Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “MATRICES”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Transfer matrix approach to layered systems with axial symmetry

The stress and displacement distribution in a layered medium is found by means of transfer matrices. The surface loading exhibits axial symmetry, and each layer is of infinite extent in the horizontal direction, of constant depth, and is considered to be linearly elastic, homogeneous, and isotropic. The method developed has the built-in advantage of enforcing interface continuity conditions automatically. Its application to layered composites shows the flexibility with which it predicts the local as well as the global response of the medium.

Bahar, L. Y.↗
NASA NTRS1976

Effect of fiber diameter and matrix alloys on impact-resistant boron/aluminum composites

Efforts to improve the impact resistance of B/Al are reviewed and analyzed. Nonstandard thin-sheet charpy and Izod impact tests and standard full-size Charpy impact tests were conducted on composites containing unidirectional 0.10mm, 0.14mm, and 0.20mm diameter boron fibers in 1100, 2024, 5052, and 6061 Al matrices. Impact failure modes of B/Al are proposed in an attempt to describe the mechanisms involved and to provide insight for maximizing impact resistance. The impact strength of B/Al was significantly increased by proper selection of materials and processing. The use of a ductile matrix and large diameter boron fibers gave the highest impact strengths. This combination resulted in improved energy absorption through matrix shear deformation and multiple fiber breakage.

Mcdanels, D. L.↗
NASA NTRS1975

Study of improved resins for advanced supersonic technology composites. Part 1: Heteroaromatic polymers containing ether groups. Part 2: Curing chemistry of aromatic polymers and composite studies

Fourteen ether-containing, aromatic dianhydrides have been synthesized from N-phenyl-3 or 4-nitrophthalimide and various bisphenols. The process involves nucleophilic displacement of activated nitro groups with bisphenolate ions. Ether-containing dianhydrides were indefinitely stable in the presence of atmospheric moisture. One-step, high temperature solution polymerization of the ether-containing dianhydrides with m-phenylene diamine, 4,4'-oxydianiline and 1, 3-bis(4-aminophenoxy)benzene afforded 42 polyetherimides. The polyetherimides were all soluble in m-cresol except two which were found to be crystalline. The glass transition temperatures of the polyetherimides ranged from 178 to 277 C. Soluble polybenzimidazopyrrolones containing ether groups were also prepared from the same ether-containing dianhydrides and aromatic tetraamines by one-step solution polymerization. Using low molecular weight polyetherimides, various thermoset resin systems were developed and tested as matrices for fiber-reinforced composites. The curing chemistry involving reaction of the phthalonitrile group and the o-diaminophenyl group was found to be generally applicable to crosslinking various aromatic polymers other than polyimides.

Takekoshi, T.↗
NASA NTRS1976

Considerations for the application of finite element beam modeling to vibration analysis of flight vehicle structures

The manner of representing a flight vehicle structure as an assembly of beam, spring, and rigid-body components for vibration analysis is described. The development is couched in terms of a substructures methodology which is based on the finite-element stiffness method. The particular manner of employing beam, spring, and rigid-body components to model such items as wing structures, external stores, pylons supporting engines or external stores, and sprung masses associated with launch vehicle fuel slosh is described by means of several simple qualitative examples. A detailed numerical example consisting of a tilt-rotor VTOL aircraft is included to provide a unified illustration of the procedure for representing a structure as an equivalent system of beams, springs, and rigid bodies, the manner of forming the substructure mass and stiffness matrices, and the mechanics of writing the equations of constraint which enforce deflection compatibility at the junctions of the substructures. Since many structures, or selected components of structures, can be represented in this manner for vibration analysis, the modeling concepts described and their application in the numerical example shown should prove generally useful to the dynamicist.

