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NASA NTRS1982

Controllability of inherently damped large flexible space structures

Graph theoretic techniques are used to study controllability of linear systems which represent large flexible orbiting space systems with inherent damping. The controllability of the pair of matrices representing the system state and control influence matrices is assured when all states in the model are reachable in a digraph sense from at least one input and also when the term rank of a Boolean matrix whose non trivial components are based on the state and control influence matrices has a term rank of the order of the state vector. The damping matrix does not influence the required number of actuators but gives flexibility to the possibility locations of the actuators for which the system is controllable.

Reddy, A. S. S. R.↗

NASA NTRS1982

Research on numerical algorithms for large space structures

Numerical algorithms for large space structures were investigated with particular emphasis on decoupling method for analysis and design. Numerous aspects of the analysis of large systems ranging from the algebraic theory to lambda matrices to identification algorithms were considered. A general treatment of the algebraic theory of lambda matrices is presented and the theory is applied to second order lambda matrices.

Denman, E. D.↗

NASA NTRS1982

A computer package for the design and eigenproblem solution of damped linear multidegree of freedom systems

Systems described by the matrix differental equation are considered. An interactive design routine is presented for positive definite mass, damping, and stiffness matrices. Designing is accomplished by adjusting the mass, damping, and stiffness matrices to obtain a desired oscillation behavior. The algorithm also features interactively modifying the physical structure of the system, obtaining the matrix structure and a number of other system properties. In case of a general system, where the M, C, and K matrices lack any special properties, a routine for the eigenproblem solution of the system is developed. The latent roots are obtained by computing the characteristic polynomial of the system and solving for its roots. The above routines are prepared in FORTRAN IV and prove to be usable for the machines with low core memory.

Ahmadian, M.↗

NASA NTRS1982

Direct system parameter identification of mechanical structures with application to modal analysis

In this paper a method is described to estimate mechanical structure characteristics in terms of mass, stiffness and damping matrices using measured force input and response data. The estimated matrices can be used to calculate a consistent set of damped natural frequencies and damping values, mode shapes and modal scale factors for the structure. The proposed technique is attractive as an experimental modal analysis method since the estimation of the matrices does not require previous estimation of frequency responses and since the method can be used, without any additional complications, for multiple force input structure testing.

Leuridan, J. M.↗

NASA NTRS1986

Multi-color incomplete Cholesky conjugate gradient methods for vector computers

In this research, we are concerned with the solution on vector computers of linear systems of equations, Ax = b, where A is a larger, sparse symmetric positive definite matrix. We solve the system using an iterative method, the incomplete Cholesky conjugate gradient method (ICCG). We apply a multi-color strategy to obtain p-color matrices for which a block-oriented ICCG method is implemented on the CYBER 205. (A p-colored matrix is a matrix which can be partitioned into a pXp block matrix where the diagonal blocks are diagonal matrices). This algorithm, which is based on a no-fill strategy, achieves O(N/p) length vector operations in both the decomposition of A and in the forward and back solves necessary at each iteration of the method. We discuss the natural ordering of the unknowns as an ordering that minimizes the number of diagonals in the matrix and define multi-color orderings in terms of disjoint sets of the unknowns. We give necessary and sufficient conditions to determine which multi-color orderings of the unknowns correpond to p-color matrices. A performance model is given which is used both to predict execution time for ICCG methods and also to compare an ICCG method to conjugate gradient without preconditioning or another ICCG method. Results are given from runs on the CYBER 205 at NASA's Langley Research Center for four model problems.

Poole, E. L.↗

NASA NTRS1986

The use of multidimensional scaling for facilities layout - An application to the design of the Space Station

Before an optimum layout of the facilities for the proposed Space Station can be designed, it is necessary to understand the functions that will be performed by the Space Station crew and the relationships among those functions. Five criteria for assessing functional relationships were identified. For each of these criteria, a matrix representing the degree of association of all pairs of functions was developed. The key to making inferences about the layout of the Space Station from these matrices was the use of multidimensional scaling (MDS). Applying MDS to these matrices resulted in spatial configurations of the crew functions in which smaller distances in the MDS configuration reflected closer associations. An MDS analysis of a composite matrix formed by combining the five individual matrices resulted in two dimensions that describe the configuration: a 'private-public' dimension and a 'group-individual' dimension. Seven specific recommendations for Space Station layout were derived from analyses of the MDS configurations. Although these techniques have been applied to the design of the Space Station, they can be applied to the design of any facility where people live or work.

Tullis, Thomas S.↗

NASA NTRS1987

Tensile behavior of glass/ceramic composite materials at elevated temperatures

This paper describes the tensile behavior of high-temperature composite materials containing continuous Nicalon ceramic fiber reinforcement and glass and glass/ceramic matrices. The longitudinal properties of these materials can approach theoretical expectations for brittle matrix composites, failing at a strength and ultimate strain level consistent with those of the fibers. The brittle, high-modulus matrices result in a nonlinear stress-strain curve due to the onset of stable matrix cracking at 10 to 30 percent of the fiber strain to failure, and at strains below this range in off-axis plies. Current fibers and matrices can provide attractive properties well above 1000 C, but composites experience embrittlement in oxidizing atmospheres at 800 to 1000 C due to oxidation of a carbon interface reaction layer.The oxidation effect greatly increases the interface bond strength, causing composite embrittlement.

