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NASA NTRS1987

Electron cyclotron harmonic wave acceleration

A nonlinear analysis of particle acceleration in a finite bandwidth, obliquely propagating electromagnetic cyclotron wave is presented. It has been suggested by Sprangle and Vlahos in 1983 that the narrow bandwidth cyclotron radiation emitted by the unstable electron distribution inside a flaring solar loop can accelerate electrons outside the loop by the interaction of a monochromatic wave propagating along the ambient magnetic field with the ambient electrons. It is shown here that electrons gyrating and streaming along a uniform, static magnetic field can be accelerated by interacting with the fundamental or second harmonic of a monochromatic, obliquely propagating cyclotron wave. It is also shown that the acceleration is virtually unchanged when a wave with finite bandwidth is considered. This acceleration mechanism can explain the observed high-energy electrons in type III bursts.

Karimabadi, H.↗

NASA NTRS1988

The role of unsteady aerodynamics in aeroacoustics

The role of acoustics and unsteady aerodynamics research in understanding the fundamental physics of time-dependent fluid phenomena is reviewed. The key issues are illustrated by considering the sound radiation of turbulent jets and the aeroacoustics of rotating bodies such as helicopter rotors. The importance of computational methods as a link between aerodynamics and acoustics is also discussed. It is noted that where acoustic analogy techniques are sufficiently accurate, unsteady aerodynamics can be used for acoustic prediction. In supersonic problems where acoustics and aerodynamics are coupled, an integrated nonlinear analysis can provide an accurate problem solution.

Pao, S. Paul↗

NASA NTRS1989

The 4D-TECS integration for NASA TSRV airplane

The integration of the Total Energy Control System (TECS) concept with 4D navigation is described. This integration was made to increase the operational capacity of modern aircraft and encourage incorporation of this increased capability with the evolving National Airspace System (NAS). Described herein is: 4D smoothing, the basic concepts of TECS, the spoiler integration concept, an algorithm for nulling out time error, speed and altitude profile modes, manual spoiler implementation, 4D logic, and the results of linear and nonlinear analysis.

Kaminer, I.↗

NASA NTRS1988

Computational simulation of high temperature metal matrix composites cyclic behavior

A procedure was developed and is described which can be used to computationally simulate the cyclic behavior of high temperature metal matrix composites (HTMMC) and its degradation effects on the structural response. This procedure consists of HTMMC mechanics coupled with a multifactor interaction constituent material relationship and with an incremental iterative nonlinear analysis. The procedure is implemented in a computer code that can be used to computationally simulate the thermomechanical behavior of HTMMC starting from the fabrication process and proceeding through thermomechanical cycling, accounting for the interface/interphase region. Results show that combined thermal/mechanical cycling, the interphase, and in situ matrix properties have significant effects on the structural integrity of HTMMC.

Chamis, C. C.↗

NASA NTRS1989

Assessment of SPAR elements and formulation of some basic 2-D and 3-D elements for use with testbed generic element processor

The initial Computational Structural Mechanics (CSM) Testbed was based on Level 13 of the SPAR finite element computer program. Until recently, the element library of the Testbed has been limited to those elements in Level 13 of SPAR. The development of a generic element processor has enabled element researchers to develop, implement and assess element formulations with relative ease. An assessment of new elements as well as the existing SPAR Level 13 elements has revealed some definite shortcomings with the SPAR Level 13 2-D and 3-D elements. The SPAR S81 solid element does not pass the patch test problem proposed by MacNeal-Harder. These deficiencies are identified here. The 2-D elements, however, seem to perform well taking into account the limitations imposed by the theory used to formulate them, (i.e., thin plates only). Common deficiencies of the 2-D and 3-D elements in SPAR have to do with their adaptability to the nonlinear analysis utilities developed by Lockheed Palo Alto Research Lab. Also, the EFIL format of the SPAR element data does not conform to the standard format of the Testbed.

Aminpour, Mohammad A.↗

NASA NTRS1987

Nonlinear dynamics, fractals, cardiac physiology and sudden death

The authors propose a diametrically opposite viewpoint to the generally accepted tendency of equating healthy function with order and disease with chaos. With regard to the question of sudden cardiac death and chaos, it is suggested that certain features of dynamical chaos related to fractal structure and fractal dynamics may be important organizing principles in normal physiology and that certain pathologies, including ventricular fibrillation, represent a class of 'pathological periodicities'. Some laboratory work bearing on the relation of nonlinear analysis to physiological and pathophysiological data is briefly reviewed, with tentative theories and models described in reference to the mechanism of ventricular fibrillation.

