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Results for “Analytic linearization”

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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At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Wave transience in a compressible atmosphere. I - Transient internal wave, mean-flow interaction. II - Transient equatorial waves in the quasi-biennial oscillation

Analytical and numerical solutions are obtained in an approximate quasi-linear model, to describe the way in which vertically propagating waves give rise to mean flow accelerations in an atmosphere due to the effects of wave transience. These effects in turn result from compressibility and vertical group velocity feedback, and culminate in the spontaneous formation and descent of regions of strong mean wind shear. The numerical solutions display mean flow accelerations due to Kelvin waves in the equatorial stratosphere, with wave absorption altering the transience mechanism in such significant respects as causing the upper atmospheric mean flow acceleration to be very sensitive to the precise magnitude and distribution of the damping mechanisms. The numerical simulations of transient equatorial waves in the quasi-biennial oscillation are also considered.

Dunkerton, T. J.↗
NASA NTRS1981

Magnetically induced cylindrical stress waves in a thermoelastic conductor

The problem of stress wave generation in a linear thermoelastic solid by a pulsed magnetic field is investigated both analytically and experimentally for a cylindrically symmetric conducting solid. A dynamic response analysis is developed to correlate magnetic, thermal, and stress fields in the solid with the time history of the electric current. In the experiment, a transient magnetic field was applied normal to a large conducting plate with a circular hole. Initially the field was confined to the interior of the circular hole. The field was generated by discharging a large capacitor bank through a solenoidal coil. The plane-stress cylindrical stress waves are 1-D in nature. The relative effects of the magnetic body force and thermoelastic stresses, both generated by the electromagnetic field, are assessed.

Chian, C. T.↗
NASA NTRS1983

Optimum placement of controls for static deformations of space structures

The placement of thermal or force actuators to control slowly varying disturbances in the shape of large space structures is investigated analytically. Expressions are derived based on disturbances defined as the worst linear combination of a given set of functions and minimized numerically using the NEWSUMT optimization package. Results are presented in tables and graphs for a free-free beam with equidistant controls and polynomial-form (order 2-6) disturbances. Control placement is found to be of greater importance for force actuators, but is also of significance for thermal actuators.

Haftka, R. T.↗
NASA NTRS1984

A rotor optimization using regression analysis

The design and development of helicopter rotors is subject to the many design variables and their interactions that effect rotor operation. Until recently, selection of rotor design variables to achieve specified rotor operational qualities has been a costly, time consuming, repetitive task. For the past several years, Kaman Aerospace Corporation has successfully applied multiple linear regression analysis, coupled with optimization and sensitivity procedures, in the analytical design of rotor systems. It is concluded that approximating equations can be developed rapidly for a multiplicity of objective and constraint functions and optimizations can be performed in a rapid and cost effective manner; the number and/or range of design variables can be increased by expanding the data base and developing approximating functions to reflect the expanded design space; the order of the approximating equations can be expanded easily to improve correlation between analyzer results and the approximating equations; gradients of the approximating equations can be calculated easily and these gradients are smooth functions reducing the risk of numerical problems in the optimization; the use of approximating functions allows the problem to be started easily and rapidly from various initial designs to enhance the probability of finding a global optimum; and the approximating equations are independent of the analysis or optimization codes used.

Giansante, N.↗
NASA NTRS1987

Dynamic performance of squeeze-film bearings

Earlier work has shown that oil-film forces can be modelled by linear coefficients. Identification techniques were used to generate numerical values for these coefficients. This paper has shown the invalidity of applying the perturbation techniques normally used in bearing studies to derive expressions for linearized coefficients to represent a cavitated oil-film. An alternative approach was developed based upon energy techniques to obtain estimates for linearized coefficients. Some current work being undertaken suggests that an alternative analytical approach is possible. These results will be reported in due course.

Burrow, C. R.↗
NASA NTRS1988

The nonlinear dynamics of a spacecraft coupled to the vibration of a contained fluid

The dynamics of a linear spacecraft mode coupled to a nonlinear low gravity slosh of a fluid in a cylindrical tank is investigated. Coupled, nonlinear equations of motion for the fluid-spacecraft dynamics are derived through an assumed mode Lagrangian method. Unlike linear fluid slosh models, this nonlinear slosh model retains two fundamental slosh modes and three secondary modes. An approximate perturbation solution of the equations of motion indicates that the nonlinear coupled system response involves fluid-spacecraft modal resonances not predicted by either a linear, or a nonlinear, uncoupled slosh analysis. Experimental results substantiate the analytical predictions.

