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At least 1,603 records · Page 89
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NASA NTRS1992

A weakly nonlinear theory based explanation for wave interactions in rotating channel flow

A weakly nonlinear wave-interaction theory is used to explain the decay of linearly unstable oblique waves in rotating channel flow at low Reynolds number. At the low Reynolds number studied, the waves tend to stabilize each other and therefore when no waves are preferentially excited, the linearly most unstable mode reaches a nonlinear amplitude first and causes the stabilization of all competing modes.

Singer, Bart A.↗
NASA NTRS1991

Nonlinear dynamics near the stability margin in rotating pipe flow

The nonlinear evolution of marginally unstable wave packets in rotating pipe flow is studied. These flows depend on two control parameters, which may be taken to be the axial Reynolds number R and a Rossby number, q. Marginal stability is realized on a curve in the (R, q)-plane, and the entire marginal stability boundary is explored. As the flow passes through any point on the marginal stability curve, it undergoes a supercritical Hopf bifurcation and the steady base flow is replaced by a traveling wave. The envelope of the wave system is governed by a complex Ginzburg-Landau equation. The Ginzburg-Landau equation admits Stokes waves, which correspond to standing modulations of the linear traveling wavetrain, as well as traveling wave modulations of the linear wavetrain. Bands of wavenumbers are identified in which the nonlinear modulated waves are subject to a sideband instability.

Yang, Z.↗
NASA NTRS1989

Nonlinear triggered lightning models for use in finite difference calculations

Two nonlinear triggered lightning models have been developed for use in finite difference calculations. Both are based on three species of air chemistry physics and couple nonlinearly calculated air conductivity to Maxwell's equations. The first model is suitable for use in three-dimensional modeling and has been applied to the analysis of triggered lightning on the NASA F106B Thunderstorm Research Aircraft. The model calculates number densities of positive ions, negative ions, and electrons as a function of time and space through continuity equations, including convective derivative terms. The set of equations is closed by using experimentally determined mobilities, and the mobilities are also used to determine the air conductivity. Results from the model's application to the F106B are shown. The second model is two-dimensional and incorporates an enhanced air chemistry formulation. Momentum conservation equations replace the mobility assumption of the first model. Energy conservation equations for neutrals, heavy ions, and electrons are also used. Energy transfer into molecular vibrational modes is accounted for. The purpose for the enhanced model is to include the effects of temperature into the air breakdown, a necessary step if the model is to simulate more than the very earliest stages of breakdown. Therefore, the model also incorporates a temperature-dependent electron avalanche rate. Results from the model's application to breakdown around a conducting ellipsoid placed in an electric field are shown.

Rudolph, Terence↗
NASA NTRS1992

Computational modeling of nonlinear electromagnetic phenomena

A new algorithm has been developed that permits, for the first time, the direct time integration of the full-vector nonlinear Maxwell's equations. This new capability permits the modeling of linear and nonlinear, instantaneous and dispersive effects in the electric polarization material media. Results are presented of first-time calculations in 1D of the propagation and collision of femtosecond electromagnetic solitons that retain the optical carrier.

Goorjian, Peter M.↗
NASA NTRS1992

On the nonlinear development of three-dimensional instability waves in natural transition

The nonlinear development of a pair of symmetrical three-dimensional oblique instability waves in transitioning boundary layers is investigated based on critical-layer nonlinearity (CLN). Particular emphasis is placed on understanding the mechanisms leading to the naturally occurring transition in which the amplitudes of the plane and oblique modes can be of the same order. Results indicate that the self-interaction of the oblique waves reduces their growth rate. A relatively large oblique mode can either suppress or enhance the growth of the plane mode, depending on the initial phase difference. If the plane mode amplitude is not negligible with respect to that of the oblique modes, it causes a strong amplification of the oblique mode at the subharmonic frequency. The comparison with observations are quite encouraging and several novel features of the natural transition process are revealed.

Mankbadi, Reda R.↗
NASA NTRS1991

Design of multi-layer neural networks for accurate identification of nonlinear mappings

Guidelines for the design of multilayer neural networks for the identification of nonlinear mappings are considered. Since nonlinear mappings can be approximated by a one-hidden-layer neural network, an approach to determine the sufficient number of hidden layer nodes to achieve a global minima of the identification error function is considered.