Mandell, J. F.↗

NASA NTRS1987

Analysis of laser extracted volatiles in carbonaceous chondrites

It is scientifically important to understand the composition of volatile compounds from interplanetary dust particles (IDPs) because they may be related to the primordial inventory of planetary materials which were necessary to provide environments conducive to the formation of life. The use of a laser microprobe to measure volatiles in IDPs was evaluated. Because primitive meteorites are thought to be closely related to IDPs, carbonaceous chondrites were used for the evaluation. Three sets of experiments were performed to determine the volatiles released from potential substrate materials, to analyze the volatiles released from matrices of bulk samples of carbonaceous chondrites, and to analyze volatiles released from approx. 100 to 200 micron meteorite particles to simulate IDPs. Aluminum appeared to be the best choice of substrate material. Mass ratios between carbonaceous chondrite matrices of Allende and Murchison show fair reproducibility with somewhat high uncertainties. Particles from the Orgueil, Murchison, and Allende meteorites produced measurable quantities of volatiles that appear to have mass spectra comparable to the bulk matrices.

Blanford, George E.↗

NASA NTRS1987

Review of thermal properties of graphite composite materials

Flammability, thermal, and selected mechanical properties of composites fabricated with epoxy and other thermally stable resin matrices are described. Properties which were measured included limiting-oxygen index, smoke evolution, thermal degradation products, total-heat release, heat-release rates, mass loss, flame spread, ignition resistance, thermogravimetric analysis, and selected mechanical properties. The properties of 8 different graphite composite panels fabricated using four different resin matrices and two types of graphite reinforcement are described. The resin matrices included: XU71775/H795, a blend of vinyl polystyryl pyridine and bismaleimide; H795, a bismaleimide; Cycom 6162, a phenolic; and PSP 6022M, a polystyryl pyridine. The graphite fiber used was AS-4 in the form of either tape or fabric. The properties of these composites were compared with epoxy composites. It was determined that the blend of vinyl polystyryl pyridine and bismaleimide (XU71775/H795) with the graphite tape was the optimum design giving the lowest heat release rate.

Kourtides, D. A.↗

NASA NTRS1987

Aqueous alteration in carbonaceous chondrites - Mass balance constraints on matrix mineralogy

Bulk chemical compositions of matrix material were determined in eleven Antarctic CM chondrites and five non-Antarctic CM and CI chondrites, using microprobe defocused-beam technique. The results, along with previously published data, are used to provide mass balance constraints on the relative proportions of intergrown and intermixed phyllosilicate phases in carbonaceous chondrite matrices. In terms of Fe, Si, and Mg, the CM matrix bulk compositions plot within a triangle defined by the compositions of PCP (a mixture of 25 percent tochilinite and 75 percent cronstedtite), Mg-rich serpentine, and Fe-rich serpentine. Results indicate differing amounts of PCP and serpentines in individual CM matrices. The discrepancies found between predicted and measured S and Ni values require additional sulfide phases. CI matrices were found to contain little, if any, PCP; they consist mostly of serpentine and montmorillonite.

Mcsween, Harry Y., Jr.↗

NASA NTRS1988

Bismaleimide-vinylpolystyrylpyridine graphite composites

Flammability, thermal, and selected mechanical properties of composites fabricated with epoxy and other thermally stable resin matrices are described. Properties which were measured included limiting-oxygen index, smoke evolution, thermal degradation products, total-heat release, heat-release rates, mass loss, flame spread, ignition resistance, thermogravimetric analysis and selected mechanical properties. This paper describes the properties of eight different graphite composite panels fabricated using four different resin matrices and two types of graphite reinforcement. The resin matrices included: XU71775/H795, a blend of vinylpolystyrylpyridine and bismaleimide; H795, a bismaleimide; Cycom 6162, a phenolic; and PSP 6022M, a polystyrylpyridine. The graphite fiber used was AS-4 in the form of either tape or fabric. The properties of these composites were compared with epoxy composites. It was determined that the blend of vinylpolystyrylpyridine and bismaleimide (XU71775/H795) with the graphite tape was the optimum design giving the lowest heat release rate.

Kourtides, D. A.↗

NASA NTRS1989

FREQ: A computational package for multivariable system loop-shaping procedures

Many approaches in the field of linear, multivariable time-invariant systems analysis and controller synthesis employ loop-sharing procedures wherein design parameters are chosen to shape frequency-response singular value plots of selected transfer matrices. A software package, FREQ, is documented for computing within on unified framework many of the most used multivariable transfer matrices for both continuous and discrete systems. The matrices are evaluated at user-selected frequency-response values, and singular values against frequency. Example computations are presented to demonstrate the use of the FREQ code.