Peterson, Lee D.↗
NASA NTRS1988

Direct assessment of two-dimensional wind-tunnel interference from measurements on two interfaces

A direct assessment of two-dimensional wind-tunnel wall interference using upwash component measured on two interfaces has been formulated by the Prandtl-Glauert equation of the flow field and solved by the Fourier transform technique. The analytic formulae obtained for the interference of upwash and pressure on the model are presented. The formulae have been applied successfully to the analytic models for lifting and blockage interferences induced by the general linear slotted and perforated tunnel wall boundary conditions. The formulae have been derived in terms of Fourier coefficients of the measured upwash and illustrated its merits applying to a wavy-wall model case.

Lo, Ching F.↗
NASA NTRS1989

Characterization of the bending stiffness of large space structure joints

A technique for estimating the bending stiffness of large space structure joints is developed and demonstrated for an erectable joint concept. Experimental load-deflection data from a three-point bending test was used as input to solve a closed-form expression for the joint bending stiffness which was derived from linear beam theory. Potential error sources in both the experimental and analytical procedures are identified and discussed. The bending stiffness of a mechanically preloaded erectable joint is studied at three applied moments and seven joint orientations. Using this technique, the joint bending stiffness was bounded between 6 and 17 percent of the bending stiffness of the graphite/epoxy strut member.

Wu, K. Chauncey↗
NASA NTRS1991

Sliding mode control of magnetic suspensions for precision pointing and tracking applications

A recently developed nonlinear control method, sliding mode control, is examined as a means of advancing the achievable performance of space-based precision pointing and tracking systems that use nonlinear magnetic actuators. Analytic results indicate that sliding mode control improves performance compared to linear control approaches. In order to realize these performance improvements, precise knowledge of the plant is required. Additionally, the interaction of an estimating scheme and the sliding mode controller has not been fully examined in the literature. Estimation schemes were designed for use with this sliding mode controller that do not seriously degrade system performance. The authors designed and built a laboratory testbed to determine the feasibility of utilizing sliding mode control in these types of applications. Using this testbed, experimental verification of the authors' analyses is ongoing.

Misovec, Kathleen M.↗
NASA NTRS1991

Dynamic characteristics of joint dominated space trusses

The rotational stiffness of hinge joints, and the gap of the joints applied in large deployable trusses, have been experimentally shown to have a significant role in determining such structures' dynamic behavior; an analytical validation of these results is presented for the case where linear rotation springs are used to model the hinge joints employed in a simple beam in trusses. The results obtained indicate that the natural frequencies of these structures depend not only on joint stiffness but also on joint location. Such gap parameters as gap size, stiffness, position, and excitation-force levels, are discussed with a view to a deeper understanding of their effects on a space interferometry system's simulated dynamic responses.

Shih, Choon-Foo↗
NASA NTRS1993

Summation by parts, projections, and stability

We have derived stability results for high-order finite difference approximations of mixed hyperbolic-parabolic initial-boundary value problems (IBVP). The results are obtained using summation by parts and a new way of representing general linear boundary conditions as an orthogonal projection. By slightly rearranging the analytic equations, we can prove strict stability for hyperbolic-parabolic IBVP. Furthermore, we generalize our technique so as to yield strict stability on curvilinear non-smooth domains in two space dimensions. Finally, we show how to incorporate inhomogeneous boundary data while retaining strict stability. Using the same procedure one can prove strict stability in higher dimensions as well.

Olsson, Pelle↗
NASA NTRS1994

Analytical procedures for estimating structural response to acoustic fields generated by advanced launch systems, phase 2

This report supplements a previous report of the same title submitted in June, 1992. It summarizes additional analytical techniques which have been developed for predicting the response of linear and nonlinear structures to noise excitations generated by large propulsion power plants. The report is divided into nine chapters. The first two deal with incomplete knowledge of boundary conditions of engineering structures. The incomplete knowledge is characterized by a convex set, and its diagnosis is formulated as a multi-hypothesis discrete decision-making algorithm with attendant criteria of adaptive termination.

Elishakoff, Isaac↗
NASA NTRS1996

Conversion of Osculating Orbital Elements to Mean Orbital Elements

Orbit determination and ephemeris generation or prediction over relatively long elapsed times can be accomplished with mean elements. The most simple and efficient method for orbit determination, which is also known as epoch point conversion, performs the conversion of osculating elements to mean elements by iterative procedures. Previous epoch point conversion methods are restricted to shorter elapsed times with linear convergence. The new method presented in this paper calculates an analytic initial guess of the unknown mean elements from a first order theory of secular perturbations and computes a transition matrix with accurate numerical partials. It thereby eliminates the problem of an inaccurate initial guess and an identity transition matrix employed by previous methods. With a good initial guess of the unknown mean elements and an accurate transition matrix, converging osculating elements to mean elements can be accomplished over long elapsed times with quadratic convergence.

