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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Statistical analysis of the modal properties of large structural systems.

A theory is developed to predict eigenvalue and eigenvector uncertainty in large dynamic models. The uncertainty is based on physical property uncertainty and should not be confused with numerical roundoff, although the method can be extended to include the latter. The theory, when implemented on a computer, is used to analyze the uncertainties in frequencies and mode shapes based on uncertainties in mass, stiffness, modulus of elasticity, etc. The method incorporates a linear statistical model which is quite adequate for handling property uncertainties of 10% or more. The model is not limited to small systems but uses certain statistical assumptions as well as selective matrix manipulations to keep the size of all matrix operations to within the number of degrees of freedom of the system. Examples are given for two longitudinal vibration problems, and the results are supported by a Monte Carlo analysis.

Collins, J. D.↗
NASA NTRS1972

Buckling and vibration analysis for stiffened orthotropic shells of revolution.

Development of a numerical method, using the multistep integration approach, in which the buckling and vibration analyses are formulated as a succession of linear eigenvalue problems. The method does not require an estimate of the eigenvector, and once an eigenvalue has been converged good estimates for other eigenvalues are automatically available. This is accomplished through the use of an in-core Householder scheme for solution of the eigenvalue problem. Furthermore, since the method uses an eigenvalue solution, the possibility of missing modes is eliminated.

Svalbonas, V.↗
NASA NTRS1972

Spectral factorization in periodically time-varying systems and application to navigation problems.

Spectral factorization has been used previously to derive the steady-state solution of Kalman filtering equations without iteration for constant coefficient systems. The present work extends the spectral factorization algorithm to time-varying systems having periodic coefficient matrices for cases of both discrete and continuous systems. Time-consuming, expensive iterations of sequential covariance equations are not required to reach the final solution since this is an algebraic algorithm employing existing eigenvalue, eigenvector subroutines. The computer program incorporating the algorithm is suitable for sensitivity studies in formulating navigation and guidance strategies of low-thrust interplanetary missions. The determination of an optimum tracking pattern from an earth station is examined as an example.

Nishimura, T.↗
NASA NTRS1973

Mixed finite-difference scheme for free vibration analysis of noncircular cylinders

A mixed finite-difference scheme is presented for the free-vibration analysis of simply supported closed noncircular cylindrical shells. The problem is formulated in terms of eight first-order differential equations in the circumferential coordinate which possess a symmetric coefficient matrix and are free of the derivatives of the elastic and geometric characteristics of the shell. In the finite-difference discretization, two interlacing grids are used for the different fundamental unknowns in such a way as to avoid averaging in the difference-quotient expressions used for the first derivative. The resulting finite-difference equations are symmetric. The inverse-power method is used for obtaining the eigenvalues and eigenvectors.

Noor, A. K.↗
NASA NTRS1973

A unified development of several techniques for the representation of random vectors and data sets

Linear vector space theory is used to develop a general representation of a set of data vectors or random vectors by linear combinations of orthonormal vectors such that the mean squared error of the representation is minimized. The orthonormal vectors are shown to be the eigenvectors of an operator. The general representation is applied to several specific problems involving the use of the Karhunen-Loeve expansion, principal component analysis, and empirical orthogonal functions; and the common properties of these representations are developed.

Bundick, W. T.↗
NASA NTRS1973

The inference of atmospheric ozone using satellite nadir measurements in the 1042/cm band

A description and detailed analysis of a technique for inferring atmospheric ozone information from satellite nadir measurements in the 1042 cm band are presented. A method is formulated for computing the emission from the lower boundary under the satellite which circumvents the difficult analytical problems caused by the presence of atmospheric clouds and the watervapor continuum absorption. The inversion equations are expanded in terms of the eigenvectors and eigenvalues of a least-squares-solution matrix, and an analysis is performed to determine the information content of the radiance measurements. Under favorable conditions there are only two pieces of independent information available from the measurements: (1) the total ozone and (2) the altitude of the primary maximum in the ozone profile.

Russell, J. M., III↗
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

Divergence and Necessary Conditions for Extremums

The problem is considered of finding a dimension reducing transformation matrix B that maximizes the divergence in the reduced dimension for multi-class cases. A comparitively simple expression for the gradient of the average divergence with respect to B is developed. The developed expression for the gradient contains no eigenvectors or eigenvalues; also, all matrix inversions necessary to evaluate the gradient are available from computing the average divergence.

Quirein, J. A.↗
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

Unsteady, combined radiation and conduction in an absorbing, scattering, and emitting medium.

The transient cooldown of a gray, absorbing, isotropic scattering, emitting, and conducting medium bounded by gray, diffusely emitting and reflecting parallel plates is considered. Numerical solutions are obtained for the initial boundary-value problem with a discontinuous decrease in temperature at one boundary. The quasi-steady equation of radiative transfer is solved using Gaussian quadrature and a matrix eigenvector technique together with explicit numerical solution of the unsteady energy equation. Temperature and energy flux distributions are presented for variations of optical thickness, boundary emissivity, albedo, and conduction-radiation parameter.

Weston, K. C.↗
NASA NTRS1973

A NASTRAN DMAP alter for determining a local stiffness modification to obtain a specified eigenvalue

A technique is described which has been programmed as a DMAP Alter to Rigid Format 3, for determining a stiffness matrix modification to obtain a specified eigenvalue for a structure. The stiffness matrix modifications allowable are those that can be described as the product of a single scalar variable and a matrix of constant coefficients input by the user. The program solves for the scalar variable multiplier which will yield a specified eigenvalue for the complete structure (provided it exists), makes the modification to the stiffness matrix, and proceeds in Rigid Format 3 to obtain the eigenvalues and eigenvectors of the modified structure.

