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NASA NTRS1996

The Development of Computational Techniques for the Nonlinear Analysis of Composite Structures at High Temperature

The objective of this research project was to develop robust and efficient computational tools for deformation and life analysis techniques. This included: development of viscoplastic continuum models, associated numerical integration techniques, suitable micromechanics models/methods, and coupled deformation and damage algorithms. The work was involved with models/methods applicable to composite structures on both microscale and macroscale levels. The microscale analysis utilized Aboudi's generalized method of cells (GMS) micromechanical model as well as finite element models of similar composite architectures, i.e., square and hexagonal fiber pack models.

Keith, Theo G., Jr.↗

NASA NTRS1996

Vibrating Systems with Singular Mass-Inertia Matrices

Vibrating systems with singular mass-inertia matrices arise in recent continuum models of Smart Structures (beams with PZT strips) in assessing the damping attainable with rate feedback. While they do not quite yield 'distributed' controls, we show that they can provide a fixed nonzero lower bound for the damping coefficient at all mode frequencies. The mathematical machinery for modelling the motion involves the theory of Semigroups of Operators. We consider a Timoshenko model for torsion only, a 'smart string,' where the damping coefficient turns out to be a constant at all frequencies. We also observe that the damping increases initially with the feedback gain but decreases to zero eventually as the gain increases without limit.

Balakrishnan, A. V.↗

NASA NTRS1996

Dynamics and Control of Articulated Anisotropic Timoshenko Beams

The paper illustrates the use of continuum models in control design for stabilizing flexible structures. A 6-DOF anisotropic Timoshenko beam with discrete nodes where lumped masses or actuators are located provides a sufficiently rich model to be of interest for mathematical theory as well as practical application. We develop concepts and tools to help answer engineering questions without having to resort to ad hoc heuristic ("physical") arguments or faith. In this sense the paper is more mathematically oriented than engineering papers and vice versa at the same time. For instance we make precise time-domain solutions using the theory of semigroups of operators rather than formal "inverse Laplace transforms." We show that the modes arise as eigenvalues of the generator of the semigroup, which are then related to the eigenvalues of the stiffness operator. With the feedback control, the modes are no longer orthogonal and the question naturally arises as to whether there is still a modal expansion. Here we prove that the eigenfunctions yield a biorthogonal Riesz basis and indicate the corresponding expansion. We prove mathematically that the number of eigenvalues is nonfinite, based on the theory of zeros of entire functions. We make precise the notion of asymptotic modes and indicate how to calculate them. Although limited by space, we do consider the root locus problem and show for instance that the damping at first increases as the control gain increases but starts to decrease at a critical value, and goes to zero as the gain increases without bound. The undamped oscillatory modes remain oscillatory and the rigid-body modes go over into deadbeat modes. The Timoshenko model dynamics are translated into a canonical wave equation in a Hilbert space. The solution is shown to require the use of an "energy" norm which is no more than the total energy: potential plus kinetic. We show that, under an appropriate extension of the notion of controllability, rate feedback with a collocated sensor can stabilize the structure in the sense that all modes are damped and the energy decays to zero. An example, non-numeric, is worked out in some detail illustrating the concepts and theory developed.

Balakrishnan, A. V.↗

NASA NTRS2000

Efficient Analysis of Complex Structures

Last various accomplishments achieved during this project are : (1) A Survey of Neural Network (NN) applications using MATLAB NN Toolbox on structural engineering especially on equivalent continuum models (Appendix A). (2) Application of NN and GAs to simulate and synthesize substructures: 1-D and 2-D beam problems (Appendix B). (3) Development of an equivalent plate-model analysis method (EPA) for static and vibration analysis of general trapezoidal built-up wing structures composed of skins, spars and ribs. Calculation of all sorts of test cases and comparison with measurements or FEA results. (Appendix C). (4) Basic work on using second order sensitivities on simulating wing modal response, discussion of sensitivity evaluation approaches, and some results (Appendix D). (5) Establishing a general methodology of simulating the modal responses by direct application of NN and by sensitivity techniques, in a design space composed of a number of design points. Comparison is made through examples using these two methods (Appendix E). (6) Establishing a general methodology of efficient analysis of complex wing structures by indirect application of NN: the NN-aided Equivalent Plate Analysis. Training of the Neural Networks for this purpose in several cases of design spaces, which can be applicable for actual design of complex wings (Appendix F).

