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Results for “Perturbative methods”

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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

Aircraft trajectory optimization using singular perturbation methods

Singular perturbation methods are used to derive nonlinear feedback control laws for aircraft minimum time long range interception under the assumption of complete time scale separation. The resulting algorithms are in feedback form and can be implemented on a microcomputer for on-line trajectory optimization.

Mehra, R. K.↗
NASA NTRS1992

Comparison of the Unified Perturbation Method with the two-scale expansion

The Unified Perturbation Method (UPM) converges faster over a wider domain of surface roughness than other perturbations, such as the small perturbation method, the phase perturbation method, the Kirchhoff approximation, and the momentum transfer expansion. It can be shown that UPM intrinsically possess characteristics similar to the two-scale expansion without requiring a free parameter. This paper considers whether the UPM can be improved by applying the two-scale concept to the method. In order to do so, the unknown source current is expanded in a two-scale manner starting from the extinction theorem. Several two-scale expansions are derived and are compared with the conventional two-scale approximation. It is shown that the UPM performs best without two-scale expansions.

Kim, Yunjin↗
NASA NTRS1972

Analysis of wave propagation in elastic cylindrical shells by the perturbation method.

Description of the perturbation method for solving propagation problems of transient, axisymmetric stress waves in elastic cylindrical shells. It is shown that the method provides remarkably accurate solutions for these problems and that it can be applied to a variety of related problems, such as the propagation of compressional waves in elastic rods.

Geers, T. L.↗
NASA NTRS1977

Application of perturbation methods to improve analytical model correlation with test data

A linear perturbation method developed by White (1972) to improve the correlation between analytical models and experimental data is applied to modeling of the Viking Propulsion Subsystem (VPS), flown successfully as part of the Viking Spacecraft launch of 1975. Analytical models and modal test data developed for the VPS are employed in the application; a set of mathematically generated data and a corresponding perturbed analytical model, representative of actual flight hardware, are also subjected to the White method. It is found that the linear perturbation method does not yield a single unique improved model.

Garba, J. A.↗
NASA NTRS1980

A nonlinear, discrete-vortex-perturbation method for unsteady lifting-surface problems with edge separations

The nonlinear-discrete vortex method is coupled with a perturbation method to solve the problem of a rectangular wing with small oscillation about high angles of attack. The solution of the problem is based on decoupling the steady and unsteady effects. The steady part of the problem is a nonlinear one and is solved by the nonlinear-discrete vortex method. The unsteady part of the problem is a linear one and is solved directly without any iteration. So far, the developed method is restricted to flat rectangular surfaces with pitching oscillations. Total and distributed loads of several rectangular wings are presented as numerical results.

Kandil, O. A.↗
NASA NTRS1987

Current distribution in a three-dimensional IC analyzed by a perturbation method. Part 1: A simple steady state theory

The steady state current distribution in a three dimensional integrated circuit is presented. A device physics approach, based on a perturbation method rather than an equivalent lumped circuit approach, is used. The perturbation method allows the various currents to be expressed in terms of elementary solutions which are solutions to very simple boundary value problems. A Simple Steady State Theory is the subtitle because the most obvious limitation of the present version of the analysis is that all depletion region boundary surfaces are treated as equipotential surfaces. This may be an adequate approximation in some applications but it is an obvious weakness in the theory when applied to latched states. Examples that illustrate the use of these analytical methods are not given because they will be presented in detail in the future.

Edmonds, Larry D.↗
NASA NTRS1984

Development of a turbomachinery design optimization procedure using a multiple-parameter nonlinear perturbation method

An investigation was carried out to complete the preliminary development of a combined perturbation/optimization procedure and associated computational code for designing optimized blade-to-blade profiles of turbomachinery blades. The overall purpose of the procedures developed is to provide demonstration of a rapid nonlinear perturbation method for minimizing the computational requirements associated with parametric design studies of turbomachinery flows. The method combines the multiple parameter nonlinear perturbation method, successfully developed in previous phases of this study, with the NASA TSONIC blade-to-blade turbomachinery flow solver, and the COPES-CONMIN optimization procedure into a user's code for designing optimized blade-to-blade surface profiles of turbomachinery blades. Results of several design applications and a documented version of the code together with a user's manual are provided.

Stahara, S. S.↗
NASA NTRS1990

A perturbation method and some applications

For differential equations with one fast variable, a perturbation method is introduced that transforms a solution valid over only a short time interval to a new solution composed of averaged variables plus a periodic function of the averaged variables. The averaged variables are governed by a set of differential equations where the fast variable has been removed and thus can be numerically integrated quickly or solved directly. This method is applied to a perturbed harmonic oscillator with a cubic perturbation, van der Pol's equation, coorbital motion in the restricted three-body problem, and to nearly circular motion of a particle near one of the primaries in the restricted three-body problem.

Konopliv, Alex↗
NASA NTRS1974

A numerical-perturbation method for the nonlinear analysis of structural vibrations

A numerical-perturbation method is proposed for the determination of the nonlinear forced response of structural elements. Purely analytical techniques are capable of determining the response of structural elements having simple geometries and simple variations in thickness and properties, but they are not applicable to elements with complicated structure and boundaries. Numerical techniques are effective in determining the linear response of complicated structures, but they are not optimal for determining the nonlinear response of even simple elements when modal interactions take place due to the complicated nature of the response. Therefore, the optimum is a combined numerical and perturbation technique. The present technique is applied to beams with varying cross sections.

Nayfeh, A. H.↗
NASA NTRS2013

Analytic Perturbation Method for Estimating Ground Flash Fraction from Satellite Lightning Observations

An analytic perturbation method is introduced for estimating the lightning ground flash fraction in a set of N lightning flashes observed by a satellite lightning mapper. The value of N is large, typically in the thousands, and the observations consist of the maximum optical group area produced by each flash. The method is tested using simulated observations that are based on Optical Transient Detector (OTD) and Lightning Imaging Sensor (LIS) data. National Lightning Detection NetworkTM (NLDN) data is used to determine the flash‐type (ground or cloud) of the satellite-observed flashes, and provides the ground flash fraction truth for the simulation runs. It is found that the mean ground flash fraction retrieval errors are below 0.04 across the full range 0‐1 under certain simulation conditions. In general, it is demonstrated that the retrieval errors depend on many factors (i.e., the number, N, of satellite observations, the magnitude of random and systematic measurement errors, and the number of samples used to form certain climate distributions employed in the model).

Koshak, William↗