once controllability is established for a set of actuator locations, control law development is based on decoupling, pole placement, and linear optimal control theory. Frequencies and elastic modal shape functions are obtained using a finite element computer algorithm, two different approximate analytical methods, and the results of the three methods compared.

Bainum, P. M.↗

NASA NTRS1980

Numerical methods for studying anharmonic oscillator approximations to the phi super 4 sub 2 quantum field theory

This paper is an expanded version of a talk given at the 1979 T.I.C.O.M. conference. It is a self-contained introduction, for applied mathematicians and numerical analysts, to quantum mechanics and quantum field theory. It also contains a brief description of the authors' numerical approach to the problems of quantum field theory, which may best be summarized by the question; Can we compute the eigenvalues and eigenfunctions of Schrodinger operators in infinitely many variables.

Isaacson, D.↗