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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Vanishing of dipole matrix elements at level crossings.

Demonstration that the vanishing of certain coupling matrix elements at level crossings follow from angular momentum commutation relations. A magnetic dipole transition having delta M = plus or minus 1, induced near a crossing of the levels in a nonzero magnetic field, is found to have a dipole matrix element comparable to or smaller than the quotient of the level separation and the field. This result also applies in the analogous electric field electric dipole case.

Kocher, C. A.↗
NASA NTRS1973

Improved procedures for mass matrix-reductions in eigenvalue solutions

Analytical models of three structures were used to test mass matrix-reduction schemes. Accuracy of four mode shapes and frequencies was tracked through successive mass matrix-reductions with diminishing numbers of indicator degrees of freedom. Results were consistently disappointing. Two new procedures were developed in attempt to improve accuracy.

Levy, R.↗
NASA NTRS1972

A parametric study of planform and aeroelastic effects on aerodynamic center, alpha- and q- stability derivatures. Appendix B: Method for computing the strucutral influence coefficient matrix of nonplanar wing body tail configurations

The method used in computing the structural influence coefficient matrix of the computer program of Reference 1 (appendix A of the Summary Report) is reported. This matrix is computed for complete wing-body-tail configurations by assuming that all major airplane components can be structurally represented by a slender beam called the elastic axis. A structural influence coefficient is defined as the rotation about the Y-stability axis at panel j induced by a unit load on panel k. A description of how a structural breakdown is performed in detail is included.

Roskam, J.↗
NASA NTRS1972

A parametric study of planform and aeroelastic effects on aerodynamic center, alpha- and q- stability derivatives. Appendix C: Method for computing the aerodynamic influence coefficient matrix of nonplanar wing-body-tail configurations

Expressions are derived for computing the aerodynamic influence coefficient matrix for nonplanar wing-body-tail configurations. An aerodynamic influence coefficient is defined as the load in lbs. induced on a panel as a result of a unit angle of attack on another panel. Fuselage, wing and tail thickness are assumed to be small with the result that the thickness effect on the flow-field is negligible. The method for determining the aerodynamic influence coefficient matrix is based on the lifting solution to the small perturbation, steady potential flow equation.

Roskam, J.↗
NASA NTRS1973

An algorithm for calculation of the Jordan canonical form of a matrix

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.

Sridhar, B.↗
NASA NTRS1973

Hot hardness characteristics of ausformed AISI M-50, Matrix 2, WD-65, modified AISI 440-C, and Super Nitralloy

Short-term hot hardness studies were performed with ausformed AISI M-50, Matrix 2, WD-65, modified AISI 440-C (14-4-1) and case hardened Super Nitralloy. Hardness levels of each material were measured at elevated temperatures in an electric furnace with a low oxygen environment. Test temperatures ranged from 294 to 877 K. The hot hardness characteristics of the ausformed AISI-M-50, Matrix 2 WD-65, and modified AISI 440-C were the same as those determined for high-speed tool steels. Hot hardness for these steels can be predicted within one point Rockwell C. The hot hardness characteristics of both the case and core of Super Nitralloy were superior to AISI 52100 but inferior to the high-speed tool steels. The short-term Rockwell C hardness at temperature for the Super Nitralloy material between 294 and 769 K can be predicted within one point Rockwell C hardness.

Chevalier, J. L.↗
NASA NTRS1973

Matrix Perturbation Techniques in Structural Dynamics

Matrix perturbation are developed techniques which can be used in the dynamical analysis of structures where the range of numerical values in the matrices extreme or where the nature of the damping matrix requires that complex valued eigenvalues and eigenvectors be used. The techniques can be advantageously used in a variety of fields such as earthquake engineering, ocean engineering, aerospace engineering and other fields concerned with the dynamical analysis of large complex structures or systems of second order differential equations. A number of simple examples are included to illustrate the techniques.

Caughey, T. K.↗
NASA NTRS1973

Theorems on symmetries and flux conservation in radiative transfer using the matrix operator theory.

The matrix operator approach to radiative transfer is shown to be a very powerful technique in establishing symmetry relations for multiple scattering in inhomogeneous atmospheres. Symmetries are derived for the reflection and transmission operators using only the symmetry of the phase function. These results will mean large savings in computer time and storage for performing calculations for realistic planetary atmospheres using this method. The results have also been extended to establish a condition on the reflection matrix of a boundary in order to preserve reciprocity. Finally energy conservation is rigorously proven for conservative scattering in inhomogeneous atmospheres.

Kattawar, G. W.↗
NASA NTRS1973

Influence matrix program for aerodynamic lifting surface theory

A users manual is described for a USA FORTRAN 4 computer program which computes an aerodynamic influence matrix and is one of several computer programs used to analyze lifting, thin wings in steady, subsonic flow according to a kernel function method lifting surface theory. The most significant features of the program are that it can treat unsymmetrical wings, control points can be placed on the leading and/or trailing edges, and a stable, efficient algorithm is used to compute the influence matrix.

