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At least 1,045 records · Page 58

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NASA NTRS1971

Generalized invariance principles and the theory of stability.

Description of some recent extensions of the invariance principle to more generalized dynamical systems where the state space is not locally compact and the flow is unique only in the forward direction of time. A sufficient condition for asymptotic stability of an invariant set is obtained which does not require that the Liapunov function be positive-definite. A recently developed generalized invariance principle is described which is applicable to functional differential equations, partial differential equations, and, in particular, to certain stability problems arising in thermoelasticity, viscoelasticity, and distributed nonlinear networks.

Lasalle, J. P.↗

NASA NTRS1972

System modeling and optimal design of a Mars-roving vehicle.

The problem of systematically determining the optimal design for an unmanned Mars-roving vehicle is considered. A system model, identifying all feasible designs, is generated by consideration of the physical constraints on the design parameters, and the requirement that the system be deliverable to the Mars surface. An expression which evaluates system performance relative to mission goals is developed. The model and objective function together allow simulation of the effects of design trade-offs upon system performance for all feasible designs. Nonlinear programming techniques are utilized to identify the optimal design.

Smith, E. J.↗

NASA NTRS1973

A class of all digital phase locked loops - Modeling and analysis

An all digital phase locked loop which tracks the phase of the incoming signal once per carrier cycle is proposed. The different elements and their functions, and the phase lock operation are explained in detail. The general digital loop operation is governed by a nonlinear difference equation from which a suitable model is developed. The lock range for the general model is derived. The performance of the digital loop for phase step and frequency step inputs for different levels of quantization without loop filter are studied. The analytical results are checked by simulating the actual system on the digital computer.

Reddy, C. P.↗

NASA NTRS1981

Estimation of airplane stability and control derivatives at high angles of attack

A technique for extracting approximate aircraft stability and control derivatives over a broad range of angle of attack from a single large amplitude maneuver which encompasses that range is presented. The results from the application of this technique to flight data are shown to agree well with derivatives extracted from several maneuvers which are more restricted in range of angle of attack. The technique consists of dividing the data from the large maneuver into bins that are a function of angle of attack. The binned data is then analyzed with a modified stepwise regression. The identification of nonlinear terms in the aerodynamic model is shown to discern regions of rapid change in aircraft behavior.

Batterson, J. G.↗

NASA NTRS1985

Simulation of the electron acoustic instability in the polar cusp

A computer simulation of the beam-driven electron acoustic instability in the polar cusp is used to investigate the temporal evolution of typical cusp electron distribution functions in self-consistently generated wave fields. The simulation results are compared with linear, second-order, and nonlinear theory. The behavior of the instability over a range of plasma parameters, such as beam speed and the cold electron density, is shown. The saturation mechanism of the instability is examined, and the relevance of the results for observations of cusp hiss are discussed.

Lin, C. S.↗

NASA NTRS1986

Stress analysis of the cracked lap shear specimens: An ASTM round robin

This ASTM Round Robin was conducted to evaluate the state of the art in stress analysis of adhesively bonded joint specimens. Specifically, the participants were asked to calculate the strain-energy-release rate for two different geometry cracked lap shear (CLS) specimens at four different debond lengths. The various analytical techniques consisted of 2- and 3-dimensional finite element analysis, beam theory, plate theory, and a combination of beam theory and finite element analysis. The results were examined in terms of the total strain-energy-release rate and the mode I to mode II ratio as a function of debond length for each specimen geometry. These results basically clustered into two groups: geometric linear or geometric nonlinear analysis. The geometric nonlinear analysis is required to properly analyze the CLS specimens. The 3-D finite element analysis gave indications of edge closure plus some mode III loading. Each participant described his analytical technique and results. Nine laboratories participated.

Johnson, W. S.↗

NASA NTRS1985

A theory of post-stall transients in axial compression systems. I - Development of equations

An approximate theory is presented for post-stall transients in multistage axial compression systems. The theory leads to a set of three simultaneous nonlinear third-order partial differential equations for pressure rise, and average and disturbed values of flow coefficient, as functions of time and angle around the compressor. By a Galerkin procedure, angular dependence is averaged, and the equations become first order in time. These final equations are capable of describing the growth and possible decay of a rotating-stall cell during a compressor mass-flow transient. It is shown how rotating-stall-like and surgelike motions are coupled through these equations, and also how the instantaneous compressor pumping characteristic changes during the transient stall process.

