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NASA NTRS1988

Non-isothermal elastoviscoplastic analysis of planar curved beams

The development of a general mathematical model and solution methodologies, to examine the behavior of thin structural elements such as beams, rings, and arches, subjected to large nonisothermal elastoviscoplastic deformations is presented. Thus, geometric as well as material type nonlinearities of higher order are present in the analysis. For this purpose a complete true abinito rate theory of kinematics and kinetics for thin bodies, without any restriction on the magnitude of the transformation is presented. A previously formulated elasto-thermo-viscoplastic material constitutive law is employed in the analysis. The methodology is demonstrated through three different straight and curved beams problems.

Simitses, G. J.↗

NASA NTRS1974

On the shock-on-shock interaction problem

The unsteady, inviscid flowfield that results when a supersonic vehicle strikes a planar oblique shock wave, though difficult to simulate experimentally, is quite easy to model and compute numerically. The complicated flowfield, which contains multiple shock wave interactions, is determined using a second-order, shock-capturing, finite-difference approach which solves the time-dependent Euler equations under a self-similar transformation. A series of numerical results for a simple two-dimensional wedge is presented which describes the entire disturbed region, including the wave structure, and shows good agreement with the available two- and three-dimensional experimental data.-

Kutler, P.↗

NASA NTRS2006

Spade: An H Chondrite Impact-melt Breccia that Experienced Post-shock Annealing

The low modal abundances of relict chondrules (1.8 Vol%) and of coarse (i.e. >= 2200 micron-size) isolated mafic silicate grains (1.8 Vol%) in Spade relative to mean H6 chondrites (11.4 and 9.8 vol%, respectively) show Spade to be a rock that has experienced a significant degree of melting. Various petrographic features (e.g., chromite-plagioclase assemblages, chromite veinlets, silicate darkening) indicate that melting was caused by shock. Plagioclase was melted during the shock event and flowed so that it partially to completely surrounded nearby mafic silicate grains. During crystallization, plagioclase developed igneous zoning. Low-Ca pyroxene that crystallized from the melt (or equilibrated with the melt at high temperatures) acquired relatively high amounts of CaO. Metallic Fe-Ni cooled rapidly below the Fe-Ni solws and transformed into martensite. Subsequent reheating of the rock caused transformation of martensite into abundant duplex plessite. Ambiguities exist in the shock stage assignment of Spade. The extensive silicate darkening, the occurrence of chromite-plagioclase assemblages, and the impact-melted characteristics of Spade are consistent with shock stage S6. Low shock (stage S2) is indicated by the undulose extinction and lack of planar fractures in olivine. This suggests that Spade reached a maximum prior shock level equivalent to stage S6 and then experienced post-shock annealing (probably to stage Sl). These events were followed by a less intense impact that produced the undulose extinction in the olivine, characteristic of shock stage S2. Annealing could have occurred if Spade were emplaced near impact melts beneath the crater floor or deposited in close proximity to hot debris within an ejecta blanket. Spade firmly establishes the case for post-shock annealing. This may have been a common process on ordinary chondrites (OC) asteroids.

Rubin, Alan E.↗

NASA NTRS2021

Safe Tracking Control of an Uncertain Euler-Lagrange System with Full-State Constraints using Barrier Functions

This paper presents a novel, safe tracking control design method that learns the parameters of an uncertain Euler-Lagrange (EL) system online using adaptive learning laws. A barrier function (BF) is first used to transform the full-state constrained EL-dynamics into an equivalent unconstrained dynamics. An adaptive tracking controller is then developed along with the parameter update law in the transformed state space such that the states remain bounded for all time within a prescribed bound. A stability analysis is developed that considers the EL-dynamics’ uncertainty, yielding a semi-globally uniformly ultimately bounded (SGUUB) tracking error and the parameter estimation error. The controller design is validated in simulations using a two-link planar manipulator. The results show the proposed method’s ability to track the reference trajectory while remaining inside each of the predefined state bounds.

Robots↗

NASA NTRS1980

A plane-polar approach for far-field construction from near-field measurements

The planar configuration with a probe scanning a polar geometry is discussed with reference to its usefulness in the determination of a far field from near-field measurements. The accuracy of the method is verified numerically, using the concept of probe compensation as a vector deconvolution. Advantages of the Jacobi-Bessel series over the fast Fourier transforms for the plane-polar geometry are demonstrated. Finally, the far-field pattern of the Viking high gain antenna is constructed from the plane-polar near-field measured data and compared with the previously measured far-field pattern.