Goldberger, Ary L.↗

NASA NTRS1989

Analytic theory for the selection of Saffman-Taylor fingers in the presence of thin film effects

An analytic theory is presented for the width selection of Saffman-Taylor fingers in the presence of thin film effect. In the limit of small capillary number Ca and small gap to width ratio epsilon, such that epsilon much less than Ca much less than 1, it is found that fingers with relative width lambda less than 1/2 are possible such that lambda squared (1-lambda)/(1-2 lambda) = k epsilon/Ca(sup 3/2), where the positive constant k depends on the branch of solution and equals 2.776 for the first branch. A fully nonlinear analysis is necessary in this problem even to obtain the correct scaling law. It is also shown how in principle, the selection rule for arbitrary Ca can be obtained.

Tanveer, S.↗

NASA NTRS1990

Computation of the unsteady facilitated transport of oxygen in hemoglobin

The transport of a reacting permeant diffusing through a thin membrane is extended to more realistic dissociation models. A new nonlinear analysis of the reaction-diffusion equations, using implicit finite-difference methods and direct block solvers, is used to study the limits of linearized and equilibrium theories. Computed curves of molecular oxygen permeating through hemoglobin solution are used to illustrate higher-order reaction models, the effect of concentration boundary layers at the membrane interfaces, and the transient buildup of oxygen flux.

Davis, Sanford↗

NASA NTRS1990

On the instability of Goertler vortices to nonlinear travelling waves

Recent theoretical work by Hall and Seddougui (1989) has shown that strongly nonlinear, high wavenumber Goertler vortices developing within a boundary layer flow are susceptible to a secondary instability which takes the form of travelling waves confined to a thin region centered at the outer edge of the vortex. The case is considered in which the secondary mode could be satisfactorily described by a linear stability theory and herein the objective is to extend this investigation of Hall and Seddougui (1989) into the nonlinear regime. It was found that at this stage not only does the secondary mode become nonlinear but it also interacts with itself so as to modify the governing equations for the primary Goertler vortex. In this case then, the vortex and the travelling wave drive each other and, indeed, the whole flow structure is described by an infinite set of coupled, nonlinear differential equations. A Stuart-Watson type of weakly nonlinear analysis of these equations is undertaken and concluded, in particular, that on this basis there exist stable flow configurations in which the travelling mode is of finite amplitude. Implications of the findings for practical situations are discussed and it is shown that the theoretical conclusions drawn here are in good qualitative agreement with available experimental observations.

Seddougui, Sharon O.↗

NASA NTRS1990

Modification of the background flow by roll vortices

Use of observed wind profiles, such as those obtained from ascent or descent aircraft soundings, for the identification of the expected roll modes is hindered by the fact that these modes are able to modify the wind profiles. When such modified wind profiles are utilized to estimate the critical values of the dynamic and thermodynamic forcing rates, large errors in the preferred orientation angles and aspect ratios of the rolls may result. Nonlinear analysis of a 14 coefficient spectral model of roll circulations shows that the primary modification of the background wind is the addition of a linear component. When the linear profile having the correct amount of shear is subtracted from the observed cross-roll winds, then the pre-roll wind profile can be estimated. A preliminary test of this hypothesis is given for a case in which cloud streets were observed during FIRE.

Shirer, Hampton N.↗

NASA NTRS1990

Evaluation of alternatives for best-fit paraboloid for deformed antenna surfaces

Paraboloid antenna surfaces suffer performance degradation due to structural deformation. A first step in the prediction of the performance degradation is to find the best-fit paraboloid to the deformed surface. Examined here is the question of whether rigid body translations perpendicular to the axis of the paraboloid should be included in the search for the best-fit paraboloid. It is shown that if these translations are included the problem is ill-conditioned, and small structural deformation can result in large translations of the best-fit paraboloid with respect to the original surface. The magnitude of these translations then requires nonlinear analysis for finding the best-fit paraboloid. On the other hand, if these translations are excluded, or if they are limited in magnitude, the errors with respect to the restricted not-so-best-fit paraboloid can be much greater than the errors with respect to the true best-fit paraboloid.

Baruch, Menahem↗

NASA NTRS1990

Theory of finite disturbances in a centrifugal compression system with a vaneless radial diffuser

A previous small perturbation analysis of circumferential waves in circumferential compression systems, assuming inviscid flow, is shown to be consistent with observations that narrow diffusers are more stable than wide ones, when boundary layer displacement effect is included. The Moore-Greitzer analysis for finite strength transients containing both surge and rotating stall in axial machines is adapted for a centrifugal compression system. Under certain assumptions, and except for a new second order swirl, the diffuser velocity field, including resonant singularities, can be carried over from the previous inviscid linear analysis. Nonlinear transient equations are derived and applied in a simple example to show that throttling through a resonant value of flow coefficient must occur in a sudden surge-like drop, accompanied by a transient rotating wave. This inner solution is superseded by an outer surge response on a longer time scale. Surge may occur purely as result of circumferential wave resonance. Numerical results are shown for various parametric choices relating to throttle schedule and the characteristic slope. A number of circumferential modes considered simultaneously is briefly discussed.

