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Results for “eigenvalue analysis”

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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Visualization of 2-D and 3-D Tensor Fields

In previous work we have developed a novel approach to visualizing second order symmetric 2-D tensor fields based on degenerate point analysis. At degenerate points the eigenvalues are either zero or equal to each other, and the hyperstreamlines about these points give rise to trisector or wedge points. These singularities and their connecting hyperstreamlines determine the topology of the tensor field. In this study we are developing new methods for analyzing and displaying 3-D tensor fields. This problem is considerably more difficult than the 2-D one, as the richness of the data set is much larger. Here we report on our progress and a novel method to find, analyze and display 3-D degenerate points. First we discuss the theory, then an application involving a 3-D tensor field, the Boussinesq problem with two forces.

Hesselink, Lambertus↗
NASA NTRS1997

Visualization of 2-D and 3-D Tensor Fields

In previous work we have developed a novel approach to visualizing second order symmetric 2-D tensor fields based on degenerate point analysis. At degenerate points the eigenvalues are either zero or equal to each other, and the hyper-streamlines about these points give rise to tri-sector or wedge points. These singularities and their connecting hyper-streamlines determine the topology of the tensor field. In this study we are developing new methods for analyzing and displaying 3-D tensor fields. This problem is considerably more difficult than the 2-D one, as the richness of the data set is much larger. Here we report on our progress and a novel method to find , analyze and display 3-D degenerate points. First we discuss the theory, then an application involving a 3-D tensor field, the Boussinesq problem with two forces.

Hesselink, Lambertus↗
NASA NTRSDate not supplied

Coherent Mode Decomposition for Kolmogorov Optical Turbulence in a Finite Aperture

An analysis of the coherent mode decomposition of an optical field after propagation through atmospheric turbulence is presented. The coherent modes represent an ideal basis by which to decompose the field for design of mode-limited optical systems. Using the rotational symmetry of the Fredholm integral operator for Kolmogorov optical turbulence, it is shown that the coherent modes exhibit separable solutions classified by radial and azimuthal quantum numbers. The study of the coherent modes is then reduced that of the radial functions determined by the aperture-coherence diameter ratio and obscuration ratio. Analysis of the spectrum of eigenvalues yields sharp bounds on the efficiency of receivers using incoherent or coherent combining with mode-limited photonic devices in the presence of Kolmogorov turbulence. The effective number of modes needed to represent Kolmogorov optical turbulence is studied via the von Neumann entropy, purity, and largest eigenvalue, and the differences in the different definitions is discussed. The similarity of the coherent modes to linearly polarized (LP) fiber modes is quantified yielding a precise characterization of the maximum gain that can be achieved in mode-limited systems via mode shaping techniques. As a final application, a mode sorting technique is presented for optimally splitting power from atmospherically degraded light into a finite number of modes simultaneously maximizing total coupling efficiency and minimizing the average and instantaneous power ratio between channels.

free-space optical communication↗
NASA NTRSDate not supplied

Coherent Mode Decomposition for Kolmogorov Optical Turbulence in a Finite Aperture

An analysis of the coherent mode decomposition of an optical field after propagation through atmospheric turbulence is presented. The coherent modes represent an ideal basis by which to decompose the field for design of mode-limited optical systems. Due to rotational symmetry of the Fredholm integral operator for Kolmogorov optical turbulence, the coherent modes exhibit separable solutions classified by a radial and azimuthal mode index. The study of the coherent modes is then reduced to that of the radial functions determined by the coherence ratio and obscuration ratio. Analysis of the spectrum of eigenvalues yields sharp bounds on the efficiency of receivers using incoherent or coherent combining with mode-limited photonic devices in the presence of Kolmogorov turbulence. The effective number of modes needed to represent Kolmogorov optical turbulence is studied via the von Neumann entropy, purity, and largest eigenvalue, and the differences in the different definitions is discussed. The similarity of the coherent modes to linearly polarized (LP) fiber modes is quantified yielding a precise characterization of the maximum gain that can be achieved in mode-limited systems via mode shaping techniques. As a final application, a mode sorting technique is presented for optimally splitting power from atmospherically degraded light into a finite number of modes simultaneously maximizing total coupling efficiency and minimizing the difference in average power between channels.

free-space optical communication↗
DOE OSTI2025

Automated Direct Perturbation Calculations with SCALE TSUNAMI [Abstract]