Der, Gim J.↗
NASA NTRS2003

Analytical and Experimental Study of Near-Threshold Interactions Between Crack Closure Mechanisms

The results of an analytical closure model that considers contributions and interactions between plasticity-, roughness-, and oxide-induced crack closure mechanisms are presented and compared with experimental data. The analytical model is shown to provide a good description of the combined influences of crack roughness, oxide debris, and plasticity in the near-threshold regime. Furthermore, analytical results indicate that closure mechanisms interact in a non-linear manner such that the total amount of closure is not the sum of closure contributions for each mechanism.

Newman, John A.↗
NASA NTRS2012

Calculation of Sensitivity Derivatives in an MDAO Framework

During gradient-based optimization of a system, it is necessary to generate the derivatives of each objective and constraint with respect to each design parameter. If the system is multidisciplinary, it may consist of a set of smaller "components" with some arbitrary data interconnection and process work ow. Analytical derivatives in these components can be used to improve the speed and accuracy of the derivative calculation over a purely numerical calculation; however, a multidisciplinary system may include both components for which derivatives are available and components for which they are not. Three methods to calculate the sensitivity of a mixed multidisciplinary system are presented: the finite difference method, where the derivatives are calculated numerically; the chain rule method, where the derivatives are successively cascaded along the system's network graph; and the analytic method, where the derivatives come from the solution of a linear system of equations. Some improvements to these methods, to accommodate mixed multidisciplinary systems, are also presented; in particular, a new method is introduced to allow existing derivatives to be used inside of finite difference. All three methods are implemented and demonstrated in the open-source MDAO framework OpenMDAO. It was found that there are advantages to each of them depending on the system being solved.

Moore, Kenneth T.↗
NASA NTRS2013

Analytical Algorithms to Quantify the Uncertainty in Remaining Useful Life Prediction

This paper investigates the use of analytical algorithms to quantify the uncertainty in the remaining useful life (RUL) estimate of components used in aerospace applications. The prediction of RUL is affected by several sources of uncertainty and it is important to systematically quantify their combined effect by computing the uncertainty in the RUL prediction in order to aid risk assessment, risk mitigation, and decisionmaking. While sampling-based algorithms have been conventionally used for quantifying the uncertainty in RUL, analytical algorithms are computationally cheaper and sometimes, are better suited for online decision-making. While exact analytical algorithms are available only for certain special cases (for e.g., linear models with Gaussian variables), effective approximations can be made using the the first-order second moment method (FOSM), the first-order reliability method (FORM), and the inverse first-order reliability method (Inverse FORM). These methods can be used not only to calculate the entire probability distribution of RUL but also to obtain probability bounds on RUL. This paper explains these three methods in detail and illustrates them using the state-space model of a lithium-ion battery.

Sankararaman, Shankar↗
NASA NTRS2020

Non-linear Least Square Fitting Technique for the Determination of Field Line Resonance Frequency in Ground Magnetometer Data: Application to Remote Sensing of Plasmaspheric Mass Density

The accurate determination of the Field Line Resonance (FLR) frequency of a resonating geomagnetic field line is necessary to remotely monitor the plasmaspheric mass density during geomagnetic storms and quiet times alike. Under certain assumptions the plasmaspheric mass density at the equator is inversely proportional to the square of the FLR frequency. The most common techniques to determine the FLR frequency from ground magnetometer measurements are the amplitude ratio and phase difference techniques, both based on geomagnetic field observations at two latitudinally separated ground stations along the same magnetic meridian. Previously developed automated techniques have used statistical methods to pinpoint the FLR frequency using the amplitude ratio and phase difference calculations. We now introduce a physics-based automated technique, using non-linear least square fitting of the ground magnetometer data to the analytical resonant wave equations, that reproduces the wave characteristics on the ground, and from those determine the FLR frequency. One of the advantages of the new technique is the estimation of physics-based errors of the FLR frequency, and as a result of the equatorial plasmaspheric mass density. We present analytical results of the new technique, and test it using data from the Inner-Magnetospheric Array for Geospace Science (iMAGS) ground magnetometer chain along the coast of Chile and the east coast of the United States. We compare the results with the results of previously published statistical automated techniques.

A. Boudouridis↗