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At least 289 records · Page 16

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NASA NTRS1979

Numbers of center points appropriate to blocked response surface experiments

Tables are given for the numbers of center points to be used with blocked sequential designs of composite response surface experiments as used in empirical optimum seeking. The star point radii for exact orthogonal blocking is presented. The center point options varied from a lower limit of one to an upper limit equal to the numbers proposed by Box and Hunter for approximate rotatability and uniform variance, and exact orthogonal blocking. Some operating characteristics of the proposed options are described.

Holms, A. G.↗

NASA NTRS1979

Polarization-sensitive spectroradiometer - Two methods for overcoming the problems of measuring reflectance spectra

The spectra obtained using a spectroradiometer are incorrect if the incident light from the sample is polarized, and if, at the same time, polarization is introduced into the transmitted beam by components of the spectroradiometer. Two methods are proposed for obtaining correct power reflectance spectra. One way is to average two incorrect reflectance spectra, which are taken at mutually orthogonal angles of rotation of the radiometer about its optical axis. Another way is by averaging reflectance spectra of mutually orthogonal polarized light components. When the orientation of one component is chosen such that it is in the plane of polarization of the incoming light, the latter method also gives the correct degree of polarization.

Auer, S.↗

NASA NTRS1979

The problem of an inclined crack in an orthotropic strip

The elastostatic problem for an infinite orthotropic strip containing a crack is considered. It is assumed that the orthogonal axes of material orthotropy may have an arbitrary angular orientation with respect to the orthogonal axes of geometric symmetry of the uncracked strip. The crack is located along an axis of orthotropy, hence at an arbitrary angle with respect to the sides of the strip. The general problem is formulated in terms of a system of singular integral equations for arbitrary crack surface tractions. As examples Modes I and II stress-intensity factors are calculated for the strip having an internal or an edge crack with various lengths and angular orientations. In most calculations uniform tension or uniform bending away from the crack region is used as the external load. Limited results are also given for uniform normal or shear tractions on the crack surface.

Delale, F.↗

NASA NTRS1979

Numbers of center points appropriate to blocked response surface experiments

Tables are given for the numbers of center points to be used with blocked sequential designs of composite response surface experiments as used in empirical optimum seeking. The tables also give the star point radii for exact orthogonal blocking. The center point options vary from a lower limit of one to an upper limit equal to the numbers proposed by Box and Hunter for approximate rotatability and uniform variance, and exact orthogonal blocking. Some operating characteristics of the proposed options are described.

Holms, A. G.↗

NASA NTRS1980

Comparison of structural behavior of superplastically formed/diffusion-bonded sandwich structures and honeycomb core sandwich structures

A superplasticity formed/diffusion-bonded (SPF/DB) orthogonally corrugated core sandwich structure is discussed and its structural behavior is compared to that of a conventional honeycomb core sandwich structure. The stiffness and buckling characteristics of the two types of sandwich structures are compared under conditions of equal structural density. It is shown that under certain conditions, the SPF/DB orthogonally corrugated core sandwich structure is slightly more efficient than the optimum honeycomb core (square-cell core) sandwich structure. However, under different conditions, this effect can be reversed.

Ko, W. L.↗

NASA NTRS1980

On optical imaging through aircraft turbulent boundary layers

Optical resolution quality as affected by aircraft turbulent boundary layers is analyzed. Wind-tunnel data was analyzed to obtained the variation of boundary layer turbulence scale length and mass density rms fluctuations with Mach number. The data gave good agreement with a mass density fluctuation turbulence spectrum that is either isotropic of orthogonally anisotropic. The data did not match an isotropic turbulence velocity spectrum which causes an anisotropic non-orthogonal mass density fluctuation spectrum. The results indicate that the average mass density rms fluctuation is about 10% of the maximum mass density across the boundary layer and that the transverse turbulence scale size is about 10% of the boundary layer thickness. The results indicate that the effect of the turbulent boundary layer is large angle scattering which decreases contrast but not resolution. Using extinction as a criteria the range of acceptable aircraft operating conditions are given.