In nuclear criticality safety analysis, the sensitivity of the eigenvalue keff to uncertainties in nuclear data and its evaluation are crucial. The TSUNAMI sequences within the SCALE code system offer users various options with both multigroup (MG) and continuous-energy (CE) 3D Monte Carlo (MC) transport capabilities for calculating keff sensitivity coefficients and storing them in a sensitivity data file (SDF). Each methodology available in TSUNAMI offers distinct advantages and limitations, and its effectiveness can vary based on the specific problem being solved. As a best practice, practitioners typically use the direct perturbation (DP) method as a confirmatory step alongside their sensitivity calculations to verify the accuracy of the sensitivity data generated. In this process, DP calculations are usually performed on select nuclides, those considered most important for validating their total sensitivities. However, because of code limitations, analysts use a workaround method when conducting DP calculations for a single nuclide: rather than perturbing the nuclide's microscopic cross section, an equivalent number density for this nuclide is calculated to reflect the effect of a change in the macroscopic cross section due to a perturbation in the microscopic cross section. The current approach requires rerunning the CSAS criticality calculation several times with model changes. Although this method can yield results with acceptable accuracy, it is labor-intensive and prone to errors.

AZURE: SAMMY↗
NASA NTRS2004

LINFLUX-AE: A Turbomachinery Aeroelastic Code Based on a 3-D Linearized Euler Solver

This report describes the development and validation of LINFLUX-AE, a turbomachinery aeroelastic code based on the linearized unsteady 3-D Euler solver, LINFLUX. A helical fan with flat plate geometry is selected as the test case for numerical validation. The steady solution required by LINFLUX is obtained from the nonlinear Euler/Navier Stokes solver TURBO-AE. The report briefly describes the salient features of LINFLUX and the details of the aeroelastic extension. The aeroelastic formulation is based on a modal approach. An eigenvalue formulation is used for flutter analysis. The unsteady aerodynamic forces required for flutter are obtained by running LINFLUX for each mode, interblade phase angle and frequency of interest. The unsteady aerodynamic forces for forced response analysis are obtained from LINFLUX for the prescribed excitation, interblade phase angle, and frequency. The forced response amplitude is calculated from the modal summation of the generalized displacements. The unsteady pressures, work done per cycle, eigenvalues and forced response amplitudes obtained from LINFLUX are compared with those obtained from LINSUB, TURBO-AE, ASTROP2, and ANSYS.

Reddy, T. S. R.↗
NASA NTRS1996

Thermal and Mechanical Buckling Analysis of Hypersonic Aircraft Hat-Stiffened Panels With Varying Face Sheet Geometry and Fiber Orientation

Mechanical and thermal buckling behavior of monolithic and metal-matrix composite hat-stiffened panels were investigated. The panels have three types of face-sheet geometry: Flat face sheet, microdented face sheet, and microbulged face sheet. The metal-matrix composite panels have three types of face-sheet layups, each of which is combined with various types of hat composite layups. Finite-element method was used in the eigenvalue extractions for both mechanical and thermal buckling. The thermal buckling analysis required both eigenvalue and material property iterations. Graphical methods of the dual iterations are shown. The mechanical and thermal buckling strengths of the hat-stiffened panels with different face-sheet geometry are compared. It was found that by just microdenting or microbulging of the face sheet, the axial, shear, and thermal buckling strengths of both types of hat-stiffened panels could be enhanced considerably. This effect is more conspicuous for the monolithic panels. For the metal-matrix composite panels, the effect of fiber orientations on the panel buckling strengths was investigated in great detail, and various composite layup combinations offering, high panel buckling strengths are presented. The axial buckling strength of the metal-matrix panel was sensitive to the change of hat fiber orientation. However, the lateral, shear, and thermal buckling strengths were insensitive to the change of hat fiber orientation.

Ko, William L.↗
NASA NTRS1998

High-Alpha Research Vehicle Lateral-Directional Control Law Description, Analyses, and Simulation Results

This report contains a description of a lateral-directional control law designed for the NASA High-Alpha Research Vehicle (HARV). The HARV is a F/A-18 aircraft modified to include a research flight computer, spin chute, and thrust-vectoring in the pitch and yaw axes. Two separate design tools, CRAFT and Pseudo Controls, were integrated to synthesize the lateral-directional control law. This report contains a description of the lateral-directional control law, analyses, and nonlinear simulation (batch and piloted) results. Linear analysis results include closed-loop eigenvalues, stability margins, robustness to changes in various plant parameters, and servo-elastic frequency responses. Step time responses from nonlinear batch simulation are presented and compared to design guidelines. Piloted simulation task scenarios, task guidelines, and pilot subjective ratings for the various maneuvers are discussed. Linear analysis shows that the control law meets the stability margin guidelines and is robust to stability and control parameter changes. Nonlinear batch simulation analysis shows the control law exhibits good performance and meets most of the design guidelines over the entire range of angle-of-attack. This control law (designated NASA-1A) was flight tested during the Summer of 1994 at NASA Dryden Flight Research Center.