Medan, R. T.↗
NASA NTRS1974

A computational procedure to analyze metal matrix laminates with nonlinear lamination residual strains

An approximate computational procedure is described for the analysis of angleplied laminates with residual nonlinear strains. The procedure consists of a combination of linear composite mechanics and incremental linear laminate theory. The procedure accounts for initial nonlinear strains, unloading, and in-situ matrix orthotropic nonlinear behavior. The results obtained in applying the procedure to boron/aluminum angleplied laminates show that this is a convenient means to accurately predict the initial tangent properties of angleplied laminates in which the matrix has been strained nonlinearly by the lamination residual stresses. The procedure predicted initial tangent properties results which were in good agreement with measured data obtained from boron/aluminum angleplied laminates.

Chamis, C. C.↗
NASA NTRS1972

Precision state and filter weighting matrix extrapolation, revision 3

The matrix extrapolation routine presented is a coded algorithm for the numerical solution of modified forms of the basic differential equations which are satisfied by the geocentric state vector of a spacecraft's center of mass and by the filter-weighting matrix. The equations are described in detail and the various input and output variables designated. The capability is thus established to extrapolate any spacecraft's geocentric state vector, either backwards or forwards in time, through a force field consisting of the earth's primary central-force gravitational attraction, and a superimposed perturbing acceleration.

Robertson, W. M.↗
NASA NTRS1973

A penny-shaped crack in a filament reinforced matrix. 1: The filament model

The electrostatic problem of a penny-shaped crack in an elastic matrix which reinforced by filaments or fibers perpendicular to the plane of the crack was studied. The elastic filament model was developed for application to evaluation studies of the stress intensity factor along the periphery of the crack, the stresses in the filaments or fibers, and the interface shear between the matrix and the filaments or fibers. The requirements expected of the model are a sufficiently accurate representation of the filament and applicability to the interaction problems involving a cracked elastic continuum with multi-filament reinforcements. The technique for developing the model and numerical examples of it are shown.

Erdogan, F.↗
NASA NTRS1973

A penny shaped crack in a filament-reinforced matrix. 2: The crack problem

The elastostatic interaction problem between a penny-shaped crack and a slender inclusion or filament in an elastic matrix was formulated. For a single filament as well as multiple identical filaments located symmetrically around the crack the problem is shown to reduce to a singular integral equation. The solution of the problem is obtained for various geometries and filament-to-matrix stiffness ratios, and the results relating to the angular variation of the stress intensity factor and the maximum filament stress are presented.

Pacella, A. H.↗
NASA NTRS1972

A matrix equation solution by an optimization technique

The computer solution of matrix equations is often difficult to accomplish due to an ill-conditioned matrix or high noise levels. Two methods of solution are compared for matrices of various degrees of ill-conditioning and for various noise levels in the right hand side vector. One method employs the usual Gaussian elimination. The other solves the equation by an optimization technique and employs a function minimization subroutine.

Johnson, M. J.↗
NASA NTRS1973

Stability of matrix equations arising in electromagnetics

Many problems in electromagnetics can be formulated as a Fredholm equation of the first kind. In these problems it is desired to determine some function f(x) from its integral transform g(y). Except for special cases for which an explicit inverse operator is known, the equation is usually discretized by the method of moments into a matrix equation Af = g, which is then solved on a computer. A method of calculating the sensitivity of the solution of Af = g due to errors in either the vector g or the matrix A is developed. The usefulness of this method is demonstrated with problems from antenna theory, scattering theory, and remote sensing.

Klein, C.↗
NASA NTRS1974

Useful extremum principle for the variational calculation of matrix elements

Variational principles are considered for the approximate evaluation of the diagonal matrix elements of an arbitrary known linear Hermitian operator. A method is derived that is immediately applicable to the variational determination of both the off-diagonal and diagonal matrix elements of normal and modified Green's functions.

Gerjuoy, E.↗
NASA NTRS1974

The tensile failure modes of metal-matrix composite materials

The strengths of individual boron fibers extracted from various as-received and thermally fatigued aluminum alloy matrix materials were measured. The results are described in terms of a Weibull distribution, and strengths of composites fabricated from these fibers are calculated in terms of lower and upper bounds. Tests conducted on composite specimens indicated that strengths approaching the upper bounds can be achieved in composites fabricated by normal diffusion bonding techniques. Cyclic temperature changes effectively reduced the strength values toward the lower bounds. It was concluded that this effect resulted from the degradation of the strength of the fiber-matrix bond.

Wright, M. A.↗
NASA NTRS1974

Connective stability of nonlinear matrix systems

Consideration of stability under structural perturbations of free dynamic systems described by the differential equation dx/dt = A(t,x)x, where the matrix A(t,x) has time-varying nonlinear elements. The concept of 'connective stability' is introduced to study the structural properties of competitive-cooperative nonlinear matrix systems. It is shown that stability reliability in such systems is high and that they remain stable despite time-varying (including 'on-off') interaction among individual agents present in the system. The results obtained can be used to study stability aspects of mathematical models arising in as diverse fields as economics, biology, arms races, and transistor circuits.

Siljak, D. D.↗