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NASA NTRS1984

Acoustic-radiation stress in solids. I - Theory

The general case of acoustic-radiation stress associated with quasi-compressional and quasi-shear waves propagating in infinite and semiinfinite lossless solids of arbitrary crystalline symmetry is studied. The Boussinesq radiation stress is defined and found to depend directly on an acoustic nonlinearity parameter which characterizes the radiation-induced static strain, a stress-generalized nonlinearity parameter which characterizes the stress nonlinearity, and the energy density of the propagating wave. Application of the Boltzmann-Ehrenfest principle of adiabatic invariance to a self-constrained system described by the nonlinear equations of motion allows the acoustic-radiation-induced static strain to be identified with a self-constrained variation in the time-averaged product of the internal energy density and displacement gradient. The time-averaged product is scaled by the acoustic nonlinearity parameter and represents the first-order nonlinearity in the virial theorem. Finally, the relationship between the Boussinesq and the Cauchy radiation stress is obtained in a closed three-dimensional form.

Cantrell, J. H., Jr.↗

NASA NTRS2002

A Nonlinear Viscoelastic Model for Ceramics at High Temperatures

High-temperature creep behavior of ceramics is characterized by nonlinear time-dependent responses, asymmetric behavior in tension and compression, and nucleation and coalescence of voids leading to creep rupture. Moreover, creep rupture experiments show considerable scatter or randomness in fatigue lives of nominally equal specimens. To capture the nonlinear, asymmetric time-dependent behavior, the standard linear viscoelastic solid model is modified. Nonlinearity and asymmetry are introduced in the volumetric components by using a nonlinear function similar to a hyperbolic sine function but modified to model asymmetry. The nonlinear viscoelastic model is implemented in an ABAQUS user material subroutine. To model the random formation and coalescence of voids, each element is assigned a failure strain sampled from a lognormal distribution. An element is deleted when its volumetric strain exceeds its failure strain. Element deletion has been implemented within ABAQUS. Temporal increases in strains produce a sequential loss of elements (a model for void nucleation and growth), which in turn leads to failure. Nonlinear viscoelastic model parameters are determined from uniaxial tensile and compressive creep experiments on silicon nitride. The model is then used to predict the deformation of four-point bending and ball-on-ring specimens. Simulation is used to predict statistical moments of creep rupture lives. Numerical simulation results compare well with results of experiments of four-point bending specimens. The analytical model is intended to be used to predict the creep rupture lives of ceramic parts in arbitrary stress conditions.

Powers, Lynn M.↗

NASA NTRS2000

Wormhole Formation in RSRM Nozzle Joint Backfill

The RSRM nozzle uses a barrier of RTV rubber upstream of the nozzle O-ring seals. Post flight inspection of the RSRM nozzle continues to reveal occurrence of "wormholes" into the RTV backfill. The term "wormholes", sometimes called "gas paths", indicates a gas flow path not caused by pre-existing voids, but by a little-understood internal failure mode of the material during motor operation. Fundamental understanding of the mechanics of the RSRM nozzle joints during motor operation, nonlinear viscoelastic characterization of the RTV backfill material, identification of the conditions that predispose the RTV to form wormholes, and screening of candidate replacement materials is being pursued by a joint effort between Thiokol Propulsion, NASA, and the Army Propulsion & Structures Directorate at Redstone Arsenal. The performance of the RTV backfill in the joint is controlled by the joint environment. Joint movement, which applies a tension and shear load on the material, coupled with the introduction of high pressure gas in combination create an environment that exceeds the capability of the material to withstand the wormhole effect. Little data exists to evaluate why the material fails under the modeled joint conditions, so an effort to characterize and evaluate the material under these conditions was undertaken. Viscoelastic property data from characterization testing will anchor structural analysis models. Data over a range of temperatures, environmental pressures, and strain rates was used to develop a nonlinear viscoelastic model to predict material performance, develop criteria for replacement materials, and quantify material properties influencing wormhole growth. Three joint simulation analogs were developed to analyze and validate joint thermal barrier (backfill) material performance. Two exploratory tests focus on detection of wormhole failure under specific motor operating conditions. A "validation" test system provides data to "validate" computer models and predictions. Finally, two candidate replacement materials are being screened and "validated" using the developed test systems.

