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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Discrete integration of continuous Kalman filtering equations for time invariant second-order structural systems

A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.

Park, K. C.↗
NASA NTRS1989

Experimental investigation of the hydrodynamic forces on the shroud of a centrifugal pump impeller

Fluid-induced forces acting on a rotating impeller are known to cause rotor-dynamic problems in turbomachines. The forces generated by leakage flow along the front shroud surface of a centrifugal turbomachine impeller play an important role among these fluid-induced forces. The present research was aimed to gain a better understanding of these shroud forces. An experimental apparatus was designed and constructed to simulate the impeller shroud leakage flow. Hydrodynamic forces and steady and unsteady pressure distributions on the rotating shroud were measured as functions of eccentricity, width of shroud clearance, face seal clearance and shaft rotating speed. The forces measured from the dynamometer and manometers agreed well. The hydrodynamic force matrices were found skew-symmetric and statically unstable. This is qualitatively similar to the result of previous hydrodynamic volute force measurements. Nondimensionalized normal and tangential forces decrease slightly as Reynolds number increases. As the width of the shroud clearance decreases and/or the eccentricity increases, the hydrodynamic forces increase nonlinearly. There was some evidence found that increased front seal clearance could reduce the radial shroud forces and the relative magnitude of the destabilizing tangential force. Subharmonic pressure fluctuations were also observed which may adversely affect the behavior of the rotor system.

Zhuang, Fei↗
NASA NTRS1991

Discrete Kalman filtering equations of second-order form for control-structure interaction simulations

A second-order form of discrete Kalman filtering equations is proposed as a candidate state estimator for efficient simulations of control-structure interactions in coupled physical coordinate configurations as opposed to decoupled modal coordinates. The resulting matrix equation of the present state estimator consists of the same symmetric, sparse N x N coupled matrices of the governing structural dynamics equations as opposed to unsymmetric 2N x 2N state space-based estimators. Thus, in addition to substantial computational efficiency improvement, the present estimator can be applied to control-structure design optimization for which the physical coordinates associated with the mass, damping and stiffness matrices of the structure are needed instead of modal coordinates.

Park, K. C.↗
NASA NTRS1997

Graph Embedding Techniques for Bounding Condition Numbers of Incomplete Factor Preconditioning

We extend graph embedding techniques for bounding the spectral condition number of preconditioned systems involving symmetric, irreducibly diagonally dominant M-matrices to systems where the preconditioner is not diagonally dominant. In particular, this allows us to bound the spectral condition number when the preconditioner is based on an incomplete factorization. We provide a review of previous techniques, describe our extension, and give examples both of a bound for a model problem, and of ways in which our techniques give intuitive way of looking at incomplete factor preconditioners.

Guattery, Stephen↗
NASA NTRS1984

System identification of analytical models of damped structures

A procedure is presented for identifying linear nonproportionally damped system. The system damping is assumed to be representable by a real symmetric matrix. Analytical mass, stiffness and damping matrices which constitute an approximate representation of the system are assumed to be available. Given also are an incomplete set of measured natural frequencies, damping ratios and complex mode shapes of the structure, normally obtained from test data. A method is developed to find the smallest changes in the analytical model so that the improved model can exactly predict the measured modal parameters. The present method uses the orthogonality relationship to improve mass and damping matrices and the dynamic equation to find the improved stiffness matrix.

Fuh, J.-S.↗
NASA NTRS1986

A generalized theory for eccentric and misalignment effects in high-pressure annular seals

High-pressure annular seal leakage and dynamic coefficients vary with eccentricity and misalignment. Recent seal leakage data with both concentric and fully eccentric alignments support the seal leakage model with surface roughness and eccentricity effects included. In this paper, the seal dynamic coefficient calculation has been generalized and allows direct calculation of the seal dynamic coefficients at any circumferential location. The generalized solution agrees with the results obtained by using the calculated values of an earlier paper and performing a coordinate transformation. The analysis results coincide with the measured data in showing that the stiffness and damping matrices of seal coefficients are not skew symmetric, and the main diagonal seal coefficients are not equal. The measured direct stiffnesses were found higher than predicted by the concentric seal theory, but this may be explained by the presence of eccentricity in the test operating mode.

