Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “SERIES EXPANSION”

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.

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

At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

Approximation methods for combined thermal/structural design

Two approximation concepts for combined thermal/structural design are evaluated. The first concept is an approximate thermal analysis based on the first derivatives of structural temperatures with respect to design variables. Two commonly used first-order Taylor series expansions are examined. The direct and reciprocal expansions are special members of a general family of approximations, and for some conditions other members of that family of approximations are more accurate. Several examples are used to compare the accuracy of the different expansions. The second approximation concept is the use of critical time points for combined thermal and stress analyses of structures with transient loading conditions. Significant time savings are realized by identifying critical time points and performing the stress analysis for those points only. The design of an insulated panel which is exposed to transient heating conditions is discussed.

Haftka, R. T.↗
NASA NTRS1974

The application of MINIQUASI to thermal program boundary and initial value problems

The feasibility of applying the solution techniques of Miniquasi to the set of equations which govern a thermoregulatory model is investigated. For solving nonlinear equations and/or boundary conditions, a Taylor Series expansion is required for linearization of both equations and boundary conditions. The solutions are iterative and in each iteration, a problem like the linear case is solved. It is shown that Miniquasi cannot be applied to the thermoregulatory model as originally planned.

Source record↗
NASA NTRS1973

Program for the solution of multipoint boundary value problems of quasilinear differential equations

Linear equations are solved by a method of superposition of solutions of a sequence of initial value problems. For nonlinear equations and/or boundary conditions, the solution is iterative and in each iteration a problem like the linear case is solved. A simple Taylor series expansion is used for the linearization of both nonlinear equations and nonlinear boundary conditions. The perturbation method of solution is used in preference to quasilinearization because of programming ease, and smaller storage requirements; and experiments indicate that the desired convergence properties exist although no proof or convergence is given.

Source record↗
NASA NTRS1978

On isostatic geoid anomalies

In regions of slowly varying lateral density changes, the gravity and geoid anomalies may be expressed as power series expansions in topography. Geoid anomalies in isostatically compensated regions can be directly related to the local dipole moment of the density-depth distribution. This relationship is used to obtain theoretical geoid anomalies for different models of isostatic compensation. The classical Pratt and Airy models give geoid height-elevation relationships differing in functional form but predicting geoid anomalies of comparable magnitude. The thermal cooling model explaining ocean floor subsidence away from mid-ocean ridges predicts a linear age-geoid height relationship of 0.16 m/m.y. Geos 3 altimetry profiles were examined to test these theoretical relationships. A profile over the mid-Atlantic ridge is closely matched by the geoid curve derived from the thermal cooling model. The observed geoid anomaly over the Atlantic margin of North America can be explained by Airy compensation. The relation between geoid anomaly and bathymetry across the Bermuda Swell is consistent with Pratt compensation with a 100-km depth of compensation.

Haxby, W. F.↗
NASA NTRS1978

Second order approximation of natural frequency constraints in structural synthesis

The paper is concerned with structural optimization problems in which the constraints consist of limits imposed on the natural frequencies of the structure. Improvements in the quality of approximations for the frequency constraints are sought by considering second-order Taylor series expansions. Analysis of the second-order sensitivity of natural frequencies is carried out. As an example, the design of a midplane symmetric aluminum beam of constant depth supporting three nonstructural masses is considered. Web thickness and chord member areas were determined so as to achieve minimum structural mass while maintaining the fundamental frequency at or above 30 Hz.

Miura, H.↗
NASA NTRS1978

Five micron limb-darkening and the structure of the Jovian atmosphere

A combined radiative, dynamical, and chemical model of the Jovian atmosphere is presented which reproduces the observed IR limb-darkening curves for several regions on the disk of Jupiter. Two approaches are used to perform the inversion required for determination of the source function, and a power-series-expansion model is examined, along with a convective-equilibrium model, cloud and intermediate-zone models, and a thin-shell model. The statistical methods used in the analysis are outlined, and model fits to the observations are discussed. The chemistry of phase transitions in the hot spots of Jupiter's equatorial belt is briefly investigated.

Newman, W. I.↗
NASA NTRS1978

Calculation of optical depths from an integral of the Voigt function

The optical depth along a vertical path in an atmosphere in hydrostatic equilibrium can be calculated from an integral of the Voigt function for the case where the absorption is due to spectral lines. Series expansions are presented that allow rapid evaluation of this integral over all values of the independent variables, frequency and pressure.