Moore, F. K.↗

NASA NTRS1987

Computable optimal value bounds for generalized convex programs

It has been shown by Fiacco that convexity or concavity of the optimal value of a parametric nonlinear programming problem can readily be exploited to calculate global parametric upper and lower bounds on the optimal value function. The approach is attractive because it involves manipulation of information normally required to characterize solution optimality. A procedure is briefly described for calculating and improving the bounds as well as its extensions to generalized convex and concave functions. Several areas of applications are also indicated.

Fiacco, Anthony V.↗

NASA NTRS1987

Particle simulation of plasmas on the massively parallel processor

Particle simulations, in which collective phenomena in plasmas are studied by following the self consistent motions of many discrete particles, involve several highly repetitive sets of calculations that are readily adaptable to SIMD parallel processing. A fully electromagnetic, relativistic plasma simulation for the massively parallel processor is described. The particle motions are followed in 2 1/2 dimensions on a 128 x 128 grid, with periodic boundary conditions. The two dimensional simulation space is mapped directly onto the processor network; a Fast Fourier Transform is used to solve the field equations. Particle data are stored according to an Eulerian scheme, i.e., the information associated with each particle is moved from one local memory to another as the particle moves across the spatial grid. The method is applied to the study of the nonlinear development of the whistler instability in a magnetospheric plasma model, with an anisotropic electron temperature. The wave distribution function is included as a new diagnostic to allow simulation results to be compared with satellite observations.

Gledhill, I. M. A.↗

NASA NTRS1987

Stress analysis of the cracked-lap-shear specimen - An ASTM round-robin

Johnson, W. S.↗

NASA NTRS1990

Improved operation of magnetic bearings for flywheel energy storage system

Analysis and operation of prototype 500-Wh flywheel at low speeds have shown that many factors affect the correct functioning of the magnetic bearings. An examination is made of a number of these, including magnetic bearing control system nonlinearities and displacement transducer positioning, and their effects upon the successful operation of the suspension system. It is observed that the bearing control system is extremely sensitive to actuator parameters such as coil inductance. As a consequence of the analysis of bearing relaxation oscillations, the bearing actuator design methodology which has previously been used, where coil parameter selection is based upon static considerations, has been revised. Displacement transducer sensors which overcome the collocation problem are discussed.

Zmood, R. B.↗

NASA NTRS1991

Least-squares/parabolized Navier-Stokes procedure for optimizing hypersonic wind tunnel nozzles

A new procedure is demonstrated for optimizing hypersonic wind-tunnel-nozzle contours. The procedure couples a CFD computer code to an optimization algorithm, and is applied to both conical and contoured hypersonic nozzles for the purpose of determining an optimal set of parameters to describe the surface geometry. A design-objective function is specified based on the deviation from the desired test-section flow-field conditions. The objective function is minimized by optimizing the parameters used to describe the nozzle contour based on the solution to a nonlinear least-squares problem. The effect of the changes in the nozzle wall parameters are evaluated by computing the nozzle flow using the parabolized Navier-Stokes equations. The advantage of the new procedure is that it directly takes into account the displacement effect of the boundary layer on the wall contour. The new procedure provides a method for optimizing hypersonic nozzles of high Mach numbers which have been designed by classical procedures, but are shown to produce poor flow quality due to the large boundary layers present in the test section. The procedure is demonstrated by finding the optimum design parameters for a Mach 10 conical nozzle and a Mach 6 and a Mach 15 contoured nozzle.

Korte, John J.↗

NASA NTRS1993

Neural network-based control using Lyapunov functions

We have successfully demonstrated how the problem of stabilization of plants can be reduced to a problem of approximation of functions. Neural networks have been shown to have approximating and interpolating properties. This approach is good for linear and nonlinear plants. Software has been generated to demonstrate this approach.