Rahmat-Samii, Y.↗

NASA NTRS1987

Characteristics of inhomogeneous coupled cylindrical striplines

Using conformal transformation, closed-form expressions for the even and odd mode impedances of inhomogeneous coupled cylindrical striplines are presented. It is shown that the analysis can be extended for the calculation of characteristics of coupled cylindrical microstrip lines. The analysis can also be extended to reveal the effects of warping due to environmental changes on an otherwise planar structure.

Reddy, C. J.↗

NASA NTRS1994

Experimental measurement and calculation of losses in planar radial magnetic bearings

The loss mechanisms associated with magnetic bearings have yet to be adequately characterized or modeled analytically and thus pose a problem for the designer of magnetic bearings. This problem is particularly important for aerospace applications where low power consumption of components is critical. Also, losses are expected to be large for high speed operation. The iron losses in magnetic bearings can be divided into eddy current losses and hysteresis losses. While theoretical models for these losses exist for transformer and electric motor applications, they have not been verified for magnetic bearings. This paper presents the results from a low speed experimental test rig and compares them to calculated values from existing theory. Experimental data was taken over a range of 90 to 2,800 rpm for several bias currents and two different pole configurations. With certain assumptions agreement between measured and calculated power losses was within 16 percent for a number of test configurations.

Kasarda, M. E. F.↗

NASA NTRS1978

Sonic-box method employing local Mach number for oscillating wings with thickness

A computer program was developed to account approximately for the effects of finite wing thickness in the transonic potential flow over an oscillating wing of finite span. The program is based on the original sonic-box program for planar wing which was previously extended to include the effects of the swept trailing edge and the thickness of the wing. Account for the nonuniform flow caused by finite thickness is made by application of the local linearization concept. The thickness effect, expressed in terms of the local Mach number, is included in the basic solution to replace the coordinate transformation method used in the earlier work. Calculations were made for a delta wing and a rectangular wing performing plunge and pitch oscillations, and the results were compared with those obtained from other methods. An input quide and a complete listing of the computer code are presented.

Ruo, S. Y.↗

NASA NTRS1992

A planar quasi-optical SIS receiver for array applications

A planar, quasi-optical SIS receiver operating at 230 GHz is described. The receiver consists of a 2 x 5 array of half wave dipole antennas with ten niobium-aluminum oxide-niobium SIS junctions on a quartz dielectric-filled parabola. The 1.4 GHz intermediate frequency is coupled from the mixer via coplanar strip transmission lines and 4:1 balun transformers. The receiver is operated at 4.2 K in a liquid helium immersion cryostat. We report accurate measurements of the performance of single receiver elements. A mixer noise temperature of 89 K DSB, receiver noise temperature of 156 K DSB, and conversion loss of 3 dB into a matched load have been obtained.

Stimson, Philip A.↗

NASA NTRS1993

A planar quasi-optical SIS receiver

Stimson, Philip A.↗

NASA NTRS2021

Empirical Constraints on Progressive Shock Metamorphism of Magnetite from the Siljan Impact Structure, Sweden

Little is known about the microstructural behavior of magnetite during hypervelocity impact events, even though it is a widespread accessory mineral and important magnetic carrier in terrestrial and extraterrestrial rocks. We report systematic electron backscatter diffraction crystallographic analysis of shock features in magnetite, from a transect across the 52-km diameter ~380 Ma Siljan impact structure in Sweden. Magnetite grains in granitoid samples contain brittle fracturing, crystal-plasticity, and lamellar twins. Deformation twins along {111} with shear direction of <112> are consistent with spinel-law twins. Inferred bulk shock pressures for investigated samples, as constrained by planar deformation features (PDFs) in quartz and shock twins in zircon, range from 0–20 GPa; onset of shock-induced twinning in magnetite is observed at >5 GPa. These results highlight the utility of magnetite to record shock deformation in rocks that experience shock pressures >5 GPa, which may be useful in quartz-poor samples. Despite significant hydrothermal alteration, and variable transformation of host magnetite to hematite, shock effects are preserved, demonstrating that magnetite is a reliable mineral for preserving shock deformation over geologic time.