Teixeira, Edilberto↗
NASA NTRS1991

Higher-order harmonics in electromagnetic scattering from a nonlinear anisotropic cylinder

The general solution of the scattering of harmonic signals, by a medium which has nonlinear constitutive relations, contains higher harmonics. The scattering amplitude consists of the linear component and additional correction terms that depend on the amplitude of the incident wave. In this paper, we examine the effects of nonlinearities on the field components and on the radar cross section at the second and third harmonics.

Hasan, Moh'd A.↗
NASA NTRS1992

Linear and nonlinear propagation of water wave groups

Results are presented from a study of the evolution of waveforms with known analytical group shapes, in the form of both transient wave groups and the cloidal (cn) and dnoidal (dn) wave trains as derived from the nonlinear Schroedinger equation. The waveforms were generated in a long wind-wave tank of the Canada Centre for Inland Waters. It was found that the low-amplitude transients behaved as predicted by the linear theory and that the cn and dn wave trains of moderate steepness behaved almost as predicted by the nonlinear Schroedinger equation. Some of the results did not fit into any of the available theories for waves on water, but they provide important insight on how actual groups of waves propagate and on higher-order effects for a transient waveform.

Pierson, W. J., Jr.↗
NASA NTRS1992

The nonlinear bending response of thin-walled laminated composite cylinders

The geometrically nonlinear Donnell shell theory is applied to the problem of stable bending of thin-walled circular cylinders. Responses are computed for cylinders with a radius-to-thickness ratio of 50 and length-to-radius ratios of 1 and 5. Four laminated composite cylinders and an aluminum cylinder are considered. Critical moment estimates are presented for short cylinders for which compression-type buckling behavior is important, and for very long cylinders for which the cross-section flattening, i.e., Brazier effect, is important. A finite element analysis is used to estimate the critical end rotation in addition to establishing the range of validity of the prebuckling analysis. The radial displacement response shows that the character of the boundary layer is significantly influenced by the geometric nonlinearities. Application of a first ply failure analysis using the maximum stress criterion suggests that in nearly all instances material failure occurs before buckling. Failure of the composite cylinders can be attributed to fiber breakage. Striking similarities are seen between the prebuckling displacements of the bending problem and axial compression problem for short cylinders.

Fuchs, Hannes P.↗
NASA NTRS1992

Determining design gust loads for nonlinear aircraft similarity between methods based on matched filter theory and on stochastic simulation

This is a work-in-progress paper. It explores the similarity between the results from two different analysis methods - one deterministic, the other stochastic - for computing maximized and time-correlated gust loads for nonlinear aircraft. To date, numerical studies have been performed using two different nonlinear aircraft configurations. These studies demonstrate that results from the deterministic analysis method are realizable in the stochastic analysis method.

Scott, Robert C.↗
NASA NTRS1992

Finite element nonlinear panel flutter with arbitrary temperatures in supersonic flow

A finite element frequency domain method for predicting nonlinear flutter response of panels with temperature effects is presented. By using the principle of virtual work, the element nonlinear stiffness formulation for a panel under a combined thermal and aerodynamic loads is derived on the bases of von Karman's large deflection plate theory, the first-order piston theory aerodynamics and the quasi-steady thermal stress theory. The system equations of motion can be mathematically separated into two sets of equations and then solved in sequence. The first set of equations yields the panel thermal-aerodynamic equilibrium and the second set of equations of motion leads to the flutter limit-cycle oscillations. Stability and flutter boundaries can also be obtained from the two sets of system equations. Finite element large amplitude limit-cycle flutter results at different uniform temperatures are obtained for a simply supported square panel and are compared with existing Galerkin/time integration and other finite element solutions. Effects of nonuniform temperature distributions, panel length-to-width ratios, and boundary conditions on flutter responses of rectangular and triangular panels are presented.

Xue, David Y.↗
NASA NTRS1991

Subharmonic Route to Boundary-Layer Transition - Critical Layer Nonlinearity

The linear and nonlinear dynamics of a triad of initially linear stability waves comprising a single plane wave at fundamental frequency and two symmetric oblique waves with half the frequency and streamwise wave number of the plane wave are presented. Analysis is performed for the initial nonlinear development of the waves where the order of the oblique waves' amplitude is equal to or less than that of the plane wave. Results show that the fundamental basically follows the linear theory, while the subharmonic follows an exponential-of-an-exponential growth.