Kapania, Rakesh K.↗

NASA NTRS2000

On the Dynamics of Two Dimensional Array Beam Scanning Via Coupled Oscillators

This presentation will begin with a description of the previous published work contributing to the results reported here. The previously developed one dimensional continuum model will be generalized to two dimensions and a Green's function for the resulting differential equation will be obtained as an eigenfunction expansion. This will be used to obtain dynamic solutions relevant to the steering of the radiated beam. Finally, some remarks concerning limitations on the interoscillator phase difference will be provided.

Pogorzelski, R. J.↗

NASA NTRS2002

Optimization of Designs for Nanotube-based Scanning Probes

Optimization of designs for nanotube-based scanning probes, which may be used for high-resolution characterization of nanostructured materials, is examined. Continuum models to analyze the nanotube deformations are proposed to help guide selection of the optimum probe. The limitations on the use of these models that must be accounted for before applying to any design problem are presented. These limitations stem from the underlying assumptions and the expected range of nanotube loading, end conditions, and geometry. Once the limitations are accounted for, the key model parameters along with the appropriate classification of nanotube structures may serve as a basis for the design optimization of nanotube-based probe tips.

Harik, V. M.↗

NASA NTRS2003

X-ray QPOs from the Ultra-luminous X-ray Source in M82: Evidence Against Beaming

We report the discovery with the European Photon Imaging Camera (EPIC) CCD cameras onboard XMM-Newton of a 54 mHz quasiperiodic oscillation (QPO) in the greater than 2 keV X-ray flux from the ultra-luminous X-ray source (ULX) X41.4+60 in the starburst galaxy M82. This is the first detection of a QPO in the X-ray flux from an extra-Galactic ULX, and confirms that the source is a compact object. The QPO is detected in the combined PN and MOS data at the approx. 6sigma level, and separately at lower significances in both the PN and MOS instruments. It had a centroid frequency of 54.3 +/- 0.9 mHz, a coherence Q is identical with nu(sub 0)/Delta nu(sub fwhm) is approx. 5, and an amplitude (rms) in the 2 - 10 keV band of 8.5%. Below about 0.2 Hz the power spectrum can be described by a power-law with index approx. 1, and integrated amplitude (rms) of 13.5%. The X-ray spectrum requires a curving continuum, with a disk-blackbody (diskbb) at T = 3.1 keV providing an acceptable, but not unique, fit. A broad Fe line centered at 6.55 keV is required in all fits, but the equivalent width (EW) of the line is sensitive to the choice of continuum model. There is no evidence of a reflection component. The implied bolometric luminosity is approx. 4 - 5 x 10(exp 40) ergs/s. Data from several archival Rossi X-ray Timing Explorer (RXTE) pointings at M82 also show evidence for QPOs in the 50 - 100 mHz frequency range. Several Galactic black hole candidates (BHCs), including GRS 1915+105, GRO J1655-40, and XTE 1550-564, show QPOs in the same frequency range as the 50 - 100 mHz QPOs in X41.4+60, which at first glance suggests a possible connection with such objects. However, strong, narrow QPOs provide solid evidence for disk emission, and thus present enormous theoretical difficulties for models which rely on either geometrically or relativistically beamed emission to account for the high X-ray luminosities. We discuss the implications of our findings for models of the ULX sources.

Strohmayer, Tod E.↗

NASA NTRS2003

Simulating the Effect of Space Vehicle Environments on Directional Solidification of a Binary Alloy

