SEARCH · Engineering Papers

Results for “nonlinear elimination”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2

All sources NASA NTRS DOE OSTI

NASA NTRS1997

On the Role of Resonances in Nonradial Pulsators

Resonances or near resonances are ubiquitous among the excited nonradial pulsation modes of variable stars and they must play an important role in determining their pulsational behavior. Here in a first step at nonlinear asteroseismology, we explore some of the consequences of resonances by means of the amplitude equation formalism. We show how parity and angular momentum constraints can be used to eliminate many of the possible nonlinear resonant couplings between modes (and multiplets of modes), and how the amplitude equations can thus be simplified. Even when we may not be able, nor wish, to make an ab initio computation of the values of the coupling coefficients, it is still possible to obtain constraints on the nature of the excited modes if a resonance between observed frequencies can be identified. Resonances can cause nonlinear frequency locking of modes. This means that the observed frequencies appear in exact resonance even though the linear frequencies are only approximately in resonance. The nonlinear frequency lock, when it occurs, it does so over a range of departures from linear resonance, and it is accompanied by constant pulsation amplitudes. The locked, nonlinear frequencies can differ noticeably from their nonresonant counterparts which are usually used in seismology. This is particularly true for multiplets of modes split by rotation. Beyond the regime of the frequency lock, amplitude and frequency modulations can appear in the pulsations. Far from the resonance condition one recovers the regime of steady pulsations with nonresonant frequencies for which the seismological studies, as they are presently carried out, are justified (provided furthermore, of course, that nonlinear frequency shifts are negligible). Success in identifying a resonance in an observed power spectrum depends on the quality of the data. While keeping this limitation in mind, ew discuss the possible existence of peculiar resonances the pulsations specific variable white dwarfs and delta Scuti stars.

Buchler, J. R.↗

NASA NTRS1995

Nonlinear structure formation in flat cosmological models

This paper describes the formation of nonlinear structure in flat (zero curvature) Friedmann cosmological models. We consider models with two components: the usual nonrelativistic component that evolves under gravity and eventually forms the large-scale structure of the universe, and a uniform dark matter component that does not clump under gravity, and whose energy density varies with the scale factor a(t) like a(t)(sup -n), where n is a free parameter. Each model is characterized by two parameters: the exponent n and the present density parameter Omega(sub 0) of the nonrelativistic component. The linear perturbation equations are derived and solved for these models, for the three different cases n = 3, n is greater than 3, and n is less than 3. The case n = 3 is relevant to model with massive neutrinos. The presence of the uniform component strongly reduces the growth of the perturbation compared with the Einstein-de Sitter model. We show that the Meszaros effect (suppression of growth at high redshift) holds not only for n = 4, radiation-dominated models, but for all models with n is greater than 3. This essentially rules out any such model. For the case n is less than 3, we numerically integrate the perturbation equations from the big bang to the present, for 620 different models with various values of Omega(sub 0) and n. Using these solutions, we show that the function f(Omega(sub 0), n) = (a/delta(sub +))d(delta)(sub +)/da, which enters in the relationship between the present density contrast delta(sub 0) and peculiar velocity field u(sub 0) is essentially independent of n. We derive approximate solutions for the second-order perturbation equations. These second-order solutions are tested against the exact solutions and the Zel'dovich approximation for spherically symmetric perturbations in the marginally nonlinear regime (the absolute value of delta is less than or approximately 1). The second-order and Zel'dovich solutions have comparable accuracy, significantly higher than the accuracy of the linear solutions. We then investigate the dependence of the delta(sub 0) - u(sub 0) relationship upon the value of n in the nonlinear regime using the second-order solutions for marginally nonlinear, general perturbations, and the exact solutions for strongly nonlinear, spherically symmetric perturbations. In both cases, we find that the delta(sub 0) - u(sub 0) relationship remains independent of n. We speculate that this result extends to strongly nonlinear, general perturbations as well. This eliminates any hope to determine the presence of the uniform component or the value of n using dynamical methods. Finally, we compute the nonlinear evolution of the skewness of the distribution of values of delta, assuming Gaussian initial conditions. We find that the skewness is not only independent of n, but also of Omega(sub 0). Thus the skewness cannot be used to discriminate among various models with Gaussian initial conditions. However, it can be used for testing the Gaussianity of the initial conditions themselves. We conclude that the uniform component leaves no observable signature in the present large-scale structure of the universe. To determine its presence and nature, we must investigate the relationship between the past and present universe, using redshift-dependent tests.