Moore, F. K.↗

NASA NTRS1990

Analyzing Thought-related Electroencephalographic Data Using Nonlinear Techniques

A unique method is presented for collecting, studying and interpreting thought-related electroencephalogram (EEG) data. The use of a chaos based nonlinear analysis technique is shown to be promising in providing insight into relating conscious thought to specific EEG data. A discussion of the practical limitations of this technique is also included.

Skidmore, Trent↗

NASA NTRS1990

Computational simulation of high-temperature metal matrix composites cyclic behavior

A procedure was developed and is described that can be used to computationally simulate the cyclic behavior of high-temperature metal matrix composites (HTMMC) and its degradation effects on the structural response. This procedure consists of HTMMC mechanics coupled with a multifactor-interaction constituent material relationship and with an incremental iterative nonlinear analysis. The procedure is implemented in a computer code that can be used to computationally simulate the thermomechanical behavior of HTMMC starting from the fabrication process and proceeding through thermomechanical cycling, accounting for the interface/interphase region. Results show that combined thermal/mechanical cycling, the interphase, and in situ matrix properties have significant effects on the structural integrity of HTMMC.

Chamis, Christos C.↗

NASA NTRS1990

The effect of an electric field on the morphological stability of the crystal-melt interface of a binary alloy. III - Weakly nonlinear theory

The effect of a constant electric current on the crystal-melt interface morphology during directional solidification at constant velocity of a binary alloy is considered. A linear temperature field is assumed, and thermoelectric effects and Joule heating are neglected; electromigration and differing electrical conductivities of crystal and melt are taken into account. A two-dimensional weakly nonlinear analysis is carried out to third order in the interface amplitude, resulting in a cubic amplitude equation that describes whether the bifurcation from the planar state is supercritical or subcritical. For wavelengths corresponding to the most dangerous mode of linear theory, the demarcation between supercritical and subcritical behavior is calculated as a function of processing conditions and material parameters. The bifurcation behavior is a sensitive function of the magnitude and direction of the electric current and of the electrical conductivity ratio.

Wheeler, A. A.↗

NASA NTRS1990

Analytic theory for the selection of Saffman-Taylor fingers in the presence of thin film effects

The present analytic theory for the width selection of Saffman-Taylor (1958) fingers in the presence of the thin film effect establishes that, in the limit of a small capillary number and a small gap-to-width ratio, fingers whose relative width is smaller than 1/2 are possible. It is established that a fully nonlinear analysis is required for this problem in order to obtain even the correct (and rather preliminary) scaling law. The way in which the selection rule for arbitrary small capillary number is obtainable is also presented.

Tanveer, S.↗

NASA NTRS1991

Postbuckling response and failure prediction of flat rectangular graphite-epoxy plates loaded in axial compression

The objectives of the study are to assess the capability of a first-order shear deformable degenerated shell finite element theory to predict the postbuckling response and failure modes of various graphite-epoxy panels loaded in axial compression. Two panels without holes and one with a hole are studied, and the resulting responses and failure modes correlated well with the experimental results. A progressive damage failure mechanism is applied in the nonlinear analysis, which proved successful in predictions of failure location, mode, and load.

Engelstad, S. P.↗

NASA NTRS1991

The first ANDES elements: 9-DOF plate bending triangles

New elements are derived to validate and assess the assumed natural deviatoric strain (ANDES) formulation. This is a brand new variant of the assumed natural strain (ANS) formulation of finite elements, which has recently attracted attention as an effective method for constructing high-performance elements for linear and nonlinear analysis. The ANDES formulation is based on an extended parametrized variational principle developed in recent publications. The key concept is that only the deviatoric part of the strains is assumed over the element whereas the mean strain part is discarded in favor of a constant stress assumption. Unlike conventional ANS elements, ANDES elements satisfy the individual element test (a stringent form of the patch test) a priori while retaining the favorable distortion-insensitivity properties of ANS elements. The first application of this formulation is the development of several Kirchhoff plate bending triangular elements with the standard nine degrees of freedom. Linear curvature variations are sampled along the three sides with the corners as gage reading points. These sample values are interpolated over the triangle using three schemes. Two schemes merge back to conventional ANS elements, one being identical to the Discrete Kirchhoff Triangle (DKT), whereas the third one produces two new ANDES elements. Numerical experiments indicate that one of the ANDES element is relatively insensitive to distortion compared to previously derived high-performance plate-bending elements, while retaining accuracy for nondistorted elements.

Militello, Carmelo↗