Kvaternik, R. G.↗
NASA NTRS1977

Ultra high tip speed (670.6 m/sec) fan stage with composite rotor: Aerodynamic and mechanical design

A highly loaded, single-stage compressor having a tip speed of 670.6 m/sec was designed for the purpose of investigating very high tip speeds and high aerodynamic loadings to obtain high stage pressure ratios at acceptable levels of efficiency. The design pressure ratio is 2.8 at an adiabatic efficiency of 84.4%. Corrected design flow is 83.4 kg/sec; corrected design speed is 15,200 rpm; and rotor inlet tip diameter is 0.853 m. The rotor uses multiple-circular-arc airfoils from 0 to 15% span, precompression airfoils assuming single, strong oblique shocks from 21 to 43% span, and precompression airfoils assuming multiple oblique shocks from 52% span to the tip. Because of the high tip speeds, the rotor blades are designed to be fabricated of composite materials. Two composite materials were investigated: Courtaulds HTS graphite fiber in a Kerimid 601 polyimide matrix and the same fibers in a PMR polyimide matrix. In addition to providing a description of the aerodynamic and mechanical design of the 670.0 m/sec fan, discussion is presented of the results of structural tests of blades fabricated with both types of matrices.

Halle, J. E.↗
NASA NTRS1976

A NASTRAN implementation of the doubly asymptotic approximation for underwater shock response

A detailed description is given of how the decoupling approximation known as the doubly asymptotic approximation is implemented with NASTRAN to solve shock problems for submerged structures. The general approach involves locating the nonsymmetric terms (which couple structural and fluid variables) on the right hand side of the equations. This approach results in coefficient matrices of acceptable bandwidth but degrades numerical stability, requiring a smaller time step size than would otherwise be used. It is also shown how the structure's added (virtual) mass matrix, is calculated with NASTRAN.

Everstine, G. C.↗
NASA NTRS1977

A practical Hadamard transform spectrometer for astronomical application

The mathematical properties of Hadamard matrices and their application to spectroscopy are discussed. A comparison is made between Fourier and Hadamard transform encoding in spectrometry. The spectrometer is described and its laboratory performance evaluated. The algorithm and programming of inverse transform are given. A minicomputer is used to recover the spectrum.

Tai, M. H.↗
NASA NTRS1976

Stiffness coupling application to modal synthesis program, users guide

A FORTRAN IV computer program used to perform modal synthesis of structures by stiffness coupling, using the dynamic transformation method is described. The program was named SCAMP (Stiffness Coupling Approach Modal-Synthesis Program). The program begins with the entry of a substructure's physical mode shapes and eigenvalues or a substructure's mass and stiffness matrix. If the mass and stiffness matrices are entered, the eigen problem for the individual substructure is solved. Provisions are included for a maximum of 20 substructures which are coupled by stiffness matrix springs. Each substructure has a number degrees of freedom (DOF), except that for DOF greater than 100; vector sets having maximum row and column size of 100 were generated prior to entering SCAMP. The substructures are then coupled together via coupling springs, and the dynamic transformation is used to reduce the size of the eigen problem.

Kuhar, E. J.↗
NASA NTRS1976

An algorithm for automatic reduction of complex signal flow graphs

A computer algorithm is developed that provides efficient means to compute transmittances directly from a signal flow graph or a block diagram. Signal flow graphs are cast as directed graphs described by adjacency matrices. Nonsearch computation, designed for compilers without symbolic capability, is used to identify all arcs that are members of simple cycles for use with Mason's gain formula. The routine does not require the visual acumen of an interpreter to reduce the topology of the graph, and it is particularly useful for analyzing control systems described for computer analyses by means of interactive graphics.

Young, K. R.↗
NASA NTRS1976

An iterative decoupling solution method for large scale Lyapunov equations

A great deal of attention has been given to the numerical solution of the Lyapunov equation. A useful classification of the variety of solution techniques are the groupings of direct, transformation, and iterative methods. The paper summarizes those methods that are at least partly favorable numerically, giving special attention to two criteria: exploitation of a general sparse system matrix structure and efficiency in resolving the governing linear matrix equation for different matrices. An iterative decoupling solution method is proposed as a promising approach for solving large-scale Lyapunov equation when the system matrix exhibits a general sparse structure. A Fortran computer program that realizes the iterative decoupling algorithm is also discussed.

Athay, T. M.↗
NASA NTRS1977

Computational tests of angular momentum decoupling approximations for pressure broadening cross sections

The utility of several approximate scattering methods for predicting collision induced spectral pressure broadening has been tested by comparison with accurate close coupling results. In particular, broadening of the pure rotational spectra of HD, HCl, CO, and HCN - all perturbed by low energy collisions with He atoms - has been computed using the effective potential formalism of Rabitz, the decoupled l-dominant approximation of DePristo and Alexander, and the j(2)-conserving coupled states method of McGuire and Kouri. For this last method, pressure broadening cross sections have been obtained with the new, correct expression recently derived by Goldflam and Kouri as well as with an earlier formalism based on an incorrect labeling of the scattering matrices. These methods were found to be generally diasppointing for predicting pressure broadening with the exception of the new, correctly formulated j(2)-conserving coupled states method which was found to agree quantitatively (better than 5%) with close coupling values for all cases studied.