Martel, Hugo↗

NASA NTRS1999

Studies in Thermocapillary Convection of the Marangoni-Benard Type

A nonlinear feedback control strategy for delaying the onset and eliminating the subcritical nature of long-wavelength Marangoni-Benard convection is investigated based on an evolution equation. A control temperature is applied to the lower wall in a gas-liquid layer otherwise heated uniformly from below. It is shown that, if the interface deflection is assumed to be known via sensing as a function of both horizontal coordinates and time, a control temperature with a cubic-order polynomial dependence on the deflection is capable of delaying the onset as well as eliminating the subcritical instability altogether, at least on the basis of a weakly nonlinear analysis. The control coefficients required for stabilization are O(1) for both delaying onset indefinitely and eliminating subcritical instability.

Kelly, R. E.↗

NASA NTRS1976

Perturbation theory in thermosphere dynamics

It is shown that density and pressure throughout the thermosphere can be adequately described in a logarithmic expansion that provides a sound basis for the application of perturbation theory. This expansion eliminates most of the important nonlinearities associated with density variations. On the basis of this expansion, the validity of perturbation theory can be extended to cover a large variety of atmospheric conditions in which the relative temperature amplitude is less than 0.5 and wind velocities are significantly less than the speed of sound.

Mayr, H. G.↗

NASA NTRS1986

A variational assimilation method for satellite and conventional data: Development of basic model for diagnosis of cyclone systems

A three-dimensional diagnostic model for the assimilation of satellite and conventional meteorological data is developed with the variational method of undetermined multipliers. Gridded fields of data from different type, quality, location, and measurement source are weighted according to measurement accuracy and merged using least squares criteria so that the two nonlinear horizontal momentum equations, the hydrostatic equation, and an integrated continuity equation are satisfied. The model is used to compare multivariate variational objective analyses with and without satellite data with initial analyses and the observations through criteria that were determined by the dynamical constraints, the observations, and pattern recognition. It is also shown that the diagnoses of local tendencies of the horizontal velocity components are in good comparison with the observed patterns and tendencies calculated with unadjusted data. In addition, it is found that the day-night difference in TOVS biases are statistically different (95% confidence) at most levels. Also developed is a hybrid nonlinear sigma vertical coordinate that eliminates hydrostatic truncation error in the middle and upper troposphere and reduces truncation error in the lower troposphere. Finally, it is found that the technique used to grid the initial data causes boundary effects to intrude into the interior of the analysis a distance equal to the average separation between observations.

Achtemeier, G. L.↗

NASA NTRS1987

Extension of a semi-implicit shock-capturing algorithm for 3-D fully coupled, chemically reacting flows in generalized coordinates

A semiimplicit high-resolution shock-capturing method for multidimensional systems of hyperbolic conservation laws with stiff source terms has been developed by Yee and Shinn (1987). The goal of this work is to extend this method to solve the three-dimensional fully coupled Navier-Stokes equations for a hypersonic chemically reacting flow in generalized coordinates. In this formulation, the global continuity equation was replaced by all the species continuity equations. The shock-capturing technique is a second-order-accurate, symmetric total-variation-diminishing method which accounts fully and directly for the coupling among the fluid and all the species. To verify the current approach, it was implemented into an existing computer code which contained the MacCormack method. Test results for a five-species reacting flow are shown to be oscillation-free around the shock, and the time spent per iteration only doubles when compared to the result using classical way of supplying numerical dissipation. The extra computation is more than justified by the elimination of spurious oscillation and nonlinear instability associated with the classical shock-capturing schemes in computing hypersonic reacting flows.