Sutton, G. W.↗

NASA NTRS1980

Eigenvector analysis of some observed and model-generated Climatological fields

An empirical orthogonal function analysis of monthly mean synoptic fields computed with a general circulation model and the corresponding observed climatological patterns is presented. A computer program was used to compute the principal components of the data matrices representing global maps of various observed and model-generated climatological fields. The variables analyzed were: 500mb geopotential height, 850 mb temperature, and sea level pressure. It is concluded that eigenvector analysis of observed and model-generated synoptic climatological fields is a useful diagnostic aid in the evaluation of global model simulation. The maps of any climatological variables are readily decomposed into a few orthogonal components which account for a large fraction of the total spatial variance, and the observed and model-generated patterns may then be compared in terms of these principal components of the original data matrices.

Dennis, M.↗

NASA NTRS1978

Modal content of noise generated by a coaxial jet in a pipe

Noise generated by air flow through a coaxial obstruction in a long, straight pipe was investigated with concentration on the modal characteristics of the noise field inside the pipe and downstream of the restriction. Two measurement techniques were developed for separation of the noise into the acoustic duct modes. The instantaneous mode separation technique uses four microphones, equally spaced in the circumferential direction, at the same axial location. The time-averaged mode separation technique uses three microphones mounted at the same axial location. A matrix operation on time-averaged data produces the modal pressure levels. This technique requires the restrictive assumption that the acoustic modes are uncorrelated with each other. The measured modal pressure spectra were converted to modal power spectra and integrated over the frequency range 200-6000 Hz. The acoustic efficiency levels (acoustic power normalized by jet kinetic energy flow), when plotted vs. jet Mach number, showed a strong dependence on the ratio of restriction diameter to pipe diameter. The acoustic energy flow analyses based on the thermodynamic energy equation and on the results of Mohring both resulted in orthogonality properties for the eigenfunctions of the radial mode shape equation. These orthogonality relationships involve the eigenvalues and derivatives of the radial mode shape functions.

Kerschen, E. J.↗

NASA NTRS1981

Effective constitutive relations for large repetitive frame-like structures

Effective mechanical properties for large repetitive framelike structures are derived using combinations of strength of material and orthogonal transformation techniques. Symmetry considerations are used in order to identify independent property constants. The actual values of these constants are constructed according to a building block format which is carried out in the three consecutive steps: (1) all basic planar lattices are identified; (2) effective continuum properties are derived for each of these planar basic grids using matrix structural analysis methods; and (3) orthogonal transformations are used to determine the contribution of each basic set to the overall effective continuum properties of the structure.

Nayfeh, A. H.↗

NASA NTRS1982

Spiral slotted phased antenna array

A flush mounting, cavity-backed, dual orthogonal slot antenna for aircraft and space vehicles is described. Improved radiation pattern characteristics are obtained by making the spiral slot pattern elliptical in the aperture plane. A cavity and a flanged aperture plate are configured such that one slot pair is orthogonal with respect to another slot pair within the aperture plate. Coaxial split-tube baluns are used to drive the junctions between corresponding slot pairs. An optional cavity dielectric is provided and a drive coupling arrangement includes a four port comparator hybrid having sum and difference ports respectively, for alternate excitation to produce a single lobe or a double lobe pattern with null. Switching apparatus is provided to connect a common terminal to either of the ports.

Ellis, H., Jr.↗

NASA NTRS1981

Principal stress formulation of continua motion

Principal stress coordinates are formulated for a material without tension, with the equations of motion projected onto a selected coordinate system. The translations are achieved by forming the local basis vector in correspondence with the local stress tensor. The principal stress coordinates are described as orthogonal and curvilinear, and the metric is defined. The kinematics and dynamics of the principal stress coordinates are analyzed, the latter in orthogonal coordinates, and an analytic formulation of the dynamics of a no-tension material is provided. Finally, elastic granular material such as sand, soil, etc., which are more complicated versions of no-tension material, are explored.

Zak, M.↗

NASA NTRS1984

Off-Resonance Acoustic Levitation Without Rotation

Orthogonal acoustic-levitation modes excited at slightly different frequencies to control rotation. Rotation of object in square cross-section acoustic-levitation chamber stopped by detuning two orthogonal (x and y) excitation drivers in plane of square cross section. Detuning done using fundamental degenerate modes or odd harmonic modes.