Milman, A. S.↗
NASA NTRS1980

Maximum likelihood method for estimating airplane stability and control parameters from flight data in frequency domain

A frequency domain maximum likelihood method is developed for the estimation of airplane stability and control parameters from measured data. The model of an airplane is represented by a discrete-type steady state Kalman filter with time variables replaced by their Fourier series expansions. The likelihood function of innovations is formulated, and by its maximization with respect to unknown parameters the estimation algorithm is obtained. This algorithm is then simplified to the output error estimation method with the data in the form of transformed time histories, frequency response curves, or spectral and cross-spectral densities. The development is followed by a discussion on the equivalence of the cost function in the time and frequency domains, and on advantages and disadvantages of the frequency domain approach. The algorithm developed is applied in four examples to the estimation of longitudinal parameters of a general aviation airplane using computer generated and measured data in turbulent and still air. The cost functions in the time and frequency domains are shown to be equivalent; therefore, both approaches are complementary and not contradictory. Despite some computational advantages of parameter estimation in the frequency domain, this approach is limited to linear equations of motion with constant coefficients.

Klein, V.↗
NASA NTRS1979

Shuttle program. Onorbit navigation integrator results for typical shuttle orbits

Three types of navigation onorbit numerical integrators were evaluated: (1) power integrators with no delta-V incorporation, just coasting (using Taylor series expansion integrators); (2) coasting integrators using the Cowell method of special perturbations; and (3) coasting integrator using the Pines variation of parameter perturbation method. Results show that the super G integrator is a very simple and effective for 2 and 4 second time steps. Since IMU delta-V data can be easily incorporated in the integration scheme, its use as the standard onorbit navigation propagator for the maintenance of the current state was implemented in the onboard navigation software. The Pines formulation method with a Runge-Kutta-Gill fourth-order integrator method produces excellent results up to 300 second time steps. On orbit prediction with this method was implemented in the onboard onorbit navigation scheme. The Runge-Kutta third order, using Cowell's method, is an excellent general purpose determination integrator for time steps up to a 60 second duration.

Olszewski, O. W.↗
NASA NTRS1980

A mathematical representation of an advanced helicopter for piloted simulator investigations of control system and display variations

A mathematical model of an advanced helicopter is described. The model is suitable for use in control/display research involving piloted simulation. The general design approach for the six degree of freedom equations of motion is to use the full set of nonlinear gravitational and inertial terms of the equations and to express the aerodynamic forces and moments as the reference values and first order terms of a Taylor series expansion about a reference trajectory defined as a function of longitudinal airspeed. Provisions for several different specific and generic flight control systems are included in the model. The logic required to drive various flight control and weapon delivery symbols on a pilot's electronic display is also provided. Finally, the model includes a simplified representation of low altitude wind and turbulence effects. This model was used in a piloted simulator investigation of the effects of control system and display variations for an attack helicopter mission.

Aiken, E. W.↗
NASA NTRS1979

SCF and CI calculations of the dipole moment function of ozone

The constant and linear terms in a Taylor series expansion of the dipole moment function of the ground state of ozone are calculated with Cartesian Gaussian basis sets ranging in quality from minimal to double zeta plus polarization. Results are presented at both the self-consistent field and configuration-interaction levels. Although the algebraic signs of the linear dipole moment derivatives are all established to be positive, the absolute magnitudes of these quantities, as well as the infrared intensities calculated from them, vary considerably with the level of theory.

Curtiss, L. A.↗
NASA NTRS1980

Iterative solutions for one-dimensional diffusion with time varying surface composition and composition-dependent diffusion coefficient

Solutions are given for one-dimensional diffusion problems with a time varying surface composition and also a composition dependent diffusion coefficient. The most general solution does not require special mathematical functions to fit the variation in surface composition or D(C). In another solution, a series expansion may be used to fit the time dependent surface concentration. These solutions make use of iterative calculations that converge rapidly and are highly stable. Computer times are much shorter than that required for finite difference calculations and can efficiently make use of interactive graphics terminals. Existing gas carburization data were used to provide an illustration of an iterative approach with a time varying carbon composition at the free surface.