Mankbadi, Reda R.↗
NASA NTRS1992

Paneling methods with vorticity effects and corrections for nonlinear compressibility

Supersonic panel methods and axisymmetric body-modeling singularity methods are presently combined with corrections for nonlinear flow phenomena to a complete missile, its airbreathing inlets, and wing-body combinations. The computer code LRCDM2 is used as an illustrative example of the methods in question. Attention is given to a preliminary method which employs panels to estimate additive drag and lift acting on supersonic rectangular inlets, as well as to the method used to correct off-body flowfields for the presence of a shock. Examples of missile applications of these methods with the appropriate nonlinear corrections are presented.

Dillenius, Marnix F. E.↗
NASA NTRS1992

Nonlinear control design for slightly nonminimum phase systems - Application to V/STOL aircraft

The paper describes the application of techniques of exact I/O linearization of nonlinear control systems to the flight control of V/STOL aircraft. It is seen that the application of the theory to this example is not straightforward; in particular, the direct application of the theory yielded an undesirable controller. The situation was remedied by neglecting the coupling between the rolling moment input to the aircraft dynamics and the dynamics along the y-axis. An approximate I/O linearization procedure developed for slightly nonminimum phase nonlinear systems is shown to be effective for V/STOL aircraft.

Hauser, John↗
NASA NTRS1992

Simulating the arcjet thruster using a nonlinear active load

Arcjet thrusters are known to have distinctly nonlinear electrical characteristics with negative incremental resistance throughout their normal operating region. The 1-kW arcjet simulator proposed here accurately mimics these characteristics statically, and dynamically up to 40 kHz. Testing with a power-processing unit (PPU) and the simulator, a 1-kW arcjet, and a resistive load bank established that the simulator accurately predicted the transient behavior of the PPU-arcjet combination, while the resistive load bank did not. The simulator uses resistors and insulated-gate bipolar transistors to dissipate the PPU output power; a nonlinear feedback is applied to produce the desired v-i characteristics. This feedback is analyzed dynamically. The arcjet simulator allows development of a PPU to a higher level of confidence before beginning testing at an arcjet facility.

Altenburger, Gene P.↗
NASA NTRS1992

A fully nonlinear, mixed spectral and finite difference model for thermally driven, rotating flows

Finite difference in time and the meridional plane, in conjunction with a spectral technique in the azimuthal direction, are used to approximate the Navier-Stokes equations in a model that can simulate a variety of thermally driven rotating flows in cylindrical and spherical geometries. Axisymmetric flow, linearized waves relative to a fixed or changing axisymmetric flow, nonlinear waves without wave-wave interaction, and fully nonlinear 3D flow, can in this way be calculated. A reexamination is conducted of the steady baroclinic wave case previously treated by Williams (1971) and Quon (1976).

Miller, Timothy L.↗
NASA NTRS1992

A nonlinear dynamical analogue model of geomagnetic activity

Consideration is given to the solar wind-magnetosphere interaction within the framework of deterministic nonlinear dynamics. An earlier dripping faucet analog model of the low-dimensional solar wind-magnetosphere system is reviewed, and a plasma physical counterpart to that model is constructed. A Faraday loop in the magnetotail is considered, and the relationship of electric potentials on the loop to changes in the magnetic flux threading the loop is developed. This approach leads to a model of geomagnetic activity which is similar to the earlier mechanical model but described in terms of the geometry and plasma contents of the magnetotail. The model is characterized as an elementary time-dependent global convection model. The convection evolves within a magnetotail shape that varies in a prescribed manner in response to the dynamical evolution of the convection. The result is a nonlinear model capable of exhibiting a transition from regular to chaotic loading and unloading. The model's behavior under steady loading and also some elementary forms of time-dependent loading is discussed.

Klimas, A. J.↗
NASA NTRS1993

Synthesizing Diacetylenes With Nonlinear Optical Properties

Diacetylene compounds being investigated to determine whether they have nonlinear optical properties making them useful for four-wave mixing, generation of third harmonics, phase conjugation, and like. Diacetylene monomers synthesized by sequences of chemical reactions. Monomers polymerized by ultraviolet light, forming potentially useful nonlinear optical materials.

Mcmanus, Samuel P.↗