Davidson, John B.↗
NASA NTRS1976

Eigenvalue properties of structural mean-axis systems

The authors review some of the properties of the pseudoinverse and oblique pseudoinverse of a linear transformation T from one finite-dimensional inner-product space into another, and then use these properties and a theorem of Milne (1968), which states that the oblique pseudoinverse can be expressed in terms of a weak generalized inverse and two projection operators, in order to compute a mean-axis influence coefficient matrix for the dynamic analysis of an elastic body. Some eigenvalue invariance properties of the mean-axis structural dynamics equations are demonstrated, and on the simple example of a uniform beam, it is shown that the finite frequencies and mode shapes of the mean axis structural system are identical to the nonzero frequencies and mode shapes of the free structure.

Cavin, R. K., III↗
NASA NTRS1992

A study of the control problem of the shoot side environment delivery system of a closed crop growth research chamber

The details of our initial study of the control problem of the crop shoot environment of a hypothetical closed crop growth research chamber (CGRC) are presented in this report. The configuration of the CGRC is hypothetical because neither a physical subject nor a design existed at the time the study began, a circumstance which is typical of large scale systems control studies. The basis of the control study is a mathematical model which was judged to adequately mimic the relevant dynamics of the system components considered necessary to provide acceptable realism in the representation. Control of pressure, temperature, and flow rate of the crop shoot environment, along with its oxygen, carbon dioxide, and water concentration is addressed. To account for mass exchange, the group of plants is represented in the model by a source of oxygen, a source of water vapor, and a sink for carbon dioxide. In terms of the thermal energy exchange, the group of plants is represented by a surface with an appropriate temperature. Most of the primitive equations about an experimental operating condition and a state variable representation which was extracted from the linearized equations are presented. Next, we present the results of a real Jordan decomposition and the repositioning of an undesirable eigenvalue via full state feedback. The state variable representation of the modeling system is of the nineteenth order and reflects the eleven control variables and eight system disturbances. Five real eigenvalues are very near zero, with one at zero, three having small magnitude positive values, and one having a small magnitude negative value. A Singular Value Decomposition analysis indicates that these non-zero eigenvalues are not results of numerical error.

Blackwell, C. C.↗
NASA NTRS1975

Numerical solution of quadratic matrix equations for free vibration analysis of structures

This paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.

Gupta, K. K.↗
NASA NTRS2013

Buckling Testing and Analysis of Honeycomb Sandwich Panel Arc Segments of a Full-Scale Fairing Barrel Part 1: 8-Ply In-Autoclave Facesheets: 8-Ply In-Autoclave Facesheets - Part 1

Four honeycomb sandwich panels, representing 1/16th arc segments of a 10-m diameter barrel section of the heavy lift launch vehicle, were manufactured under the NASA Composites for Exploration program and the NASA Space Launch Systems program. Two configurations were chosen for the panels: 6-ply facesheets with 1.125 in. honeycomb core and 8-ply facesheets with 1.000 in. honeycomb core. Additionally, two separate carbon fiber/epoxy material systems were chosen for the facesheets: inautoclave IM7/977-3 and out-of-autoclave T40-800b/5320-1. Smaller 3.00- by 5.00-ft panels were cut from the 1/16th barrel sections. These panels were tested under compressive loading at the NASA Langley Research Center. Furthermore, linear eigenvalue and geometrically nonlinear finite element analysis was performed to predict the compressive response of the 3.00- by 5.00-ft panels. This manuscript summarizes the experimental and analytical modeling efforts pertaining to the panel composed of 8-ply, IM7/977-3 facesheets (referred to Panel A). To improve the robustness of the geometrically nonlinear finite element model, measured surface imperfections were included in the geometry of the model. Both the linear and nonlinear models yield good qualitative and quantitative predictions. Additionally, it was predicted correctly that the panel would fail in buckling prior to failing in strength. Furthermore, several imperfection studies were performed to investigate the influence of geometric imperfections, fiber misalignments, and three-dimensional (3 D) effects on the compressive response of the panel.