Stevens, J.↗

NASA NTRS1994

Channel to energy calibration results for the BATSE large area detectors

Continuum 16 channel spectra obtained from in flight data are used to identify and correct for nonlinearities in the channel-to-energy conversion algorithm for the BATSE large area detectors. The Crab Nebula spectra obtained by the BATSE earth occultation technique are used to characterize any nonlinearities inherent in the low energy channel bin widths on a detector by detector basis. The bin widths are optimized to remove distortions from observed gamma ray spectra. The recalibrated bin edges are used in an analysis of Crab Pulsar data to verify the improvements in the calibration.

Pendleton, Geoffrey N.↗

NASA NTRS1991

Formulation of the linear model from the nonlinear simulation for the F18 HARV

The F-18 HARV is a modified F-18 Aircraft which is capable of flying in the post-stall regime in order to achieve superagility. The onset of aerodynamic stall, and continued into the post-stall region, is characterized by nonlinearities in the aerodynamic coefficients. These aerodynamic coefficients are not expressed as analytic functions, but rather in the form of tabular data. The nonlinearities in the aerodynamic coefficients yield a nonlinear model of the aircraft's dynamics. Nonlinear system theory has made many advances, but this area is not sufficiently developed to allow its application to this problem, since many of the theorems are existance theorems and that the systems are composed of analytic functions. Thus, the feedback matrices and the state estimators are obtained from linear system theory techniques. It is important, in order to obtain the correct feedback matrices and state estimators, that the linear description of the nonlinear flight dynamics be as accurate as possible. A nonlinear simulation is run under the Advanced Continuous Simulation Language (ACSL). The ACSL simulation uses FORTRAN subroutines to interface to the look-up tables for the aerodynamic data. ACSL has commands to form the linear representation for the system. Other aspects of this investigation are discussed.

Hall, Charles E., Jr.↗

NASA NTRS2007

Nonlinear Aeroelastic Analysis Using a Time-Accurate Navier-Stokes Equations Solver

A method to simulate limit cycle oscillation (LCO) due to control surface freeplay using a modified CFL3D, a time-accurate Navier-Stokes computational fluid dynamics (CFD) analysis code with structural modeling capability, is presented. This approach can be used to analyze aeroelastic response of aircraft with structural behavior characterized by nonlinearity in the force verses displacement curve. A limited validation of the method, using very low Mach number experimental data for a three-degrees-of-freedom (pitch/plunge/flap deflection) airfoil model with flap freeplay, is also presented.

Kuruvila, Geojoe↗

NASA NTRS1990

Tensile stress acoustic constants of unidirectional graphite/epoxy composites

Previously, the stress acoustic constants (SACs) of unidirectional graphite/epoxy composites were measured to determine the nonlinear moduli of this material. These measurements were made under compressive loading in order to obtain the sufficient number of values needed to calculate these moduli. However, because their strength in tension along fiber directions can be several times greater, most composites are used under tensile loading. Thus, it is important to characterize the nonlinear properties of these materials in tension as well. The SACs which are defined as the slope of the normalized change in ultrasonic 'natural' velocity as a function of stress were measured in a unidirectional laminate of T300/5208 graphite/epoxy. Tensile load was applied along the fiber axis with the ultrasonic waves propagating perpendicular to the fiber direction. Changes in velocity were measured using a pulsed phase locked loop ultrasonic interferometer with the nominal frequency of the ultrasonic waves being 2.25 MHz.