Chow, M.↗
NASA NTRS1980

Neutral stability calculations for boundary-layer flows

An analysis is presented of the parallel neutral stability of three-dimensional incompressible, isothermal boundary-layer flows. A Taylor-series expansion of the dispersion relation is used to derive the general eigenvalues. These equations are functions of the complex group velocity. These relations are verified by numerical results obtained for two- and three-dimensional disturbances in two- and three-dimensional flows.

Nayfeh, A. H.↗
NASA NTRS1980

Predicting major element mineral/melt equilibria - A statistical approach

Empirical equations have been developed for calculating the mole fractions of NaO0.5, MgO, AlO1.5, SiO2, KO0.5, CaO, TiO2, and FeO in a solid phase of initially unknown identity given only the composition of the coexisting silicate melt. The approach involves a linear multivariate regression analysis in which solid composition is expressed as a Taylor series expansion of the liquid compositions. An internally consistent precision of approximately 0.94 is obtained, that is, the nature of the liquidus phase in the input data set can be correctly predicted for approximately 94% of the entries. The composition of the liquidus phase may be calculated to better than 5 mol % absolute. An important feature of this 'generalized solid' model is its reversibility; that is, the dependent and independent variables in the linear multivariate regression may be inverted to permit prediction of the composition of a silicate liquid produced by equilibrium partial melting of a polymineralic source assemblage.

Hostetler, C. J.↗
NASA NTRS1982

Far-Field Antenna Pattern From a Near-Field Test

Plane/polar geometry simplifies measurement of near-field data for this antenna and allows a determination of far-field pattern by Jacobi-Bessel series expansion of data. Measuring probe is an undersized, dielectrically loaded and open-ended waveguide with a far-field pattern similar to that of a small magnetic dipole in its forward directions, making it unnecessary to rotate probe in direction similar to antenna rotation.

Rahmat-Samii, Y.↗
NASA NTRS1982

Dielectrophoretic levitation of droplets and bubbles

Uncharged droplets and bubbles can be levitated dielectrophoretically in liquids using strong, nonuniform electric fields. The general equations of motion for a droplet or bubble in an axisymmetric, divergence-free electrostatic field allow determination of the conditions necessary and sufficient for stable levitation. The design of dielectrophoretic (DEP) levitation electrode structures is simplified by a Taylor-series expansion of cusped axisymmetric electrostatic fields. Extensive experimental measurements on bubbles in insulating liquids verify the simple dielectrophoretic model. Other have extended dielectrophoretic levitation to very small particles in aqueous media. Applications of DEP levitation to the study of gas bubbles, liquid droplets, and solid particles are discussed. Some of these applications are of special interest in the reduced gravitational field of a spacecraft.

Jones, T. B.↗
NASA NTRS1982

Toward a better understanding of helicopter stability derivatives

An amended six degree of freedom helicopter stability and control derivative model was developed in which body acceleration and control rate derivatives were included in the Taylor series expansion. These additional derivatives were derived from consideration of the effects of the higher order rotor flapping dynamics, which are known to be inadequately represented in the conventional six degree of freedom, quasistatic stability derivative model. The amended model was a substantial improvement over the conventional model, effectively doubling the unsable bandwidth and providing a more accurate representation of the short period and cross axis characteristics. Further investigations assessed the applicability of the two stability derivative model structures for flight test parameter identification. Parameters were identified using simulation data generated from a higher order base line model having sixth order rotor tip path plane dynamics. Three lower order models were identified: one using the conventional stability derivative model structure, a second using the amended six degree of freedom model structure, and a third model having eight degrees of freedom that included a simplified rotor tip path plane tilt representation.

Hansen, R. S.↗
NASA NTRS1981

Scan performance of dual offset reflector antennas for satellite communications

The basic numerical steps of a method to analyze dual offset reflector antennas are reviewed. The technique employs an alternative approach to calculating the secondary pattern of an arbitrarily shaped offset dual reflector antenna, and is based on the application of the geometrical theory of diffraction from the subreflector and physical optics (PO) scattering from the main reflector. The PO integral is evaluated using the Jacobi-Bessel series expansions, and numerical results are presented for the off-axis scan performance of an offset clear aperture Cassegrain antenna. Results indicate that the equivalent paraboloid concept can be used to determine the location of displaced feed and define the local optimal focal plane, and the scan performance of the Cassegrain reflector can be improved if the feed is located on the true opimal surface.

Rahmat-Samii, Y.↗