Shinn, J. L.↗

NASA NTRS1972

Analyses of requirements for computer control and data processing experiment subsystems. Volume 1: ATM experiment S-056 image data processing system techniques development

The solar imaging X-ray telescope experiment (designated the S-056 experiment) is described. It will photograph the sun in the far ultraviolet or soft X-ray region. Because of the imaging characteristics of this telescope and the necessity of using special techniques for capturing images on film at these wave lengths, methods were developed for computer processing of the photographs. The problems of image restoration were addressed to develop and test digital computer techniques for applying a deconvolution process to restore overall S-056 image quality. Additional techniques for reducing or eliminating the effects of noise and nonlinearity in S-056 photographs were developed.

Source record↗

NASA NTRS1998

WARP3D-Release 10.8: Dynamic Nonlinear Analysis of Solids using a Preconditioned Conjugate Gradient Software Architecture

This report describes theoretical background material and commands necessary to use the WARP3D finite element code. WARP3D is under continuing development as a research code for the solution of very large-scale, 3-D solid models subjected to static and dynamic loads. Specific features in the code oriented toward the investigation of ductile fracture in metals include a robust finite strain formulation, a general J-integral computation facility (with inertia, face loading), an element extinction facility to model crack growth, nonlinear material models including viscoplastic effects, and the Gurson-Tver-gaard dilatant plasticity model for void growth. The nonlinear, dynamic equilibrium equations are solved using an incremental-iterative, implicit formulation with full Newton iterations to eliminate residual nodal forces. The history integration of the nonlinear equations of motion is accomplished with Newmarks Beta method. A central feature of WARP3D involves the use of a linear-preconditioned conjugate gradient (LPCG) solver implemented in an element-by-element format to replace a conventional direct linear equation solver. This software architecture dramatically reduces both the memory requirements and CPU time for very large, nonlinear solid models since formation of the assembled (dynamic) stiffness matrix is avoided. Analyses thus exhibit the numerical stability for large time (load) steps provided by the implicit formulation coupled with the low memory requirements characteristic of an explicit code. In addition to the much lower memory requirements of the LPCG solver, the CPU time required for solution of the linear equations during each Newton iteration is generally one-half or less of the CPU time required for a traditional direct solver. All other computational aspects of the code (element stiffnesses, element strains, stress updating, element internal forces) are implemented in the element-by- element, blocked architecture. This greatly improves vectorization of the code on uni-processor hardware and enables straightforward parallel-vector processing of element blocks on multi-processor hardware.

Koppenhoefer, Kyle C.↗

NASA NTRS1988

Analysis of long term heart rate variability: methods, 1/f scaling and implications

The use of spectral techniques to quantify short term heart rate fluctuations on the order of seconds to minutes has helped define the autonomic contributions to beat-to-beat control of heart rate. We used similar techniques to quantify the entire spectrum (0.00003-1.0 Hz) of heart rate variability during 24 hour ambulatory ECG monitoring. The ECG from standard Holter monitor recordings from normal subjects was sampled with the use of a phase locked loop, and a heart rate time series was constructed at 3 Hz. Frequency analysis of the heart rate signal was performed after a nonlinear filtering algorithm was used to eliminate artifacts. A power spectrum of the entire 24 hour record revealed power that was inversely proportional to frequency, 1/f, over 4 decades from 0.00003 to 0.1 Hz (period approximately 10 hours to 10 seconds). Displaying consecutive spectra calculated at 5 minute intervals revealed marked variability in the peaks at all frequencies throughout the 24 hours, probably accounting for the lack of distinct peaks in the spectra of the entire records.

Non-NASA Center↗

NASA NTRS2001

Microelectromechanical Systems (MEMS) Actuator for Reconfigurable Patch Antenna Demonstrated

A microstrip patch antenna with two contact actuators along the radiating edges for frequency reconfiguration was demonstrated at K-band frequencies. The layout of the antenna is shown in the following figure. This antenna has the following advantages over conventional semiconductor varactor-diode-tuned patch antennas: 1. By eliminating the semiconductor diode and its nonlinear I-V characteristics, the antenna minimizes intermodulation signal distortion. This is particularly important in digital wireless systems, which are sensitive to intersymbol interference caused by intermodulation products. 2. Because the MEMS actuator is an electrostatic device, it does not draw any current during operation and, hence, requires a negligible amount of power for actuation. This is an important advantage for hand-held, battery-operated, portable wireless systems since the battery does not need to be charged frequently. 3. The MEMS actuator does not require any special epitaxial layers as in the case of diodes and, hence, is cost effective.