Prosser, W. H.↗

NASA NTRS1990

Tensile Stress Acoustic Constants of Unidirectional Graphite/Epoxy Composites

Previously, the stress acoustic constants (SAC's) of unidirectional graphite/epoxy composites were measured to determine the nonlinear moduli of this material. These measurements were made under compressive loading in order to obtain the sufficient number of values needed to calculate these moduli. However, because their strength in tension along fiber directions can be several times greater, most composites are used under tensile loading. Thus, it is important to characterize the nonlinear properties of these materials in tension as well. The SAC's which are defined as the slope of the normalized change in ultrasonic "natural" velocity as a function of stress were measured in a unidirectional laminate of T300/5208 graphite/epoxy. Tensile load was applied along the fiber axis with the ultrasonic waves propagating perpendicular to the fiber direction. Changes in velocity were measured using a pulsed phase locked loop ultrasonic interferometer with the nominal frequency of the ultrasonic waves being 2.25 MHz.

Prosser, W. H.↗

NASA NTRS2011

Assessment of MODIS Thermal Emissive Band On-Orbit Calibration

Sixteen Moderate Resolution Imaging Spectroradiometer thermal emissive bands (TEBs) cover the wavelength from 3.75 to 14.24 m. TEB calibration uses data collected from the detector responses to the onboard blackbody (BB) and space view. The BB was designed to operate either at a constant temperature for detector linear gain calibration or at temperatures varying from ambient ( 270 K) to 315 K for on-orbit characterization of nonlinear coefficients. In this paper, we assess TEB on-orbit calibration performance in two aspects: One is to review the calibration trending on the orbital, daily, and multiyear timescales, and the other is to analyze the on-orbit calibration radiance uncertainty and its impact on the calibration. The calibration trending confirms the detector response dependence on the instrument temperature. The temperature trending and prelaunch characterization provide the basis for determining the calibration radiance source temperature range and uncertainties. An analytical approach was used to assess the impacts of onboard radiance uncertainties. The BB emission uncertainty, resulting from the temperature measurement error and emissivity uncertainty, causes a calibration uncertainty up to 0.3%, a value decreasing with the band wavelength. The BB nonblackness effect is analyzed and found to be insignificant. For the band with the lowest BB emissivity, the nonblackness affects the calibration radiance by less than 0.08%. The cavity emission uncertainty and the scan-mirror emission uncertainty both cause a less than 0.1% calibration uncertainty. The analysis of the nonlinear calibration coefficient uncertainty shows that its effect on the low Earth-view brightness-temperature range varies by band and is generally insignificant.

Chang, Tiejun↗

NASA NTRS1993

On acoustic radiation from a vibrating panel

An experimental and numerical study of the response and radiation from an acoustically loaded aircraft panel is presented. In the experiment, the panel is excited by a normally incident, harmonic wave. Measurements of the panel response and the resulting transmitted pressure are made in both the near- and acoustic far-fields. The numerical computations model the experiment and in particular account for the full coupling between the panel and the surrounding three dimensional acoustic fluid. The results demonstrate that for a sufficiently high excitation level, the panel response becomes nonlinear. The nonlinearity is characterized by the appearance of harmonics and subharmonics in the power spectral densities of the panel motion and consequently in the resulting acoustic radiation. The primary characteristic of the far-field acoustic radiation is the increase in harmonic content relative to the fundamental and subharmonics with increasing distance from the panel. This is shown to be a result of linear and weakly nonlinear wave propagation effects. The numerical results show that the radiated far-field pressure is strongly dependent on the position of the measurement point with respect to the panel center. The experimental and numerical results are in good qualitative agreement.

