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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Differential eigenvalue problems in which the parameter appears nonlinearly

Several methods are examined for determining the eigenvalues of a system of equations in which the parameter appears nonlinearly. The equations are the result of the discretization of differential eigenvalue problems using a finite Chebyshev series. Two global methods are considered which determine the spectrum of eigenvalues without an initial estimate. A local iteration scheme with cubic convergence is presented. Calculations are performed for a model second order differential problem and the Orr-Sommerfeld problem for plane Poiseuille flow.

Bridges, T. J.↗
DOE OSTI2022

On the structure of isometrically embeddable metric spaces

Since its popularization in the 1970s, the Fiedler vector of a graph has become a standard tool for clustering of the vertices of the graph. Recently, Mendel and Noar, Dumitriu and Radcliffe, and Radcliffe and Williamson have introduced geometric generalizations of the Fiedler vector. Motivated by questions stemming from their work, we provide structural characterizations for when a finite metric space can be isometrically embedded in a Hilbert space.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

Boundary layer stability calculations

In this paper numerical calculation of the spatial stability of disturbances in the parallel and nonparallel Blasius boundary layers is considered. Chebyshev polynomials are used for discretization. The problem with the boundary condition at infinity is overcome, and the resulting nonlinear matrix eigenvalue problem is attacked directly. The secondary eigenvalue problem for three-dimensional disturbances is shown to be uniformly stable, and particular solutions of this problem generated by the Orr-Sommerfeld equation are shown. A numerical solution of the nonparallel problem is considered using Chebyshev polynomials. The matrix equations are analyzed directly and the problem of uniqueness of the nonparallel correction is settled by careful application of the Fredholm alternative. Nonparallel corrections to the streamwise eigenfunction are shown.

Bridges, Thomas J.↗
NASA NTRSDate not supplied

Adjoint-based Sensitivities of Flutter Predictions based on the Linearized Frequency-domain Approach

Flutter is a critical factor in designing and certifying aircraft. The linearized frequency-domain method offers a lower cost alternative to time-marching computational fluid dynamics for high-fidelity flutter analysis. In this work, adjoint-based sensitivities are added to a flutter analysis based on the linearized frequency-domain method to efficiently compute derivatives of flutter cost functions with respect to design variables or uncertain parameters. The derivation of the adjoint equations, which involve complications such as derivatives of a nonlinear generalized eigenvalue problem with complex-valued inputs and derivatives of the linearized Navier-Stokes equations, is provided. The implemented adjoint terms and derivatives are verified before demonstrating the approach for derivatives of flutter dynamic pressure with respect to Mach number for the AGARD 445.6 wing.

Aeroelasticity↗
DOE OSTI2022

Multi-harmonic Rutherford island theory

Rutherford island theory, which governs the nonlinear evolution of tearing modes in tokamak plasmas, is generalized to take into account situations in which the conventional one-harmonic approximation is not valid. The analysis incorporates non-inductive currents driven by radio frequency (RF) electromagnetic waves injected into the plasma. A multi-harmonic tearing mode dispersion relation is derived that takes the form of a nonlinear inhomogeneous matrix eigenvalue problem. The dispersion relation is solved in the so-called two-harmonic approximation, in which only the principal Fourier harmonic of the perturbed magnetic flux and its first overtone are included in the calculation. In the absence of RF current drive, the nonlinear behavior of a tearing mode predicted in the two-harmonic approximation does not differ substantially from that predicted in the one-harmonic approximation. On the other hand, RF current drive that is sufficiently localized in the vicinity of the O-points of the mode's magnetic island chain is capable of triggering bifurcations of the O-points (which is impossible in the one-harmonic approximation). However, the current drive is incapable of triggering bifurcations of the island X-points. This finding is significant because Bardóczi and Evans recently observed bifurcations of magnetic island chain O-points in the presence of RF current drive in the DIII-D tokamak but did not observe bifurcations of the X-points. Finally, the changes in the topology of the magnetic island flux-surfaces induced by RF current drive are found to facilitate the stabilization of the tearing mode.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1991

A discourse on sensitivity analysis for discretely-modeled structures

A descriptive review is presented of the most recent methods for performing sensitivity analysis of the structural behavior of discretely-modeled systems. The methods are generally but not exclusively aimed at finite element modeled structures. Topics included are: selections of finite difference step sizes; special consideration for finite difference sensitivity of iteratively-solved response problems; first and second derivatives of static structural response; sensitivity of stresses; nonlinear static response sensitivity; eigenvalue and eigenvector sensitivities for both distinct and repeated eigenvalues; and sensitivity of transient response for both linear and nonlinear structural response.