Giesy, Daniel P.↗

NASA NTRS1990

SPARSKIT: A basic tool kit for sparse matrix computations

Presented here are the main features of a tool package for manipulating and working with sparse matrices. One of the goals of the package is to provide basic tools to facilitate the exchange of software and data between researchers in sparse matrix computations. The starting point is the Harwell/Boeing collection of matrices for which the authors provide a number of tools. Among other things, the package provides programs for converting data structures, printing simple statistics on a matrix, plotting a matrix profile, and performing linear algebra operations with sparse matrices.

Saad, Youcef↗

NASA NTRS1992

Dimensionally Stable Graphite-Fiber/Glass Composites

Method of making composites of glass matrices reinforced by graphite fibers provides for control of proportions, orientations, and distributions of fibers in matrices and for fused bonds between fibers and matrices. Enables fabrication of composites of high specific strength and dimensional stability. Method particularly suitable for making low-thermal-expansion platforms for optical instruments.

Harris, Robert↗

NASA NTRS1992

Time and wavelength domain algorithms for chemical analysis by laser radar

Laser-induced fluorescence (LIF) is a promising technique for laser radar applications. Laser radar using LIF has already been applied to algae blooms and oil slicks. Laser radar using LIF has great potential for remote chemical analysis because LIF spectra are extremely sensitive to chemical composition. However, most samples in the real world contain mixtures of fluorescing components, not merely individual components. Multicomponent analysis of laser radar returns from mixtures is often difficult because LIF spectra from solids and liquids are very broad and devoid of line structure. Therefore, algorithms for interpreting LIF spectra from laser radar returns must be able to analyze spectra that overlap in multicomponent systems. This paper analyzes the possibility of using factor analysis-rank annihilation (FARA) to analyze emission-time matrices (ETM) from laser radar returns instead of excitation-emission matrices (EEM). The authors here define ETM as matrices where the rows (or columns) are emission spectra at fixed times and the columns (or rows) are temporal profiles for fixed emission wavelengths. Laser radar usually uses pulsed lasers for ranging purposes, which are suitable for measuring temporal profiles. Laser radar targets are hard instead of diffuse; that is, a definite surface emits the fluorescence instead of an extended volume. A hard target would not broaden the temporal profiles as would a diffuse target. Both fluorescence lifetimes and emission spectra are sensitive to chemical composition. Therefore, temporal profiles can be used instead of excitation spectra in FARA analysis of laser radar returns. The resulting laser radar returns would be ETM instead of EEM.

Rosen, David L.↗

NASA NTRS1991

Krylov Subspace Methods for Complex Non-Hermitian Linear Systems

We consider Krylov subspace methods for the solution of large sparse linear systems Ax = b with complex non-Hermitian coefficient matrices. Such linear systems arise in important applications, such as inverse scattering, numerical solution of time-dependent Schrodinger equations, underwater acoustics, eddy current computations, numerical computations in quantum chromodynamics, and numerical conformal mapping. Typically, the resulting coefficient matrices A exhibit special structures, such as complex symmetry, or they are shifted Hermitian matrices. In this paper, we first describe a Krylov subspace approach with iterates defined by a quasi-minimal residual property, the QMR method, for solving general complex non-Hermitian linear systems. Then, we study special Krylov subspace methods designed for the two families of complex symmetric respectively shifted Hermitian linear systems. We also include some results concerning the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

Freund, Roland W.↗

NASA NTRS1993

A transfer matrix approach to vibration localization in mistuned blade assemblies

A study of mode localization in mistuned bladed disks is performed using transfer matrices. The transfer matrix approach yields the free response of a general, mono-coupled, perfectly cyclic assembly in closed form. A mistuned structure is represented by random transfer matrices, and the expansion of these matrices in terms of the small mistuning parameter leads to the definition of a measure of sensitivity to mistuning. An approximation of the localization factor, the spatially averaged rate of exponential attenuation per blade-disk sector, is obtained through perturbation techniques in the limits of high and low sensitivity. The methodology is applied to a common model of a bladed disk and the results verified by Monte Carlo simulations. The easily calculated sensitivity measure may prove to be a valuable design tool due to its system-independent quantification of mistuning effects such as mode localization.

Ottarson, Gisli↗

NASA NTRS1992

Applications of multiple-constraint matrix updates to the optimal control of large structures

Low-authority control or vibration suppression in large, flexible space structures can be formulated as a linear feedback control problem requiring computation of displacement and velocity feedback gain matrices. To ensure stability in the uncontrolled modes, these gain matrices must be symmetric and positive definite. In this paper, efficient computation of symmetric, positive-definite feedback gain matrices is accomplished through the use of multiple-constraint matrix update techniques originally developed for structural identification applications. Two systems were used to illustrate the application: a simple spring-mass system and a planar truss. From these demonstrations, use of this multiple-constraint technique is seen to provide a straightforward approach for computing the low-authority gains.

Smith, S. W.↗