Space microgravity missions are designed to provide a microgravity environment for scientific experiments, but these missions cannot provide a perfect environment, due to vibrations caused by crew activity, on-board experiments, support systems (pumps, fans, etc.), periodic orbital maneuvers, and water dumps. Therefore, it is necessary to predict the impact of these vibrations on space experiments, prior to performing them. Simulations were conducted to study the effect of the vibrations on the directional solidification of a dendritic alloy. Finite element ca!cu!attie?ls were dme with a simd2titcr based on a continuum model of dendritic solidification, using the Fractional Step Method (FSM). The FSM splits the solution of the momentum equation into two steps: the viscous intermediate step, which does not enforce continuity; and the inviscid projection step, which calculates the pressure and enforces continuity. The FSM provides significant computational benefits for predicting flows in a directionally solidified alloy, compared to other methods presently employed, because of the efficiency gains in the uncoupled solution of velocity and pressure. finite differences, arises when the interdendritic liquid reaches the eutectic temperature and concentration. When a node reaches eutectic temperature, it is assumed that the solidification of the eutectic liquid continues at constant temperature until all the eutectic is solidified. With this approach, solidification is not achieved continuously across an element; rather, the element is not considered solidified until the eutectic isotherm overtakes the top nodes. For microgravity simulations, where the convection is driven by shrinkage, it introduces large variations in the fluid velocity. When the eutectic isotherm reaches a node, all the eutectic must be solidified in a short period, causing an abrupt increase in velocity. To overcome this difficulty, we employed a scheme to numerically predict a more accurate value for the rate of change of fraction of liquid as the liquid in an element solidifies. The new method enables us to contrast results of simulations in which the alloy is subjected to no gravity or a steady-state acceleration versus simulations when the alloy is subjected to vibration disturbances; therefore, the effect of vibration disturbances can be assessed more accurately. To assess the impact of these vibration-perturbations, transient accelerometer data from a space shuttle mission are used as inputs for the simulation model. These on-orbit acceleration data were obtained from the Microgravity Science Division at Glenn Research Center (GRC- MSD) and are applied to the buoyancy term of the momentum equation in a simulation of a Pb-5.8 wt. % Sb alloy that solidifies in a thermal gradient of 4000 K/m and a translation velocity of 3 p d s . Figure 2 shows the vertical velocity of a node that begins in the all-liquid region and subsequently solidifies; the vibrations are applied at 5000 seconds in this simulation. An important difficulty, common to all solidification models based on finite elements or 2 The magnitudes of the velocity oscillations that are vibration-induced are very small and acceptable. The biggest concern is whether the concentration of the liquid near the dendrite tips is distorted because of the vibration-induced perturbations. Results for this case show no concentration oscillations present in the all-liquid region.

Westra, D. G.↗

NASA NTRS2004

Predicting the Influence of Nano-Scale Material Structure on the In-Plane Buckling of Orthotropic Plates

A multi-scale analysis of the structural stability of a carbon nanotube-polymer composite material is developed. The influence of intrinsic molecular structure, such as nanotube length, volume fraction, orientation and chemical functionalization, is investigated by assessing the relative change in critical, in-plane buckling loads. The analysis method relies on elastic properties predicted using the hierarchical, constitutive equations developed from the equivalent-continuum modeling technique applied to the buckling analysis of an orthotropic plate. The results indicate that for the specific composite materials considered in this study, a composite with randomly orientated carbon nanotubes consistently provides the highest values of critical buckling load and that for low volume fraction composites, the non-functionalized nanotube material provides an increase in critical buckling stability with respect to the functionalized system.

Gates, Thomas S.↗

NASA NTRS2003

The Effect of Chemical Functionalization on Mechanical Properties of Nanotube/Polymer Composites

The effects of the chemical functionalization of a carbon nanotube embedded in a nanotube/polyethylene composite on the bulk elastic properties are presented. Constitutive equations are established for both functionalized and non-functionalized nanotube composites systems by using an equivalent-continuum modeling technique. The elastic properties of both composites systems are predicted for various nanotube lengths, volume fractions, and orientations. The results indicate that for the specific composite material considered in this study, most of the elastic stiffness constants of the functionalized composite are either less than or equal to those of the non-functionalized composite.

Odegard, G. M.↗

NASA NTRS1993

Viewpoint 9--molecular structure of aqueous interfaces

In this review we summarize recent progress in our understanding of the structure of aqueous interfaces emerging from molecular level computer simulations. It is emphasized that the presence of the interface induces specific structural effects which, in turn, influence a wide variety of phenomena occurring near the phase boundaries. At the liquid-vapor interface, the most probable orientations of a water molecule is such that its dipole moment lies parallel to the interface, one O-H bond points toward the vapor and the other O-H bond is directed toward the liquid. The orientational distributions are broad and slightly asymmetric, resulting in an excess dipole moment pointing toward the liquid. These structural preferences persist at interfaces between water and nonpolar liquids, indicating that the interactions between the two liquids in contact are weak. It was found that liquid-liquid interfaces are locally sharp but broadened by capillary waves. One consequence of anisotropic orientations of interfacial water molecules is asymmetric interactions, with respect to the sign of the charge, of ions with the water surface. It was found that even very close to the surface ions retain their hydration shells. New features of aqueous interfaces have been revealed in studies of water-membrane and water-monolayer systems. In particular, water molecules are strongly oriented by the polar head groups of the amphiphilic phase, and they penetrate the hydrophilic head-group region, but not the hydrophobic core. At infinite dilution near interfaces, amphiphilic molecules exhibit behavior different from that in the gas phase or in bulk water. This result sheds new light on the nature of hydrophobic effect in the interfacial regions. The presence of interfaces was also shown to affect both equilibrium and dynamic components of rates of chemical reactions. Applications of continuum models to interfacial problems have been, so far, unsuccessful. This, again, underscores the importance of molecular-level information about interfaces.