Adelman, Howard M.↗
NASA NTRS1989

A hybrid-perturbation-Galerkin technique which combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be sued to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗
NASA NTRS1990

A hybrid perturbation-Galerkin technique that combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be used to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗
NASA NTRS1981

Multigrid solvers on parallel computers

Massively parallel computers, as considered in this investigation, are not yet available. However, a large-scale parallel computer cannot usefully be designed before the hypothetical algorithms which will employ it are studied. Most of the studies of parallel partial differential equations (PDE) solvers are based on solution techniques much slower (on sequential machines) than multigrid methods. Multigrid methods are highly parallelizable. Each of their processes can simultaneously be performed at all grid points. The present investigation is concerned with a preliminary exploration of the potential of multigrid, or, more generally, Multi-Level Adaptive Techniques (MLAT) on computers with many processors. Basic processes are considered, taking into account coarse-grid approximation, relaxation, coarse-grid corrections, full multigrid algorithms, nonlinear problems and eigenvalue problems, fine-to-coarse correction, and chains of problems. Details of parallel multigrid processing are also examined.

Brandt, A.↗
NASA NTRS1989

The application of TSIM software to act design and analysis on flexible aircraft

The TSIM software is described. This is a package which uses an interactive FORTRAN-like simulation language for the simulation on nonlinear dynamic systems and offers facilities which include: mixed continuous and discrete time systems, time response calculations, numerical optimization, automatic trimming of nonlinear aircraft systems, and linearization of nonlinear equations for eigenvalues, frequency responses and power spectral response evaluation. Details are given of the application of TSIM to the analysis of aeroelastic systems under the RAE Farborough extension FLEX-SIM. The aerodynamic and structural data for the equations of motion of a flexible aircraft are prepared by a preprocessor program for incorporation in TSIM simulations. Within the simulation, the flexible aircraft model may then be selected interactively for different flight conditions and modal reduction techniques applied. The use of FLEX-SIM is demonstrated by an example of the flutter prediction for a simple aeroelastic model. By utilizing the numerical optimization facility of TSIM, it is possible to undertake identification of required parameters in the TSIM model within the simulation.

Kaynes, Ian W.↗
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 NTRS2013

Buckling Testing and Analysis of Honeycomb Sandwich Panel Arc Segments of a Full-Scale Fairing Barrel: 6-Ply In-Autoclave Facesheets - Part 2

Four honeycomb sandwich panel types, representing 1/16th arc segments of a 10-m diameter barrel section of the Heavy Lift Launch Vehicle (HLLV), were manufactured and tested under the NASA Composites for Exploration program and the NASA Constellation Ares V 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: in-autoclave IM7/977-3 and out-of-autoclave T40-800b/5320-1. Smaller 3- by 5-ft panels were cut from the 1/16th barrel sections. These panels were tested under compressive loading at the NASA Langley Research Center (LaRC). Furthermore, linear eigenvalue and geometrically nonlinear finite element analyses were performed to predict the compressive response of each 3- by 5-ft panel. This manuscript summarizes the experimental and analytical modeling efforts pertaining to the panels composed of 6-ply, IM7/977-3 facesheets (referred to as Panels B-1 and B-2). 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 correctly predicted 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 angle misalignments, and three-dimensional (3-D) effects on the compressive response of the panel.