Luxemburg, Leon A.↗

NASA NTRS1997

Wavelet Analyses of F/A-18 Aeroelastic and Aeroservoelastic Flight Test Data

Time-frequency signal representations combined with subspace identification methods were used to analyze aeroelastic flight data from the F/A-18 Systems Research Aircraft (SRA) and aeroservoelastic data from the F/A-18 High Alpha Research Vehicle (HARV). The F/A-18 SRA data were produced from a wingtip excitation system that generated linear frequency chirps and logarithmic sweeps. HARV data were acquired from digital Schroeder-phased and sinc pulse excitation signals to actuator commands. Nondilated continuous Morlet wavelets implemented as a filter bank were chosen for the time-frequency analysis to eliminate phase distortion as it occurs with sliding window discrete Fourier transform techniques. Wavelet coefficients were filtered to reduce effects of noise and nonlinear distortions identically in all inputs and outputs. Cleaned reconstructed time domain signals were used to compute improved transfer functions. Time and frequency domain subspace identification methods were applied to enhanced reconstructed time domain data and improved transfer functions, respectively. Time domain subspace performed poorly, even with the enhanced data, compared with frequency domain techniques. A frequency domain subspace method is shown to produce better results with the data processed using the Morlet time-frequency technique.

Martin J Brenner↗

NASA NTRS1984

Functional integration of vertical flight path and speed control using energy principles

A generalized automatic flight control system was developed which integrates all longitudinal flight path and speed control functions previously provided by a pitch autopilot and autothrottle. In this design, a net thrust command is computed based on total energy demand arising from both flight path and speed targets. The elevator command is computed based on the energy distribution error between flight path and speed. The engine control is configured to produce the commanded net thrust. The design incorporates control strategies and hierarchy to deal systematically and effectively with all aircraft operational requirements, control nonlinearities, and performance limits. Consistent decoupled maneuver control is achieved for all modes and flight conditions without outer loop gain schedules, control law submodes, or control function duplication.

Lambregts, A. A.↗

NASA NTRS1985

Remarks on rotor stability (A contribution to discussion during symposium on instability in rotating machinery)

Influence of nonlinear factors in fluid lubricated bearings on rotor vibrations is discussed as are computation of threshold of stability for systems with multiple degrees of freedom. The reason for this investigation was to learn more about the influence of tilting pad bearings on vertical rotors. The eigenvalues, the stability threshold, the response on the Heaviside-function and the unbalance response were calculated for a rigid rotor, a Jeffcott rotor and for the finite element model of a real rotor. The comparison of the linear and nonlinear calculations shows the limit of the linear calculations. The computation is supposed to show, that the model of the Jeffcott rotor is not sufficient in most practical cases to determine the stability threshold. This was known for some years, when computed results were compared with the behavior of real machines. That's why a program was developed, which is roughly described.

Kraemer, E.↗

NASA NTRS1983

Nonlinear energy flow in a beam-plasma system

The three-dimensional character of the beam-plasma instability is investigated. The true beam-electron distribution function is resolved with a novel directional energy analyzer. The electron plasma waves are observed to develop a large spread in perpendicular wave numbers and damp in a relatively short distance producing an energetic electron tail on the background distribution. The damping is believed to be due to strong ion fluctuations which produce an anomalous resistivity.

Whelan, D. A.↗

NASA NTRS1991

Ephemeral penalty functions for contact-impact dynamics

The use of penalty functions to treat a class of structural contact-impact problems is investigated, with emphasis on ones in which the impact phenomena are primarily nondestructive in nature and in which only the gross characterization of the response is required. The dynamic equations of motion are integrated by the difference method. The penalty is represented as an ephemeral fictitious nonlinear spring that is inserted on anticipation of contact. The magnitude and variation of the penalty force is determined through energy balancing considerations. The 'bell shape' of the penalty force function for positive gap was found to be satisfactory, as it depends on only two parameters that can be directly assigned the physical meaning of force and distance. The determination of force law parameters by energy balance worked well. The incorporation of restitution coefficients by the area balancing method yielded excellent results, and no substantial modifications are anticipated. Extensional penalty springs are obviously sufficient for the simple examples treated.

De La Fuente, Horacio M.↗