Simons, Rainee N.↗

NASA NTRS1988

Accuracy versus convergence rates for a three dimensional multistage Euler code

Using a central difference scheme, it is necessary to add an artificial viscosity in order to reach a steady state. This viscosity usually consists of a linear fourth difference to eliminate odd-even oscillations and a nonlinear second difference to suppress oscillations in the neighborhood of steep gradients. There are free constants in these differences. As one increases the artificial viscosity, the high modes are dissipated more and the scheme converges more rapidly. However, this higher level of viscosity smooths the shocks and eliminates other features of the flow. Thus, there is a conflict between the requirements of accuracy and efficiency. Examples are presented for a variety of three-dimensional inviscid solutions over isolated wings.

Turkel, Eli↗

NASA NTRS1988

Accuracy versus convergence rates for a three dimensional multistage Euler code

Turkel, Eli↗

NASA NTRS1988

A multivariate variational objective analysis-assimilation method. Part 1: Development of the basic model

The variational method of undetermined multipliers is used to derive a multivariate model for objective analysis. The model is intended for the assimilation of 3-D fields of rawinsonde height, temperature and wind, and mean level temperature observed by satellite into a dynamically consistent data set. Relative measurement errors are taken into account. The dynamic equations are the two nonlinear horizontal momentum equations, the hydrostatic equation, and an integrated continuity equation. The model Euler-Lagrange equations are eleven linear and/or nonlinear partial differential and/or algebraic equations. A cyclical solution sequence is described. Other model features include a nonlinear terrain-following vertical coordinate that eliminates truncation error in the pressure gradient terms of the horizontal momentum equations and easily accommodates satellite observed mean layer temperatures in the middle and upper troposphere. A projection of the pressure gradient onto equivalent pressure surfaces removes most of the adverse impacts of the lower coordinate surface on the variational adjustment.

Achtemeier, Gary L.↗

NASA NTRS1997

Revised Simulation Model of the Control System, Displays, and Propulsion System for a ASTOVL Lift Fan Aircraft

This report describes revisions to a simulation model that was developed for use in piloted evaluations of takeoff, transition, hover, and landing characteristics of an advanced short takeoff and vertical landing lift fan fighter aircraft. These revisions have been made to the flight/propulsion control system, head-up display, and propulsion system to reflect recent flight and simulation experience with short takeoff and vertical landing operations. They include nonlinear inverse control laws in all axes (eliminating earlier versions with state rate feedback), throttle scaling laws for flightpath and thrust command, control selector commands apportioned based on relative effectiveness of the individual controls, lateral guidance algorithms that provide more flexibility for terminal area operations, and a simpler representation of the propulsion system. The model includes modes tailored to the phases of the aircraft's operation, with several response types which are coupled to the aircraft's aerodynamic and propulsion system effectors through a control selector tailored to the propulsion system. Head-up display modes for approach and hover are integrated with the corresponding control modes. Propulsion system components modeled include a remote lift fan and a lift-cruise engine. Their static performance and dynamic responses are represented by the model. A separate report describes the subsonic, power-off aerodynamics and jet induced aerodynamics in hover and forward flight, including ground effects.

Franklin, James A.↗

NASA NTRS1984

A numerical simulation of barotropic instability. II Wave-wave interaction

A fully nonlinear numerical model of the point jet barotropic instability is used to test and confirm the hypothesis that the magnitude of the wave vorticity does not exceed the magnitude of the initial shear. This result arises directly from the local conservation of vorticity following a parcel and the fact that unstable waves are principally confined to the region where the zonal mean vorticity can be smoothed by the wave so as to eliminate the instability. Comparisons are made between fully nonlinear and quasi-linear models of the point jet instability and their tracer transport properties. Differences become particularly evident after wave saturation. The most important effect neglected by the wave-mean flow model appears to be the advection of wave vorticity by the most unstable mode. However, as equilibration of the instability proceeds, the globally averaged properties of both models are found to be similar.