Case, W. R., Jr.↗
NASA NTRS1974

Results on the two population feature selection problem using probability of correct classification as a criterion

Variational equations are presented for maximizing the probability of correct classification as a function of a 1xn feature selection matrix B for the two-population problem. For the special case of equal covariance matrices the optimal B is unique up to scalar multiples and rank one sufficient. For equal population means, the best 1xn B is an eigenvector corresponding either to the largest or smallest eigenvalue of sigma sub 2 to the minus 1 power sigma sub 1 where sigma sub 1 and sigma sub 2 are the nxn covariance matrices of the two populations. The transformed probability of correct classification depends only on the eigenvalue. Finally, a procedure is proposed for constructing an optimal or nearly optimal kxn matrix of rank k without solving the k-dimensional variational equation.

Peters, B. C.↗
NASA NTRS1974

On the use and computation of the Jordan canonical form in system theory

This paper investigates various aspects of the application of the Jordan canonical form of a matrix in system theory and develops a computational approach to determining the Jordan form for a given matrix. Applications include pole placement, controllability and observability studies, serving as an intermediate step in yielding other canonical forms, and theorem proving. The computational method developed in this paper is both simple and efficient. The method is based on the definition of a generalized eigenvector and a natural extension of Gauss elimination techniques. Examples are included for demonstration purposes.

Sridhar, B.↗
NASA NTRS1974

Interactions between SAS-C spacecraft nutations and spin control system

The SAS-C spacecraft is stabilized by a momentum biased reaction wheel and passive nutation damper. A closed-loop low-speed spacecraft spin rate control system is included which uses a single-axis gyro and a variable speed range on the reaction wheel. Dynamic instability can result from interactions among the gyro, damper, and spacecraft dynamic unbalance. This instability may be aggravated by gyro angular misalignment, gyro error signals, and spacecraft nutations. Analytic eigenvector, and digital computer analyses of the coupled systems are presented. Mechanisms for instability are described as well as the effects that gyro error signal, tilt, and spacecraft dynamic unbalance produce on control system performance.

Tossman, B. E.↗
NASA NTRS1974

Development of technology for fluid-structure interaction modeling of a 1/8-scale dynamic model of shuttle External Tank (ET). Volume i: Technical report

A NASTRAN analysis of the external tank (ET) substructure of the 1/8-scale space shuttle structural dynamics model is described. The NASTRAN hydroelastic procedures were used to form a model of the liquid oxygen portion of the ET. Large computer storage requirements and running times were required unless these procedures were modified. Several possibilities were demonstrated including the substitution of the real for the complex eigenvalue routine and the use of the OMIT capability to reduce the number of fluid coordinates. A NASTRAN model of the complete ET was formed and reduced to 252 degrees of freedom. A review of the eigenvector extracted, using the unsymmetrical inverse power method, indicated that the structural OMIT's resulted in unsatisfactory modal deflections. Modifications to the NASTRAN hydroelastic capability appeared necessary to generate a successful ET model. An approach is described which, by assuming incompressibility, reduces the fluid representation to a symmetric mass matrix which can be added to the structural mass. The problem is solved using faster and more efficient eigenvalue routines. Using this approach the ET NASTRAN model was analyzed for three separate weight conditions.

Bernstein, M.↗
NASA NTRS1975

A table of semiempirical gf values. Part 1: Wavelengths: 5.2682 nm to 272.3380 nm

The gf values for 265,587 atomic lines selected from the line data used to calculate line-blanketed model atmospheres are tabulated. These data are especially useful for line identification and spectral synthesis in solar and stellar spectra. The gf values are calculated semiempirically by using scaled Thomas-Fermi-Dirac radial wavefunctions and eigenvectors found through least-squares fits to observed energy levels. Included in the calculation are the first five or six stages of ionization for sequences up through nickel. Published gf values are included for elements heavier than nickel. The tabulation is restricted to lines with wavelengths less than 10 micrometers.

Kurucz, R. L.↗
NASA NTRS1975

Modal coupling procedures adapted to NASTRAN analysis of the 1/8-scale shuttle structural dynamics model. Volume 1: Technical report

A dynamic substructuring analysis, utilizing the component modes technique, of the 1/8 scale space shuttle orbiter finite element model is presented. The analysis was accomplished in 3 phases, using NASTRAN RIGID FORMAT 3, with appropriate Alters, on the IBM 360-370. The orbiter was divided into 5 substructures, each of which was reduced to interface degrees of freedom and generalized normal modes. The reduced substructures were coupled to yield the first 23 symmetric free-free orbiter modes, and the eigenvectors in the original grid point degree of freedom lineup were recovered. A comparison was made with an analysis which was performed with the same model using the direct coordinate elimination approach. Eigenvalues were extracted using the inverse power method.

Zalesak, J.↗
NASA NTRS1975

Relaxation methods in fluid mechanics

The present work considers the iterative solution of a coupled set of difference equations and examines methods that carry successive approximates to a state that is invariant with further iteration and independent of the initial guess. Methods are studied with regard to their efficiency and economy of computer resources. The basic principles of classical relaxation are set forth, with attention confined to linear elliptic equations. This discussion involves the evaluation of the spectral radius that is the magnitude of the eigenvalue with largest modulus. The subject of relaxation is then related to the study of ordinary differential equations and hyperbolic partial differential equations. Problems that occur when linearly dependent eigenvectors appear in the relaxation matrix are discussed, leading to multiply connected eigenvalues in the Jordan canonical form. Finally, a brief survey of relaxation methods used in aerodynamics is given.

Lomax, H.↗