Chen, W. C.↗
NASA NTRS1989

Factorization Of Positive Definite, Banded Hermitian Matrices

Report discusses application of Cholesky factorization algorithm to positive definite, banded Hermitian matrices. Begins by extending Cholesky factorization algorithm to cover uniformly-partitioned, banded, positive definite matrices of rank n that is real symmetric or Hermitian. Then two stratagems given for use of algorithm in concurrent-processing system in which N less than it has to be to enable factorization of matrix in as few serial steps as possible and where uniformly high efficiency expected from all processing elements. One of major purposes of this and related studies to maximize speedup and efficiency in system of concurrent-data-processing elements.

Salama, Moktar A.↗
NASA NTRS1989

Ritz method for transient response in systems having unsymmetric stiffness

The DMAP coding was automated to such an extent by using the device of bubble vectors, that it is useable for analyses in its present form. This feasibility study demonstrates that the Ritz Method is so compelling as to warrant coding its modules in FORTRAN and organizing the resulting coding into a new Rigid Format. Even though this Ritz technique was developed for unsymmetric stiffness matrices, it offers advantages to problems with symmetric stiffnesses. If used for the symmetric case the solution would be simplified to one set of modes, because the adjoint would be the same as the primary. Its advantage in either type of symmetry over a classical eigenvalue modal expansion is that information density per Ritz mode is far richer than per eigenvalue mode; thus far fewer modes would be needed for the same accuracy and every mode would actively participate in the response. Considerable economy can be realized in adapting Ritz vectors for modal solutions. This new Ritz capability now makes NASTRAN even more powerful than before.

Butler, Thomas G.↗
NASA NTRS1986

Concurrent Cholesky factorization of positive definite banded Hermitian matrices

First, the Cholesky factorization is extended to cover uniformly partitioned banded positive definite matrices of rank n which may be real symmetric or Hermitian. Then, two stratagems are given for the use of the algorithm in concurrent machines where the number of processing elements is less than required to factor the matrix in as few serial steps as possible, and where uniformly high efficiency is expected from all processing elements. Expressions are given for the efficiency factor e appearing in the speed-up expression q = eN, and these are specialized for the N node hypercube machine as a function of partition size s, the number N of processing elements of the hypercube machine, and the cost mu of interelement transmission relative to computation. It is shown that the efficiency factor e is inversely proportional to mu/s, and that e is almost independent of N when N is large and mu/s = 0. The task is completed in n/s serial steps with no limit on n. The half bandwidth b of the matrix is 2 Ns.

Utku, S.↗
NASA NTRS1978

Extension of the tridiagonal reduction (FEER) method for complex eigenvalue problems in NASTRAN

As in the case of real eigenvalue analysis, the eigensolutions closest to a selected point in the eigenspectrum were extracted from a reduced, symmetric, tridiagonal eigenmatrix whose order was much lower than that of the full size problem. The reduction process was effected automatically, and thus avoided the arbitrary lumping of masses and other physical quantities at selected grid points. The statement of the algebraic eigenvalue problem admitted mass, damping, and stiffness matrices which were unrestricted in character, i.e., they might be real, symmetric or nonsymmetric, singular or nonsingular.

Newman, M.↗
NASA NTRS1984

Hydrodynamic impeller stiffness, damping, and inertia in the rotordynamics of centrifugal flow pumps

The lateral hydrodynamic forces experienced by a centrifugal pump impeller performing circular whirl motions within several volute geometries were measured. The lateral forces were decomposed into: (1) time averaged lateral forces and (2) hydrodynamic force matrices representing the variation of the lateral forces with position of the impeller center. It is found that these force matrices essentially consist of equal diagonal terms and skew symmetric off diagonal terms. One consequence of this is that during its whirl motion the impeller experiences forces acting normal and tangential to the locus of whirl. Data on these normal and tangential forces are presented; it is shown that there exists a region of positive reduced whirl frequencies, within which the hydrodynamic forces can be destablizing with respect to whirl.

