Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “matrix approximation”

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 181 records · Page 10

Tunneling calculations for GaAs-Al(x)Ga(1-x) as graded band-gap sawtooth superlattices

Quantum mechanical tunneling calculations for sawtooth (linearly graded band-gap) and step-barrier AlGaAs superlattices were performed by means of a transfer matrix method, within the effective mass approximation. The transmission coefficient and tunneling current versus applied voltage were computed for several representative structures. Particular consideration was given to effective mass variations. The tunneling properties of step and sawtooth superlattices show some qualitative similarities. Both structures exhibit resonant tunneling, however, because they deform differently under applied fields, the J-V curves differ.

Forrest, Kathrine A.↗

System Study: Technology Assessment and Prioritizing

The objective of this NASA funded project is to assess and prioritize advanced technologies required to achieve the goals for an "Intelligent Propulsion System" through collaboration among GEAE, NASA, and Georgia Tech. Key GEAE deliverables are parametric response surface equations (RSE's) relating technology features to system benefits (sfc, weight, fuel burn, design range, acoustics, emission, etc...) and listings of Technology Impact Matrix (TIM) with benefits, debits, and approximate readiness status. TIM has been completed for GEAE and NASA proposed technologies. The combined GEAE and NASA TIM input requirement is shown in Table.1. In the course of building the RSE's and TIM, significant parametric technology modeling and RSE accuracy improvements were accomplished. GEAE has also done preliminary ranking of the technologies using Georgia Tech/GEAE USA developed technology evaluation tools. System level impact was performed by combining beneficial technologies with minimum conflict among various system figures of merits to assess their overall benefits to the system. The shortfalls and issues with modeling the proposed technologies are identified, and recommendations for future work are also proposed.

Source record↗

Nanostructures Exploit Hybrid-Polariton Resonances

Nanostructured devices that exploit the hybrid-polariton resonances arising from coupling among photons, phonons, and plasmons are subjects of research directed toward the development of infrared-spectroscopic sensors for measuring extremely small quantities of molecules of interest. The spectroscopic techniques in question are surface enhanced Raman scattering (SERS) and surface enhanced infrared absorption (SEIRA). An important intermediate goal of this research is to increase the sensitivity achievable by these techniques. The basic idea of the approach being followed in this research is to engineer nanostructured devices and thereby engineer their hybrid-polariton resonances to concentrate infrared radiation incident upon their surfaces in such a manner as to increase the absorption of the radiation for SEIRA and measure the frequency shifts of surface vibrational modes. The underlying hybrid-polariton-resonance concept is best described by reference to experimental devices that have been built and tested to demonstrate the concept. The nanostructure of each such device includes a matrix of silicon carbide particles of approximately 1 micron in diameter that are supported on a potassium bromide (KBr) or poly(tetrafluoroethylene) [PTFE] window. These grains are sputter-coated with gold grains of 40-nm size (see figure). From the perspective of classical electrodynamics, in this nanostructure, that includes a particulate or otherwise rough surface, the electric-field portion of an incident electromagnetic field becomes concentrated on the particles when optical resonance conditions are met. Going beyond the perspective of classical electrodynamics, it can be seen that when the resonance frequencies of surface phonons and surface plasmons overlap, the coupling of the resonances gives rise to an enhanced radiation-absorption or -scattering mechanism. The sizes, shapes, and aggregation of the particles determine the frequencies of the resonances. Hence, the task of designing a nanostructure to exhibit the desired radiation-absorption properties translates, in large part, to selecting particle sizes and shapes to obtain the desired enhanced coupling of energy from photons to plasmons and phonons. To broaden the spectral region(s) of enhanced absorption, one would select a distribution of particle sizes and shapes.

Anderson, Mark↗

Computational Modeling of Micro-Crack Induced Attenuation in CFRP Composites

A computational study is performed to determine the contribution to ultrasound attenuation in carbon fiber reinforced polymer composite laminates of linear elastic scattering by matrix micro-cracking. Multiple scattering approximations are benchmarked against exact computational approaches. Results support linear scattering as the source of observed increased attenuation in the presence of micro-cracking.

Roberts, R. A.↗

Interface considerations in Al2O3/NiAl composite

The fiber-matrix interface requirements in an Al2O3/NiAl composite were examined from theoretical considerations. Several factors that influence the interface bonding requirements were analyzed. These include: (1) residual stresses due to fiber-matrix coefficient of thermal expansion (CTE) mismatch; (2) matrix cracking stress at room temperature; (3) fracture toughness at room temperature; (4) load transfer from the matrix to the fiber and ultimate tensile strength at the use temperature; and (5) creep resistance at high temperature. A relatively weak fiber-matrix bond, with an interfacial shear strength of approximately 15-20 MPa, might be sufficient for attaining the desired mechanical properties in the fiber direction at the use temperature. A weak fiber-matrix bond is also beneficial for increasing the fracture toughness of the composite at room temperature. In contrast, a strong fiber-matrix bond is required to withstand some of the residual stresses resulting from the fiber-matrix CTE mismatch, which are not likely to be reduced significantly by interface coatings. A relatively strong bond is also beneficial in increasing the matrix cracking stress at room temperature. Various interface coating options to accommodate the conflicting bonding requirements were reviewed. One viable coating option is to incorporate a thick, ductile interface layer well bonded to both the fiber and the matrix.