magnetite↗

NASA NTRS2014

Collisional Effects on Magnesium-rich Minerals found in Comets and Asteroids

While generally touted to be the least-altered bodies remaining from the age of the solar system's formation, comets and asteroids have undergone evolutionary processing throughout the 4.5-billion-year lifetime of the solar system. They have suffered the effects of collisions by impactors ranging in size from micrometeoroids to other comets and asteroids. As such, we must ask ourselves: can we detect these evolutionary effects remotely through telescopic observations? With this in mind, a suite of experiments were conducted, impacting magnesium-rich minerals as analogues to those that have been detected in the spectra of both asteroid surfaces and in the dust of cometary comae, including forsterite (Mg2SiO4, olivine), orthoenstatite (Mg2SiO3, pyroxene), diopside (MgCaSi2O6, monoclinic pyroxene), and magnesite (MgCO3, carbonate). These minerals were impacted at velocities ranging from 2.0 km/s to 2.8 km/s using the vertical gun in the Experimental Impact Laboratory (EIL) at NASA Johnson Space Center. These speeds mimic typical velocities of impacts occurring in the Kuiper belt [1]. Two classes of projectile were used: spherical alumina ceramic, whose density mimics that of rock, and cylinders made from the same material that they impacted (e.g., forsterite impactors for forsterite targets, etc.). The peak shock pressure varies significantly, depending on the target and impactor materials and the velocity; thus, shock effects differed in targets impacted at the same velocity but with compositionally different projectiles. The results indicate both: (a) how varying the impactor-density might change the outcome from a scientific viewpoint, as well as (b) possible contamination effects of the ceramic projectile in the resultant spectra of the target minerals from an experimental perspective. Temperature effects were also investigated by impacting samples at both 25 deg. and -25 deg. to: (a) probe whether the varying temperatures experienced by small bodies plays a role in the resultant spectra, and (b) constrain necessary experimental parameters. Analysis of Fourier Transform Infrared (FTIR) spectra obtained from the experimentally shocked materials shows clear indications of spectral shifts in wavelength, as well as a change in relative peak strengths of the spectral signatures at one wavelength compared with another, in all minerals except magnesite. Samples of the forsterite and orthoenstatite that displayed the spectral changes were examined with a transmission electron microscope, which revealed evidence of planar dislocations. The density of the dislocations in the experimentally shocked minerals mimicked the dislocation densities measured in both forsterite and enstatite grains recovered from Comet Wild 2 by the Stardust mission [2, 3, 4]. Further discussion on analyses of peak shock pressure and temperature-dependent effects can be found in Jensen et al., this meeting

Lederer, S.↗

NASA NTRS1981

Optimal trajectories in atmospheric flight

Aspects of optimization theory and switching theory are discussed, taking into account the necessary conditions for extrema, a solution subject to constraints, the calculus of variations, the Pontryagin maximum principle, the canonical transformation, Contensou's domain of maneuverability, optimal switching, a junction with singular arc, and linearized singular control. Equations of motion are considered along with aerodynamic and propulsive forces, the general properties of optimal trajectories, flight in a horizontal plane, optimal coasting flight, supersonic cruise, the supersonic turn, supersonic maneuvers in a vertical plane, energy state approximation, a modified Chapman's formulation for optimal reentry trajectories, optimal planar reentry trajectories, and an optimal glide of reentry vehicles. Orbital aerodynamic maneuvers are examined, giving attention to aerodynamic capture, a change in the apogee, a change in the eccentricity, a change in the perigee, an orbital maneuver, an aerodynamic maneuver, and a combined maneuver.

Vinh, N. X.↗

NASA NTRS1980

A three-dimensional turbulent compressible subsonic duct flow analysis for use with constructed coordinate systems

An approximate analysis, applicable to nonorthogonal coordinate systems having a curved centerline and planar transverse coordinate surfaces normal to the centerline, is presented for computation of three-dimensional subsonic flow in straight and curved diffusers. The formulation is intended to facilitate the use of constructed coordinates in circumstances where it is difficult to maintain smooth behavior in higher derivatives; the use of local Cartesian variables and fluxes leads to governing equations which require only first derivatives of the coordinate transformation. The analysis is applied to a particular family of duct and diffuser geometries having curved centerlines and superelliptic cross sections. Qualitative agreement with experimental measurements is observed with regard to streamwise vortices and distortion of the primary flow.