Green, S.↗
NASA NTRS1977

A multilevel approach for minimum weight structural design including local and system buckling constraints

A rational multilevel approach for minimum weight structural design of truss and wing structures including local and system buckling constraints is presented. Overall proportioning of the structure is achieved at the system level subject to strength, displacement and system buckling constraints, while the detailed component designs are carried out separately at the component level satisfying local buckling constraints. Total structural weight is taken to be the objective function at the system level while employing the change in the equivalent system stiffness of the component as the component level objective function. Finite element analysis is used to predict static response while system buckling behavior is handled by incorporating a geometric stiffness matrix capability. Buckling load factors and the corresponding mode shapes are obtained by solving the eigenvalue problem associated with the assembled elastic stiffness and geometric stiffness matrices for the structural system. At the component level various local buckling failure modes are guarded against using semi-empirical formulas. Mathematical programming techniques are employed at both the system and component level.

Schmit, L. A., Jr.↗
NASA NTRS1977

A statistical study of Pc 3 magnetic pulsations at synchronous orbit, ATS 6

Results are reported for a study designed to determine statistically the nature and variation of the polarization parameters of Pc3 magnetic pulsations at synchronous orbit. Data obtained with a triaxial flux gate magnetometer on the geosynchronous satellite ATS 6 are subjected to routine power spectral and polarization analyses, and the events examined are identified as peaks in the spectra. Coherence analysis of spectral matrices for these events indicates that Pc3 are very common at synchronous orbit and are primarily a local morning phenomenon with an occurrence peak around 1000 LT; that the pulsations occur at all frequencies in the Pc3 band, with the most common frequency at about 0.35 Hz; that the Pc3 at synchronous orbit are most often linear and generally transverse, but some have significant compressional components; and that based on azimuth angle, there are two distinct classes of Pc3 (azimuthal and radial) with different characteristics. These statistical results are compared with model predictions and ground-based observations.

Arthur, C. W.↗
NASA NTRS1976

A velocity-command controller for a VTOL aircraft

A technique is presented for calculating feedback and feedforward gain matrices that enable a VTOL aircraft to track input commands of forward and vertical velocity while maintaining acceptable responses to pilot inputs. Leverrier's algorithm is used for determining a set of state-variable, feedback gains that force the closed-loop poles and zeros of one pilot-input transfer function to pre-selected positions in the s-plane. This set of feedback gains is then used to calculate the feedback and feedforward gains for the velocity-command controller. The method is computationally attractive since the gains are determined by solving systems of linear, simultaneous equations. The method has been used in a digital simulation of the CH-47 helicopter to control longitudinal dynamics.

Reid, G. F.↗
NASA NTRS1976

Dynamic analysis of a class of mixed lumped-distributed parameter systems via numerical techniques

The modeling via transfer matrices of mixed lumped-distributed parameter systems with feedback control is discussed and novel methods of obtaining information on the controlled system's dynamic response via numerical methods is presented. These methods utilize numerical searches in the complex plane for the roots of the transcendental characteristic equation to determine the closed loop system eigenvalues. The fast Fourier transform (FFT) algorithm is utilized but in the inverse fashion (from frequency domain to time domain). The information obtained is identical to that contained in a model in modal coordinates, and can be used to construct such a model. An interactive computer program to do the required calculation is described, as well as its application to a manipulator arm design problem.

Book, W. J.↗
NASA NTRS1976

Lithification of vitric- and clastic-matrix breccias - SEM petrography

A scanning electron microscope was used in a petrographic investigation of the matrix textures of 41 lunar breccias ranging from very friable soil clods through coherent microbreccias and tough vitric breccias to tough, fine-grained crystalline breccias. It was found that as their coherence increases, the matrices display a gradual increase in the content of glass from 1 or 2% as filaments less than 1 micron across through 5-50% as irregularly shaped patches up to 200 microns across to over 50% as continuous networks.

Phinney, W. C.↗