Myers, David E.↗
NASA NTRSDate not supplied

Eigenvalue Sensitivity Computations for Linear Stability Theory

To realize the drag reduction benefit of boundary-layer transition control strategies, it is crucial to integrate transition prediction into the vehicle design through an optimization process. The integration of transition prediction based on linear stability analysis into adjoint d design optimization requires coupling an adjoint enabled computational fluid dynamics (CFD) solver with an adjoint enabled linear stability code. In particular, the boundary-layer transition location is often predicted using the N-factor method based on linear stability theory (LST). Thus, sensitivity of the linear-stability eigenvalues constitute an essential building block for optimizing the laminar flow performance. The present paper describes an implementation of LST eigenvalue sensitivity analysis that can be easily coupled with a CFD solver. Specifically, we describe a discrete adjoint formulation for the transition location prediction based on the N-factor method. The verification of this formulation is carried out by comparing the adjoint-based sensitivity of the local growth rate of a given instability mode with respect to the disturbance frequency, and the adjoint-based sensitivity of the transition location with respect to spanwise wavenumber with those sensitivities computed using a finite-difference approximation. Finally, the adjoint LST formulation is applied to flat-plate boundary-layer flows at transonic, supersonic, and hypersonic conditions, to determine the behavior and sensitivities of the transition location with respect to a range of disturbance spanwise wavenumbers.

Boundary Layer Transition↗
NASA NTRS1991

Eigenvalue calculation procedure for an Euler/Navier-Stokes solver with application to flows over airfoils

A Lanczos procedure is presently applied to a Navier-Stokes (N-S) solver for eigenvalues and eigenvectors associated with the small-perturbation analysis of the N-S equations' finite-difference representation for airfoil flows; the matrix used is very large, sparse, real, and nonsymmetric. The Lanczos procedure is shown to furnish complete spectral information for the eigenvalues, as required for transient-stability analysis of N-S solvers.

Mahajan, Aparajit J.↗
NASA NTRS1995

Separation analysis, a tool for analyzing multigrid algorithms

The separation of vectors by multigrid (MG) algorithms is applied to the study of convergence and to the prediction of the performance of MG algorithms. The separation operator for a two level cycle algorithm is derived. It is used to analyze the efficiency of the cycle when mixing of eigenvectors occurs. In particular cases the separation analysis reduces to Fourier type analysis. The separation operator of a two level cycle for a Schridubger eigenvalue problem, is derived and analyzed in a Fourier basis. Separation analysis gives information on how to choose performance relaxations and inter-level transfers. Separation analysis is a tool for analyzing and designing algorithms, and for optimizing their performance.

Costiner, Sorin↗
NASA NTRS1983

Reanalysis and design in structural dynamics

A unified efficient formulation for the static and dynamic reanalysis of locally modified structures is presented. The reanalysis problem is to find the structural responses when some of the element properties are adjusted as a result of design modifications or when additional structures are appended to the original system. The reanalysis problem is formulated as a problem of much lower order than the original system. This is achieved by utilizing the linearity property of the structure using the pseudoload concept together with the solution of the original system. The modifications to the structure are treated as displacement-dependent pseudoloads of the system. By expressing the modified system response as linear combinations of the response of the original system and a term depending on the pseudoload, a reduced set of response equations can be obtained. In the static and sinusoidal steady state analysis, this leads to a set of linear algebraic equations. For a free vibration analysis, this results in a reduced eigenvalue problem. Using these reduced equations, a design problem can be solved; that is, the magnitude of a specified local modification for given dynamic response characteristics can be calculated. Several examples are presented to illustrate the general formulations.

Wang, B. P.↗
NASA NTRS1982

COSAL: A black-box compressible stability analysis code for transition prediction in three-dimensional boundary layers

A fast computer code COSAL for transition prediction in three dimensional boundary layers using compressible stability analysis is described. The compressible stability eigenvalue problem is solved using a finite difference method, and the code is a black box in the sense that no guess of the eigenvalue is required from the user. Several optimization procedures were incorporated into COSAL to calculate integrated growth rates (N factor) for transition correlation for swept and tapered laminar flow control wings using the well known e to the Nth power method. A user's guide to the program is provided.

Malik, M. R.↗
NASA NTRS1993

Automatic A-set selection for dynamics analysis

A method for selecting optimum NASTRAN analysis set degrees of freedom for the dynamic eigenvalue problem is described. Theoretical development of the Guyan reduction procedure on which the method is based is first summarized. The algorithm used to select the analysis set degrees of freedom is then developed. Two example problems are provided to demonstrate the accuracy of the algorithm.

Allen, Tom↗