Misra, Ajay K.↗

Modulation of Bone Marrow Primary Cell Osteoblastogenesis and Cell Senescence by Mechanical Stimulation

Cell and animal studies conducted onboard the International Space Station and formerly the Shuttle flights have provided groundbreaking data illuminating the deleterious biological response of bone to mechanical unloading. Specifically CDKN1A/p-21 a cell senescence protein, was found to be upregulated in osteoprecursor cells of the femur during 15-day spaceflight, leading to the working hypothesis that CDKN1A/p-21 plays a role in inhibition of bone formation via mechanical regulation. To evaluate this hypothesis, utilizing a p-21 knockout mouse-line and relevant wildtype control, we cultured femoral bone marrow primary cells under unloaded (static) and cyclically stretched loading through a 30 day osteoblastogenesis protocol. Morphologic evaluation of the cultures demonstrated that mechanical stretching aligned the cells and increased the presence of defined focal adhesion expressing talin, integrin αvβ3, and PTK2 protein tyrosine kinase 2, also known as focal adhesion kinase (FAK) in both mouse strains. In corroboration with previous investigations of cell survival signals relation to FAK, our study found that with greater concentration of focal adhesions via stretch stimulation the live cell percentage was significantly higher than the unloaded controls (p-21 knockout line: +49.70%, p*=0.009, wildtype control: +18.14%, p*=.01). Also evaluated was the mineralization and ECM secretion capability of the differentiating cells. Von Kossa staining has shown that in the p-21 knockout cells unloaded cells produce more matrix that the stretch stimulated, however the matrix is unorganized presenting in sporadic nodules covering approximately 30% of the culture area at day 14 (n=6 wells) while the stretch stimulated cultures have less mineralization content the surface area containing mineralized matrix is greater (~68% at day 14). Q-PCR evaluation of the p-21 knockout cells revealed that canonical (β-catenin cascade) and non-canonical wnt11 and downstream planar cell polarity (wnt/PCP) pathway molecule RAC1 are prevalently upregulated with mechanical stimulation. Immunofluorescence for β-catenin and RAC1 showed co-localization at the nuclear membrane of the p-21 knockout cells but not the wildtype (n=1) suggesting that molecular communication via the canonical and wnt/PCP pathway are initiated by mechanical loading and experience regulation along the signaling cascade by CDKN1A/p-21. Future investigations will further elucidate this relationship and provide causal data demonstrating mechanical loading’s modulatory effect on p-21 expression change.

Juran, Cassandra M.↗

Overview of Krylov subspace methods with applications to control problems

An overview of projection methods based on Krylov subspaces are given with emphasis on their application to solving matrix equations that arise in control problems. The main idea of Krylov subspace methods is to generate a basis of the Krylov subspace Span and seek an approximate solution the the original problem from this subspace. Thus, the original matrix problem of size N is approximated by one of dimension m typically much smaller than N. Krylov subspace methods have been very successful in solving linear systems and eigenvalue problems and are now just becoming popular for solving nonlinear equations. It is shown how they can be used to solve partial pole placement problems, Sylvester's equation, and Lyapunov's equation.

Saad, Youcef↗

Evaluation of Several Approximate Methods for Calculating the Symmetrical Bending-Moment Response of Flexible Airplanes to Isotropic Atmospheric Turbulence

Several approximate procedures for calculating the bending-moment response of flexible airplanes to continuous isotropic turbulence are presented and evaluated. The modal methods (the mode-displacement and force-summation methods) and a matrix method (segmented-wing method) are considered. These approximate procedures are applied to a simplified airplane for which an exact solution to the equation of motion can be obtained. The simplified airplane consists of a uniform beam with a concentrated fuselage mass at the center. Airplane motions are limited to vertical rigid-body translation and symmetrical wing bending deflections. Output power spectra of wing bending moments based on the exact transfer-function solutions are used as a basis for the evaluation of the approximate methods. It is shown that the force-summation and the matrix methods give satisfactory accuracy and that the mode-displacement method gives unsatisfactory accuracy.