Frendi, Abdelkader↗

NASA NTRS1981

Aircraft subfloor response to crash loadings

Results are presented of an experimental and analytical study of the dynamic response to crash loadings of five different load-limiting subfloors for general aviation aircraft. These subfloors provide a high-strength structural floor platform to retain the seats and a crushable zone to absorb energy and limit vertical loads. Experimental static load-deflection data and dynamic deceleration response data for the five subfloors indicated that the high-strength floor platform performed well in that structural integrity and residual strength was maintained throughout the loading cycle. The data also indicated that some of the subfloor crush zones were more effective than others in providing nearly constant load for a range of displacement. The analytical data was generated by characterizing the nonlinear crush zones of the subfloor with static load-deflection data and using the DYCAST nonlinear finite element computer program. Comparisons between experimental and analytical data showed good correlation for the subfloors in which the static deformation mode closely approximated the dynamic deformation mode.

Carden, H. D.↗

NASA NTRS1981

Thematic mapper - An overview of spectral band registration

The Thematic Mapper (TM) is a high-resolution radiometer designed for earth resources classification and mapping. The TM employs multispectral scanning in a near polar orbit to sweep a 185-km swath. Data are obtained through a combination of spacecraft motion and the sweeping action of the scan mirror. These data are transmitted either directly to ground stations around the world or through a relay to the central data processing facility at White Sands, NM. Seven spectral passbands are employed, and applications include coastal water mapping, soil vegetation differentiation, biomass surveys, water body delineation, vegetation moisture measurement, plant heat stress management, and hydrothermal mapping. Attention is given to the scan mirror assembly, scan nonlinearities, the characterization and compensation of scan profiles, experimental performance, and a procedure for midscan correction.

Freudenstein, W. H.↗

NASA NTRS1983

Semiconductor photoelectrochemistry

Semiconductor photoelectrochemical reactions are investigated. A model of the charge transport processes in the semiconductor, based on semiconductor device theory, is presented. It incorporates the nonlinear processes characterizing the diffusion and reaction of charge carriers in the semiconductor. The model is used to study conditions limiting useful energy conversion, specifically the saturation of current flow due to high light intensity. Numerical results describing charge distributions in the semiconductor and its effects on the electrolyte are obtained. Experimental results include: an estimate rate at which a semiconductor photoelectrode is capable of converting electromagnetic energy into chemical energy; the effect of cell temperature on the efficiency; a method for determining the point of zero zeta potential for macroscopic semiconductor samples; a technique using platinized titanium dioxide powders and ultraviolet radiation to produce chlorine, bromine, and iodine from solutions containing their respective ions; the photoelectrochemical properties of a class of layered compounds called transition metal thiophosphates; and a technique used to produce high conversion efficiency from laser radiation to chemical energy.

Buoncristiani, A. M.↗

NASA NTRS1989

Nonlinear characteristics of joints as elements of multi-body dynamic systems

As the connecting elements in multi-body structures, joints play a pivotal role in the overall dynamic response of these systems. Obviously, the linear stiffness of the joint strongly influences the system frequencies, but the joints are also likely to be the dominant sources of damping and nonlinearities, especially in aircraft and space structures. The general characteristics of such joints will be discussed. Then the state of the art in nonlinear joint characterization techniques will be surveyed. Finally, the impact that joints have on the overall response of structures will be evaluated.

Crawley, Edward F.↗

NASA NTRS1990

Rapid near-optimal trajectory generation and guidance law development for single-stage-to-orbit airbreathing vehicles