Jery, S.↗
NASA NTRS1983

Vibration control of large linear quadratic symmetric systems

Some unique properties on a class of the second order lambda matrices were found and applied to determine a damping matrix of the decoupled subsystem in such a way that the damped system would have preassigned eigenvalues without disturbing the stiffness matrix. The resulting system was realized as a time invariant velocity only feedback control system with desired poles. Another approach using optimal control theory was also applied to the decoupled system in such a way that the mode spillover problem could be eliminated. The procedures were tested successfully by numerical examples.

Jeon, G. J.↗
NASA NTRS1977

Complex eigenvalue extraction in NASTRAN by the tridiagonal reduction (FEER) method

An extension of the Tridiagonal Reduction (FEER) method to complex eigenvalue analysis in NASTRAN is described. As in the case of real eigenvalue analysis, the eigensolutions closest to a selected point in the eigenspectrum are extracted from a reduced, symmetric, tridiagonal eigenmatrix whose order is much lower than that of the full size problem. The reduction process is effected automatically, and thus avoids the arbitrary lumping of masses and other physical quantities at selected grid points. The statement of the algebraic eigenvalue problem admits mass, damping and stiffness matrices which are unrestricted in character, i.e., they may be real, complex, symmetric or unsymmetric, singular or non-singular.

Newman, M.↗
NASA NTRS1975

An interactive graphics package for the automatic node renumbering of finite element matrices

An interactive graphics software package which allows users to display the non-zero structure of large sparse symmetric materials was described and methods used to implement it as a portable FORTRAN callable subroutine were summarized. In particular, the system permits the display of the resulting matrix after reordering the rows and columns, with the reordering scheme either defined by the user or automatically generated by the program with the aim of reducing matrix bandwidth and profile. Although the primary application of the package has been to the finite element analysis of structures, it is equally well suited to the many other areas of engineering and science which use sparse matrices.

Boisvert, R. F.↗
NASA NTRS1972

SYMAT, COVAR: Test Procedures for Matrix Calculations

The FORTRAN subroutine SYMAT and related subroutines are described. In essence SYMAT is an iterative algorithm in which the problem of finding eigenvalues and eigenvectors of a real symmetric matrix is transformed into an equivalent problem of finding eigenvalues and eigenvectors of an infinite sequence of matrices of order two. A DEMO PROGRAM contains a subroutine COVAR which is used to compute the covariance matrix (denoted by A) of a data matrix (denoted by X). Since a covariance matrix is symmetric it can be analyzed by using subroutine SYMAT.

Morris, W. L.↗
NASA NTRS1978

On Nth roots of positive operators

A bounded operator A on a Hilbert space H was positive. These operators were symmetric, and as such constitute a natural generalization of nonnegative real diagonal matrices. The following result is thus both well known and not surprising: A positive operator has a unique positive square root (under operator composition).

Brown, D. R.↗
NASA NTRS1990

Implementation of two projection methods on a shared memory multiprocessor - DEC VAX 6240

The relative performance of two iterative schemes, based on projection techniques, is compared on a shared memory multiprocessor - VAX 6240. The CG accelerated Block-SSOR method and the CG accelerated Symmetric-Kaczmarz method are considered for the solution of large sparse nonsymmetric systems of linear equations. It is shown that the regular structure of many matrices can be exploited by the CG-accelerated Block-SSOR method to provide good speedup in a multiprocessing environment. However, the CG accelerated Symmetric-Kaczmarz method, while being a viable alternative on a scalar machine, is unable to benefit from multiprocessing.

Kamath, C.↗
NASA NTRS1974

Spectral and textural processing of ERTS imagery

A procedure is developed to simultaneously extract textural features from all bands of ERTS multispectral scanner imagery for automatic analysis. Multi-images lead to excessively large grey tone N-tuple co-occurrence matrices; therefore, neighboring grey N-tuple differences are measured and an ellipsoidally symmetric functional form is assumed for the co-occurrence distribution of multiimage greytone N-tuple differences. On the basis of past data the ellipsoidally symmetric approximation is shown to be reasonable. Initial evaluation of the procedure is encouraging.

Haralick, R. M.↗