Bennett, Floyd V.↗

Design of multivariable feedback control systems via spectral assignment using reduced-order models and reduced-order observers

The feasibility of using reduced order models and reduced order observers with eigenvalue/eigenvector assignment procedures is investigated. A review of spectral assignment synthesis procedures is presented. Then, a reduced order model which retains essential system characteristics is formulated. A constant state feedback matrix which assigns desired closed loop eigenvalues and approximates specified closed loop eigenvectors is calculated for the reduced order model. It is shown that the eigenvalue and eigenvector assignments made in the reduced order system are retained when the feedback matrix is implemented about the full order system. In addition, those modes and associated eigenvectors which are not included in the reduced order model remain unchanged in the closed loop full order system. The full state feedback design is then implemented by using a reduced order observer. It is shown that the eigenvalue and eigenvector assignments of the closed loop full order system rmain unchanged when a reduced order observer is used. The design procedure is illustrated by an actual design problem.

Mielke, R. R.↗

Design of multivariable feedback control systems via spectral assignment using reduced-order models and reduced-order observers

The feasibility of using reduced order models and reduced order observers with eigenvalue/eigenvector assignment procedures is investigated. A review of spectral assignment synthesis procedures is presented. Then, a reduced order model which retains essential system characteristics is formulated. A constant state feedback matrix which assigns desired closed loop eigenvalues and approximates specified closed loop eigenvectors is calculated for the reduced order model. It is shown that the eigenvalue and eigenvector assignments made in the reduced order system are retained when the feedback matrix is implemented about the full order system. In addition, those modes and associated eigenvectors which are not included in the reduced order model remain unchanged in the closed loop full order system. The fulll state feedback design is then implemented by using a reduced order observer. It is shown that the eigenvalue and eigenvector assignments of the closed loop full order system remain unchanged when a reduced order observer is used. The design procedure is illustrated by an actual design problem.

Mielke, R. R.↗

Implicit application of polynomial filters in a k-step Arnoldi method

The Arnoldi process is a well known technique for approximating a few eigenvalues and corresponding eigenvectors of a general square matrix. Numerical difficulties such as loss of orthogonality and assessment of the numerical quality of the approximations as well as a potential for unbounded growth in storage have limited the applicability of the method. These issues are addressed by fixing the number of steps in the Arnoldi process at a prescribed value k and then treating the residual vector as a function of the initial Arnoldi vector. This starting vector is then updated through an iterative scheme that is designed to force convergence of the residual to zero. The iterative scheme is shown to be a truncation of the standard implicitly shifted QR-iteration for dense problems and it avoids the need to explicitly restart the Arnoldi sequence. The main emphasis of this paper is on the derivation and analysis of this scheme. However, there are obvious ways to exploit parallelism through the matrix-vector operations that comprise the majority of the work in the algorithm. Preliminary computational results are given for a few problems on some parallel and vector computers.

Sorensen, D. C.↗

Response of a Rotating Propeller to Aerodynamic Excitation

The flexural vibration of a rotating propeller blade with clamped shank is analyzed with the object of presenting, in matrix form, equations for the elastic bending moments in forced vibration resulting from aerodynamic forces applied at a fixed multiple of rotational speed. Matrix equations are also derived which define the critical speeds end mode shapes for any excitation order and the relation between critical speed and blade angle. Reference is given to standard works on the numerical solution of matrix equations of the forms derived. The use of a segmented blade as an approximation to a continuous blade provides a simple means for obtaining the matrix solution from the integral equation of equilibrium, so that, in the numerical application of the method presented, the several matrix arrays of the basic physical characteristics of the propeller blade are of simple form, end their simplicity is preserved until, with the solution in sight, numerical manipulations well-known in matrix algebra yield the desired critical speeds and mode shapes frame which the vibration at any operating condition may be synthesized. A close correspondence between the familiar Stodola method and the matrix method is pointed out, indicating that any features of novelty are characteristic not of the analytical procedure but only of the abbreviation, condensation, and efficient organization of the numerical procedure made possible by the use of classical matrix theory.

Arnoldi, Walter E.↗

Digital restoration of multichannel images

The Wiener solution of a multichannel restoration scheme is presented. Using matrix diagonalization and block-Toeplitz to block-circulant approximation, the inversion of the multichannel, linear space-invariant imaging system becomes feasible by utilizing a fast iterative matrix inversion procedure. The restoration uses both the within-channel (spatial) and between-channel (spectral) correlation; hence, the restored result is a better estimate than that produced by independent channel restoration. Simulations are also presented.