General problems associated with on-board trajectory optimization, propulsion system cycle selection, and with the synthesis of guidance laws were addressed for an ascent to low-earth-orbit of an air-breathing single-stage-to-orbit vehicle. The NASA Generic Hypersonic Aerodynamic Model Example and the Langley Accelerator aerodynamic sets were acquired and implemented. Work related to the development of purely analytic aerodynamic models was also performed at a low level. A generic model of a multi-mode propulsion system was developed that includes turbojet, ramjet, scramjet, and rocket engine cycles. Provisions were made in the dynamic model for a component of thrust normal to the flight path. Computational results, which characterize the nonlinear sensitivity of scramjet performance to changes in vehicle angle of attack, were obtained and incorporated into the engine model. Additional trajectory constraints were introduced: maximum dynamic pressure; maximum aerodynamic heating rate per unit area; angle of attack and lift limits; and limits on acceleration both along and normal to the flight path. The remainder of the effort focused on required modifications to a previously derived algorithm when the model complexity cited above was added. In particular, analytic switching conditions were derived which, under appropriate assumptions, govern optimal transition from one propulsion mode to another for two cases: the case in which engine cycle operations can overlap, and the case in which engine cycle operations are mutually exclusive. The resulting guidance algorithm was implemented in software and exercised extensively. It was found that the approximations associated with the assumed time scale separation employed in this work are reasonable except over the Mach range from roughly 5 to 8. This phenomenon is due to the very large thrust capability of scramjets in this Mach regime when sized to meet the requirement for ascent to orbit. By accounting for flight path angle and flight path angle rate in construction of the flight path over this Mach range, the resulting algorithm provides the means for rapid near-optimal trajectory generation and propulsion cycle selection over the entire Mach range from take-off to orbit.

Calise, A. J.↗

NASA NTRS1990

Elastic/viscoplastic behavior of fiber-reinforced thermoplastic composites

An elastic/viscoplastic constitutive model was used to characterize the nonlinear and rate dependent behavior of a continuous fiber-reinforced thermoplastic composite. This model was incorporated into a finite element program for the analysis of laminated plates and shells. Details on the finite element formulation with the proposed constitutive model were presented. The numerical results were compared with experimental data for uniaxial tension and three-point bending tests of (+ or - 45 deg)3s APC-2 laminates.

Wang, C.↗

NASA NTRS2003

LS-DYNA Implementation of Polymer Matrix Composite Model Under High Strain Rate Impact

A recently developed constitutive model is implemented into LS-DYNA as a user defined material model (UMAT) to characterize the nonlinear strain rate dependent behavior of polymers. By utilizing this model within a micromechanics technique based on a laminate analogy, an algorithm to analyze the strain rate dependent, nonlinear deformation of a fiber reinforced polymer matrix composite is then developed as a UMAT to simulate the response of these composites under high strain rate impact. The models are designed for shell elements in order to ensure computational efficiency. Experimental and numerical stress-strain curves are compared for two representative polymers and a representative polymer matrix composite, with the analytical model predicting the experimental response reasonably well.

Zheng, Xia-Hua↗

NASA NTRS2003

Finite-Element Methods for Real-Time Simulation of Surgery

Two finite-element methods have been developed for mathematical modeling of the time-dependent behaviors of deformable objects and, more specifically, the mechanical responses of soft tissues and organs in contact with surgical tools. These methods may afford the computational efficiency needed to satisfy the requirement to obtain computational results in real time for simulating surgical procedures as described in Simulation System for Training in Laparoscopic Surgery (NPO-21192) on page 31 in this issue of NASA Tech Briefs. Simulation of the behavior of soft tissue in real time is a challenging problem because of the complexity of soft-tissue mechanics. The responses of soft tissues are characterized by nonlinearities and by spatial inhomogeneities and rate and time dependences of material properties. Finite-element methods seem promising for integrating these characteristics of tissues into computational models of organs, but they demand much central-processing-unit (CPU) time and memory, and the demand increases with the number of nodes and degrees of freedom in a given finite-element model. Hence, as finite-element models become more realistic, it becomes more difficult to compute solutions in real time. In both of the present methods, one uses approximate mathematical models trading some accuracy for computational efficiency and thereby increasing the feasibility of attaining real-time up36 NASA Tech Briefs, October 2003 date rates. The first of these methods is based on modal analysis. In this method, one reduces the number of differential equations by selecting only the most significant vibration modes of an object (typically, a suitable number of the lowest-frequency modes) for computing deformations of the object in response to applied forces.

Basdogan, Cagatay↗