Review, Tutorial↗

NASA NTRS1998

The Dynamics of Coupled Oscillator Phase Control

Arrays of coupled oscillators have been proposed as means of realizing high power rf sources via coherent spatial power combining. In such applications, a uniform phase distribution over the aperture is usually desired. However, it has been shown that by detuning some of the oscillators away from the oscillation frequency of the ensemble of oscillators, one may achieve other useful aperture phase distributions. Of particular interest among those achievable are linear phase distributions because these result in steering of the output rf beam away from the broadside direction. The theory describing the behavior of such arrays of coupled oscillators is quite complicated since the phenomena involved are inherently nonlinear. However, a simplified theory has been developed which facilitates intuitive understanding. This simplified theory is based on a "continuum model" in which the aperture phase is represented by a continuous function of the aperture coordinates. A challenging aspect of the development of this theory is the derivation of appropriate boundary conditions at the edges or ends of the array.

Pogorzelski, R. J.↗

NASA NTRS2005

Buckling of Carbon Nanotube-Reinforced Polymer Laminated Composite Materials Subjected to Axial Compression and Shear Loadings

A multi-scale method to predict the stiffness and stability properties of carbon nanotube-reinforced laminates has been developed. This method is used in the prediction of the buckling behavior of laminated carbon nanotube-polyethylene composites formed by stacking layers of carbon nanotube-reinforced polymer with the nanotube alignment axes of each layer oriented in different directions. Linking of intrinsic, nanoscale-material definitions to finite scale-structural properties is achieved via a hierarchical approach in which the elastic properties of the reinforced layers are predicted by an equivalent continuum modeling technique. Solutions for infinitely long symmetrically laminated nanotube-reinforced laminates with simply-supported or clamped edges subjected to axial compression and shear loadings are presented. The study focuses on the influence of nanotube volume fraction, length, orientation, and functionalization on finite-scale laminate response. Results indicate that for the selected laminate configurations considered in this study, angle-ply laminates composed of aligned, non-functionalized carbon nanotube-reinforced lamina exhibit the greatest buckling resistance with 1% nanotube volume fraction of 450 nm uniformly-distributed carbon nanotubes. In addition, hybrid laminates were considered by varying either the volume fraction or nanotube length through-the-thickness of a quasi-isotropic laminate. The ratio of buckling load-to-nanotube weight percent for the hybrid laminates considered indicate the potential for increasing the buckling efficiency of nanotube-reinforced laminates by optimizing nanotube size and proportion with respect to laminate configuration.

Riddick, J. C.↗

NASA NTRS2008

Two Suzaku Observations of the Cyclotron Line Source 4U 1907+09

Suzaku observed the accreting pulsar 4U 1907+09 in May 2006 and in April 2007. We present and compare the light curves and broad band spectra of both observations. The approximately 10 mCrab source is strongly variable and shows a rich phenomenology. While the 2006 observation is dominated by typical, non-absorption-related dipping behavior, the 2007 observation shows equally typical flaring behavior in both the XIS and PIN light curves. Above 2 keV the average combined XIS and PIN broad band spectrum can be well described by standard pulsar continuum models, modified by the fundamental cyclotron resonant scattering feature at approximately 19 keV. We model the cyclotron line using the standard phenomenological Gaussian model as well as a new physically motivated Green's functions based approach (Schoenherr et al., 2007, A&A 472, 353). Below 2 keV the XIS spectra allow for the first detection of a soft excess in this source, in addition to providing the best determination of the parameters of the weak iron line at 6.4 keV (EW approximately 70 eV) to date.

Pottschmidt, Katja↗

NASA NTRS2014

Broad-Band Spectroscopy of Hercules X-1 with Suzaku

Hercules X-1 was observed with Suzaku in the main-on state from 2005 to 2010. The 0.4- 100 keV wide-band spectra obtained in four observations showed a broad hump around 4-9 keV in addition to narrow Fe lines at 6.4 and 6.7 keV. The hump was seen in all the four observations regardless of the selection of the continuum models. Thus it is considered a stable and intrinsic spectral feature in Her X-1. The broad hump lacked a sharp structure like an absorption edge. Thus it was represented by two different spectral models: an ionized partial covering or an additional broad line at 6.5 keV. The former required a persistently existing ionized absorber, whose origin was unclear. In the latter case, the Gaussian fitting of the 6.5-keV line needs a large width of sigma = 1.0-1.5 keV and a large equivalent width of 400-900 eV. If the broad line originates from Fe fluorescence of accreting matter, its large width may be explained by the Doppler broadening in the accretion flow. However, the large equivalent width may be inconsistent with a simple accretion geometry.