Galatsanos, Nikolas P.↗

Fe and O EELS Studies of Ion Irradiated Murchison CM2 Carbonaceous Chondrite Matrix

Introduction: The physical and chemical response of hydrated carbonaceous chondrite materials to space weathering processes is poorly understood. Improving this understanding is a key part of establishing how regoliths on primitive carbonaceous asteroids respond to space weathering processes, knowledge that supports future sample return missions (Hayabusa 2 and OSIRISREx) that are targeting objects of this type. We previously reported on He+ irradiation of Murchison matrix and showed that the irradiation resulted in amorphization of the matrix phyllosilicates, loss of OH, and surface vesiculation. Here, we report electron energy-loss spectroscopy (EELS) measurements of the irradiated material with emphasis on the Fe and O speciation. Sample and Methods: A polished thin section of the Murchison CM2 carbonaceous chondrite was irradiated with 4 kilovolts He(+) (normal incidence) to a total dose of 1 x 10(exp 18) He(+) per square centimeter. We extracted thin sections from both irradiated and unirradiated regions in matrix using focused ion beam (FIB) techniques with electron beam deposition for the protective carbon strap to minimize surface damage artifacts from the FIB milling. The FIB sections were analyzed using a JEOL 2500SE scanning and transmission electron microscope (STEM) equipped with a Gatan Tridiem imaging filter. EELS spectra were collected from 50 nanometer diameter regions with an energy resolution of 0.7 electronvolts FWHM at the zero loss. EELS spectra were collected at low electron doses to minimize possible artifacts from electron-beam irradiation damage. Results and Discussion: Fe L (sub 2,3) EELS spectra from matrix phyllosilicates in CM chondrites show mixed Fe(2+)/Fe(3+) oxidation states with Fe(3+)/Sigma Fe approximately 0.5. Fe L(sub 2,3) spectra from the irradiated/ amorphized matrix phyllosilicates show higher Fe(2+)/Fe(3+) ratios compared to spectra obtained from pristine material at depths beyond the implantation/amorphization layer. We also obtained O Ka spectra from phyllosilicates in both regions of the sample. The O Ka spectra show a pre-edge feature at approximately 530.5 electronvolts that is related to O 2p states hybridized with Fe 3d states. The intensity ratio of the O Ka pre-edge peak relative to the main part of the O Ka edge (that results from transitions of O 1s to 2p states) is lower in the irradiated layer compared to the pristine material and may reflect the loss of O (as OH) as was observed by IR spectroscopy. Conclusions: In addition to amorphization and OH loss, EELS spectra of He(+) irradiated matrix phyllosilicates in Murchison show that some of the Fe(3+) is reduced to Fe(2+). Spectral deconvolution is underway to extract quantitative ratios from the EELS spectra.

Keller, L. P.↗

Sapphire reinforced alumina matrix composites

Unidirectionally reinforced A1203 matrix composites have been fabricated by hot pressing. Approximately 30 volume % of either coated or uncoated sapphire fiber was used as reinforcement. Unstabilized ZrO2 was applied as the fiber coating. Composite mechanical behavior was analyzed both after fabrication and after additional heat treatment. The results of composite tensile tests were correlated with fiber-matrix interfacial shear strengths determined from fiber push-out tests. Substantially higher strength and greater fiber pull-out were observed for the coated fiber composites for all processing conditions studied. The coated fiber composites retained up to 95% and 87% of their as-fabricated strength when heat treated at 14000C for 8 or 24 hours, respectively. Electron microscopy analysis of the fracture surfaces revealed extensive fiber pull-out both before and after heat treatment.

Jaskowiak, Martha H.↗

Shrouded CMC Rotor Blades for High Pressure Turbine Applications

The density of Ceramic Matrix Compos-ite(CMC) materials is approximately 1/3 the density of metals currently used for High Pressure Turbine(HPT) blades. A lower density, and consequently lower centrifugal stresses, increases the feasibility of shrouding HPT blades. Shrouding HPT blades improves aerodynamic eciency, especially for low aspect ratio turbine blades. This paper explores aerodynamic and structural issues associated with shrouding HPT rotor blades. Detailed Navier-Stokes analysis of a rotor blade showed that shrouding improved blade row aerodynamic eciency by 1.3%, when the clearance was 2% of the blade span. Recessed casings were used. Without a shroud the depth of the recess equaled the clearance. With a shroud the recess depth increased by the shroud thickness, which included a knife seal. There was good agreement between the predicted stage eciency for the unshrouded blades and the experimentally measured efficiency. Structural analysis showed a strong interaction between stresses in the shroud and peak stresses at the hub of the blade. A thin shroud of uniform thickness only moderately increased maximum blade stress, but there were very high stresses in the shroud itself. Increasing shroud thickness reduced stresses in the shroud, but increased blade stresses near the hub. A single knife seal added to the thin shroud noticeably decreased maximum shroud stress, without increasing maximum blade stress. Maximum stresses due to pressure loads and combined pressure and centrifugal loads were nearly the same as the maximum stresses for individual pressure or cen-trifugal loads. Stresses due to a 100K temperature

Ceramic Matrix Composite↗