Nielsen, J. E.↗

NASA NTRS1998

Empirical Mode Decomposition and Hilbert Spectral Analysis

The difficult facing data analysis is the lack of method to handle nonlinear and nonstationary time series. Traditional Fourier-based analyses simply could not be applied here. A new method for analyzing nonlinear and nonstationary data has been developed. The key part is the Empirical Mode Decomposition (EMD) method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF) that serve as the basis of the representation of the data. This decomposition method is adaptive, and, therefore, highly efficient. The IMFs admit well-behaved Hilbert transforms, and yield instantaneous energy and frequency as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Among the main conceptual innovations is the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need of spurious harmonics to represent nonlinear and nonstationary signals. Examples from the numerical results of the classical nonlinear equation systems and data representing natural phenomena are given to demonstrate the power of this new method. The classical nonlinear system data are especially interesting, for they serve to illustrate the roles played by the nonlinear and nonstationary effects in the energy-frequency-time distribution.

Huang, Norden E.↗

NASA NTRS1999

A Critical Examination of Wind-Wave Spectral Functional Form

Traditionally, data from random ocean waves are presented in spectral functions. The spectra are the result of Fourier analysis. Fourier spectral analysis has dominated data analysis for, at least, the last hundred years. It has been the standard method for is examining the global amplitude-frequency distributions. Although Fourier transform valid under extremely general conditions, there are some crucial restrictions for the Fourier spectral analysis. The system must be linear, and the data must be stationary- otherwise, the resulting spectrum will make little physical sense. The stationarity requirement is also a common required criterion for most of other available data analysis methods. Nevertheless, few, if any, natural phenomena are linear and stationary. To compound these complications is the imperfection of our probes or numerical schemes the interactions of the imperfect probes even with a perfect linear system can make the final data nonlinear. Furthermore, all the available data are usually of finite duration. Under these conditions, Fourier analysis is of limited use, For lack of alternatives, however, Fourier analysis is still used to process such data. The loose application of Fourier analysis and the insouciant adoption of the stationary and linear assumptions may lead to misleading conclusions. Ocean waves are know to be nonlinear, and the wind system generating the wave field are seldom stationary- As a result, the traditional examination of the spectral form hardly made physical sense. A new method for analyzing nonlinear and nonstationary data has been developed. The key part is the Empirical Mode Decomposition (EMD) method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF) that serve as the basis of the representation of the data, This decomposition method is adaptive, and, therefore, highly efficient. The IMFs admit well-behaved Hilbert transforms, and yield instantaneous energy and frequency as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Among the main conceptual innovations is the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need of spurious harmonics to represent nonlinear and nonstationary signals. The spectral forms of the ocean waves are very different. This new method offers the first physical meaningful view of the wave spectrum. Data from laboratory and field will be presented to illustrate the differences.

Huang, Norden E.↗

NASA NTRS2007

Whirl Motion of a Seal Test Rig with Squeeze-Film Dampers

This paper presents the experimental behavior and dynamic analysis of a high speed test rig with rolling element bearings mounted in squeeze film oil damper bearings. The test rotor is a double overhung configuration with rolling element ball bearings mounted in uncentered squeeze-film oil dampers. The damper design is similar to that employed with various high-speed aircraft HP gas turbines. The dynamic performance of the test rig with the originally installed dampers with an effective damper length of length 0.23-inch was unacceptable. The design speed of 40,000 RPM could not be safely achieved as nonsynchronous whirling at the overhung seal test disk and high amplitude critical speed response at the drive spline section occurred at 32,000 RPM. In addition to the self excited stability and critical speed problems, it was later seen from FFT data analysis, that a region of supersynchronous dead band whirling occurs between 10,000 to 15,000 RPM which can lead to bearing distress and wear. The system was analyzed using both linear and nonlinear techniques. The extended length damper design resulting from the analysis eliminated the rotor subsynchronous whirling, high amplitude critical speed, and the dead band whirling region allowing the system to achieve a speed of 45,000 RPM. However, nonlinear analysis shows that damper lockup could occur with high rotor unbalance at 33,000 RPM, even with the extended squeeze-film dampers. The control of damper lockup will be addressed in a future paper.

Proctor, Margaret P.↗