X-rays: stars↗

NASA NTRS2016

Searching for Decaying Dark Matter in Deep XMM-Newton Observation of the Draco Dwarf Spheroidal

We present results of a search for the 3.5 keV emission line in our recent very long (approx. 1.4 Ms) XMM-Newton observation of the Draco dwarf spheroidal galaxy. The astrophysical X-ray emission from such dark matter-dominated galaxies is faint, thus they provide a test for the dark matter origin of the 3.5 keV line previously detected in other massive, but X-ray bright objects, such as galaxies and galaxy clusters. We do not detect a statistically significant emission line from Draco; this constrains the lifetime of a decaying dark matter particle to tau >(7-9) × 10(exp 27) s at 95% CL (combining all three XMM-Newton cameras; the interval corresponds to the uncertainty of the dark matter column density in the direction of Draco). The PN camera, which has the highest sensitivity of the three, does show a positive spectral residual (above the carefully modeled continuum) at E = 3.54 +/- 0.06 keV with a 2.3(sigma) significance. The two MOS cameras show less-significant or no positive deviations, consistently within 1(sigma) with PN. Our Draco limit on tau is consistent with previous detections in the stacked galaxy clusters, M31 and the Galactic Centre within their 1 − 2(sigma) uncertainties, but is inconsistent with the high signal from the core of the Perseus cluster (which has itself been inconsistent with the rest of the detections). We conclude that this Draco observation does not exclude the dark matter interpretation of the 3.5 keV line in those objects.

dark matter↗

NASA NTRS2016

Disk-Wind Connection During the Heartbeats of GRS 1915+105

Disk and wind signatures are seen in the soft state of Galactic black holes, while the jet is seen in the hard state. Here we study the disk-wind connection in the Rho class of variability in GRS 1915+105 using a joint NuSTAR-Chandra observation. The source shows 50 s limit cycle oscillations. By including new information provided by the reflection spectrum and using phase-resolved spectroscopy, we find that the change in the inner disk inferred from the blackbody emission is not matched by reflection measurements. The latter is almost constant, independent of the continuum model. The two radii are comparable only if the disk temperature color correction factor changes, an effect that could be due to the changing opacity of the disk caused by changes in metal abundances. The disk inclination is similar to that inferred from the jet axis, and oscillates by approx.10 deg. The simultaneous Chandra data show the presence of two wind components with velocities between 500 and 5000 km s(exp. −1), and possibly two more with velocities reaching 20,000 km s(exp. −1) (approx. 0.06 c). The column densities are approx. 5 × 10(exp. 22) cm(exp. −2). An upper limit to the wind response time of 2 s is measured, implying a launch radius of less than 6 × 10(exp. 10) cm. The changes in wind velocity and absorbed flux require the geometry of the wind to change during the oscillations, constraining the wind to be launched from a distance of 290-1300 r (sub g) from the black hole. Both data sets support fundamental model predictions in which a bulge originates in the inner disk and moves outward as the instability progresses.

accretion↗

NASA NTRS2018

3D Mapping of the Neutral X-Ray Absorption in the Local Interstellar Medium: The Gaia and XMM-Newton Synergy

We present a three-dimensional map of the hydrogen density distribution in the Galactic interstellar medium. The hydrogen-equivalent column densities were obtained from the Exploring the X-ray Transient and variable Sky project (EXTRAS) which provides equivalent NH values from X-ray spectral fits of observations within the XMM-Newton Data Release. EXTRAS include multiple fits for each source, allowing an accurate determination of the equivalent column densities, which depends on the continuum modelling of the spectra. A cross-correlation between the EXTRAS catalogue and the first Gaia Data Release was performed in order to obtain accurate parallax and distance measurements. We use a Bayesian method explained in Rezaei Kh. et al. (2017) in order to predict the most probable distribution of the density at any arbitrary point, even for lines of sight along which there are no initial observation. The resulting map shows small-scale density structures which could not have been modelled by using analytic density profiles. In this paper, we present a proof of concept of the kind of science possible with the synergy of these catalogues. However, given the systematic uncertainties connected to the source identification and to the dependence of NH on the spectral model, the present maps should be considered qualitatively at this point.

Gatuzz, Efrain↗