Barmatz, M. B.↗

NASA NTRS1982

Dielectric and permeability

Using the unabridged Maxwell equations (including vectors D, E and H) new effects in collisionless plasmas are uncovered. In a steady state, it is found that spatially varying energy density of the electric field (E perpendicular) orthogonal to B produces electric current leading, under certain conditions, to the relationship P perpendicular+B(2)/8 pi-epsilon E perpendicular(2)/8 pi = constant, where epsilon is the dielectric constant of the plasma for fields orthogonal to B. In steady state quasi-two-dimensional flows in plasmas, a general relationship between the components of electric field parallel and perpendicular to B is found. These effects are significant in goephysical and astrophysical plasmas. The general conditions for a steady state in collisionless plasma are deduced. With time variations in a plasma, slow compared to ion-gyroperiod, there is a general current, (j*), which includes the well-known polarisation current, given by J*=d/dt (ExM)+(PxB)xB B(-2) where M and P are the magnetization and polarization vectors respectively.

Cole, K. D.↗

NASA NTRS1982

A recursive algorithm for Zernike polynomials

The analysis of a function defined on a rotationally symmetric system, with either a circular or annular pupil is discussed. In order to numerically analyze such systems it is typical to expand the given function in terms of a class of orthogonal polynomials. Because of their particular properties, the Zernike polynomials are especially suited for numerical calculations. Developed is a recursive algorithm that can be used to generate the Zernike polynomials up to a given order. The algorithm is recursively defined over J where R(J,N) is the Zernike polynomial of degree N obtained by orthogonalizing the sequence R(J), R(J+2), ..., R(J+2N) over (epsilon, 1). The terms in the preceding row - the (J-1) row - up to the N+1 term is needed for generating the (J,N)th term. Thus, the algorith generates an upper left-triangular table. This algorithm was placed in the computer with the necessary support program also included.

Davenport, J. W.↗

NASA NTRS1981

Mesh generation by conformal and quasiconformal mappings

It is pointed out that many recent advances in the finite-difference solution of elliptic equations have been limited to regions whose boundary contours coincide with coordinate lines of the Cartesian coordinate system. The reason for this is related to the fact that in the case of an arbitrary curvilinear coordinate system the original equation becomes much more complex. However, there is no added complexity if an orthogonal coordinate system is generated from a conformal mapping. In the present investigation, a finite difference method developed for the construction of conformal mappings has been generalized to construct quasi-conformal mappings. It is expected that the use of more sophisticated numerical algorithms could lead to improvements in both speed and accuracy. Quasi-conformal mappings have applications not only in the solution of elliptic equations but also in other areas such as orthogonal mesh generation on surfaces and the solution of certain fluid flow problems.

Mastin, C. W.↗

NASA NTRS1982

Orientation and origin of ridges in the Lunae Palus - Coprates region of Mars

By analogy with lunar mare ridges and from morphologic evidence, such as the smooth slopes of arches, the wrinkle ridges of the Tharsis region of Mars are interpreted to primarily result from compressional folding of the volcanic plains. Comparison of ridge orientations in the Lunae Palus and Coprates quadrangles to a Tharsis center indicates that more than 60% of the total length of ridges is orthogonal to a normal from this center. Graben trends in surrounding terrain indicate that nonorthogonal ridges are not significantly affected by regional scale structures. Comparison of orthogonal and nonorthogonal ridge frequencies suggests that loading due to the Tharsis plateau produced compressional features as far as 4000 km from the center of the load, and that additional compressional stress sources are needed to account for ridge systems at greater distances from the Tharsis plateau.

Maxwell, T. A.↗

NASA NTRS1982

Boundary-fitted coordinate systems for numerical solution of partial differential equations - A review

A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given. Some general mathematical framework and error analysis common to such coordinate systems is also included. The general categories of generating systems are those based on conformal mapping, orthogonal systems, nearly orthogonal systems, systems produced as the solution of elliptic and hyperbolic partial differential equations, and systems generated algebraically by interpolation among the boundaries. Also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation. Dynamically adaptive coordinate systems, coupled with the physical solution, and time-dependent systems that follow moving boundaries are treated. References reporting experience using such coordinate systems are reviewed as well as those covering the system development.

Thompson, J. F.↗

NASA NTRS1982

Idealized dynamic grid computation of physical systems

The construction and utility of an idealized computational space for finite-difference computation of physical systems are considered. All computations are performed in tau space, which at any instant represents the dynamic grid of a subject physical system appropriately stretched into a uniform, orthogonal grid. A strain field model of physical system is described, including the sample computation of strain density fields. Dynamic grid generation using invariant-mapping is addressed, and the tau computational space is considered, including a grid dynamism constraint, a grid orthogonality constraint, and a grid smoothness constraint. The detailed tau computational space method is presented and illustrated with two sample problems.

Anyiwo, J. C.↗