Pineda, Evan J.↗
NASA NTRS2014

Buckling Testing and Analysis of Honeycomb Sandwich Panel Arc Segments of a Full-Scale Fairing Barrel: Comparison of In- and Out-of-Autoclave Facesheet Configurations

Four honeycomb sandwich panels, representing 1/16th arc segments of a 10-m diameter barrel section of the Heavy Lift Launch Vehicle, were manufactured and tested under the NASA Composites for Exploration and the NASA Constellation Ares V programs. Two configurations were chosen for the panels: 6-ply facesheets with 1.125 in. honeycomb core and 8-ply facesheets with 1.0 in. honeycomb core. Additionally, two separate carbon fiber/epoxy material systems were chosen for the facesheets: in-autoclave IM7/977-3 and out-of-autoclave T40-800b/5320-1. Smaller 3 ft. by 5 ft. panels were cut from the 1/16th barrel sections and tested under compressive loading. Furthermore, linear eigenvalue and geometrically nonlinear finite element analyses were performed to predict the compressive response of each 3 ft. by 5 ft. panel. 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 yielded good qualitative and quantitative predictions. Additionally, it was correctly predicted 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 angle misalignments, and three-dimensional effects on the compressive response of the panel.

epoxy matrix composites↗
NASA NTRS2014

Buckling Testing and Analysis of Honeycomb Sandwich Panel Arc Segments of a Full-Scale Fairing Barrel: 8-ply Out-of-Autoclave Facesheets - Part 3

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 Constellation Ares V 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- by 5-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 analyses were performed to predict the compressive response of the 3- by 5-ft panels. This manuscript summarizes the experimental and analytical modeling efforts pertaining to the panel composed of 8-ply, T40-800B/5320-1 facesheets (referred to as Panel C). 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, two-dimensional (2-D) and three-dimensional (3-D), models yield good qualitative and quantitative predictions. Additionally, it was predicted correctly that the panel would fail in buckling prior to failing in strength.

heavy lift launch vehicles↗
NASA NTRS2019

Buckling Testing and Analysis of Honeycomb Sandwich Panel Arc Segments of a Full-Scale Fairing Barrel Part 4: Six-ply Out-of-Autoclave Facesheets

Four honeycomb sandwich panel types, representing 1/16th arc segments of a 10-m diameter barrel section of the Heavy Lift Launch Vehicle (HLLV), were manufactured and tested under the NASA Composites for Exploration program and the NASA Constellation Ares V 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: in-autoclave IM7/977-3 and out-of-autoclave T40-800b/5320-1. Smaller 3 ft. by 5 ft. panels were cut from the 1/16th barrel sections. These panels were tested under compressive loading at the NASA Langley Research Center (LaRC). Furthermore, linear eigenvalue and geometrically nonlinear finite element analyses were performed to predict the compressive response of each 3 ft. by 5 ft. panel. This manuscript summarizes the experimental and analytical modeling efforts pertaining to the panels composed of 6-ply, T40-800b/5320-1 facesheets (referred to as Panels D). 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 correctly predicted that the panel would fail in buckling prior to failing in strength. Furthermore, three-dimensional (3D) effects on the compressive response of the panel were studied.

David E Myers↗
NASA NTRS1993

An efficient procedure for cascade aeroelastic stability determination using nonlinear, time-marching aerodynamic solvers

A numerical eigenvalue problem formulation and a practical calculation procedure for exact eigenvalues and corresponding eigenvectors are developed and applied to a nonlinear, two-dimensional, time-marching full potential solver for cascade aeroelastic stability analysis. This procedure is based on the Lanczos recursive method and it directly calculates stability information about a nonlinear steady state. It is compared to conventional approaches in the frequency and time domains developed earlier and is found to be 100-10.000 times more computationally efficient. Eigenvalue constellations and the flutter results for flow through a cascade SR5 propfan airfoil are presented.

Mahajan, Aparajit J.↗
NASA NTRS1986

Linear and weakly nonlinear aspects of free shear layer instability, roll-up, subharmonic interaction and wall influence

The growth of the momentum thickness and the modal disturbance energies are examined to study the nature and onset of nonlinearity in a temporally growing free shear layer. A shooting technique is used to find solutions to the linearized eigenvalue problem, and pseudospectral weakly nonlinear simulations of this flow are obtained for comparison. The roll-up of a fundamental disturbance follows linear theory predictions even with a 20 percent disturbance amplitude. A weak nonlinear interaction of the disturbance creates a finite-amplitude mean shear stress which dominates the growth of the layer momentum thickness, and the disturbance growth rate changes until the fundamental disturbance dominates. The fundamental then becomes an energy source for the harmonic, resulting in an increase in the growth rate of the subharmonic over the linear prediction even when the fundamental has no energy to give. Also considered are phase relations and the wall influence.

Cain, A. B.↗