Levy, R.↗

NASA NTRS1983

The extreme nearfield of an acoustic diffraction grating

An expression for the transmitted sound field near (within a fraction of a wavelength) an array of slits is derived under the assumption that the normal component of the particle velocity is the same, in the slits, as if no grating were present and zero everywhere else in the plane of the grating. The expression is in the form of an inverse Fourier transform and can be evaluated quickly using a standard fast-Fourier-transform (FFT) algorithm. Using this technique, the sound pressure on the axis of symmetry normal to the grating was evaluated for a plane-wave incident at various angles with respect to the normal to the grating, and the results were found to provide an excellent qualitative (and to a significant degree quantitative) description of some experimental measurements. Extensions of the method to oscillating pistons of arbitrary (but planar) configuration in a rigid baffle are indicated.

Ochs, R. L., Jr.↗

NASA NTRS2004

Transient Two-Dimensional Analysis of Side Load in Liquid Rocket Engine Nozzles

Two-dimensional planar and axisymmetric numerical investigations on the nozzle start-up side load physics were performed. The objective of this study is to develop a computational methodology to identify nozzle side load physics using simplified two-dimensional geometries, in order to come up with a computational strategy to eventually predict the three-dimensional side loads. The computational methodology is based on a multidimensional, finite-volume, viscous, chemically reacting, unstructured-grid, and pressure-based computational fluid dynamics formulation, and a transient inlet condition based on an engine system modeling. The side load physics captured in the low aspect-ratio, two-dimensional planar nozzle include the Coanda effect, afterburning wave, and the associated lip free-shock oscillation. Results of parametric studies indicate that equivalence ratio, combustion and ramp rate affect the side load physics. The side load physics inferred in the high aspect-ratio, axisymmetric nozzle study include the afterburning wave; transition from free-shock to restricted-shock separation, reverting back to free-shock separation, and transforming to restricted-shock separation again; and lip restricted-shock oscillation. The Mach disk loci and wall pressure history studies reconfirm that combustion and the associated thermodynamic properties affect the formation and duration of the asymmetric flow.

Wang, Ten-See↗

NASA NTRS1990

Real-time optical multiple object recognition and tracking system and method

System for optically recognizing and tracking a plurality of objects within a field of vision. Laser (46) produces a coherent beam (48). Beam splitter (24) splits the beam into object (26) and reference (28) beams. Beam expanders (50) and collimators (52) transform the beams (26, 28) into coherent collimated light beams (26', 28'). A two-dimensional SLM (54), disposed in the object beam (26'), modulates the object beam with optical information as a function of signals from a first camera (16) which develops X and Y signals reflecting the contents of its field of vision. A hololens (38), positioned in the object beam (26') subsequent to the modulator (54), focuses the object beam at a plurality of focal points (42). A planar transparency-forming film (32), disposed with the focal points on an exposable surface, forms a multiple position interference filter (62) upon exposure of the surface and development processing of the film (32). A reflector (53) directing the reference beam (28') onto the film (32), exposes the surface, with images focused by the hololens (38), to form interference patterns on the surface. There is apparatus (16', 64) for sensing and indicating light passage through respective ones of the positions of the filter (62), whereby recognition of objects corresponding to respective ones of the positions of the filter (62) is affected. For tracking, apparatus (64) focuses light passing through the filter (62) onto a matrix of CCD's in a second camera (16') to form a two-dimensional display of the recognized objects.

Chao, Tien-Hsin↗

NASA NTRS1983

A series expansion of the acoustic power radiated from planar sources

A series expansion in ascending powers of the wavenumber k is derived for the acoustic power delivered by baffled or unbaffled planar sources. This series provides a relatively simple means of derving expressions for the power radiated by a baffled source with a known velocity distribution and can be used for unbaffled plates when the velocity field outside the plate is also known. The terms in the series are calculated from the moments of this velocity distribution in the plane containing the source. If these moments are written as derivaties in wavenumber space, it is shown that a MacLaurin expansion of the Fourier transformed velocity provides an easy technique for computing the first few terms of the acoustic power. Examples are provided for baffled, rectangular plates with various boundary conditions. The arbirarily shaped plate with free boundaries is particularly interesting. It is proven that the volume flow across it surface must be zero and as a result corner and edge mode radiation cannot exist for this kind of source.

Willams, E. G.↗