SEARCH · Search NASA

Results for “Equivalence Method”

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 NTRS1985

Periodic solutions of second-order nonlinear difference equations containing a small parameter. II - Equivalent linearization

The classical method of equivalent linearization is extended to a particular class of nonlinear difference equations. It is shown that the method can be used to obtain an approximation of the periodic solutions of these equations. In particular, the parameters of the limit cycle and the limit points can be determined. Three examples illustrating the method are presented.

Mickens, R. E.↗

NASA NTRS1999

Static and Vibration Analyses of General Wing Structures Using Equivalent Plate Models

An efficient method, using equivalent plate model, is developed for studying the static and vibration analyses of general built-up wing structures composed of skins, spars, and ribs. The model includes the transverse shear effects by treating the built-up wing as a plate following the Reissner-Mindlin theory, the so-called First-order Shear Deformation Theory (FSDT). The Ritz method is used with the Legendre polynomials being employed as the trial functions. This is in contrast to previous equivalent plate model methods which have used simple polynomials, known to be prone to numerical ill-conditioning, as the trial functions. The present developments are evaluated by comparing the results with those obtained using MSC/NASTRAN, for a set of examples. These examples are: (i) free-vibration analysis of a clamped trapezoidal plate with (a) uniform thickness, and (b) non-uniform thickness varying as an airfoil, (ii) free-vibration and static analyses (including skin stress distribution) of a general built-up wing, and (iii) free-vibration and static analyses of a swept-back box wing. The results obtained by the present equivalent plate model are in good agreement with those obtained by the finite element method.

Kapania, Rakesh K.↗

NASA NTRS2004

Investigation of Acoustical Shielding by a Wedge-Shaped Airframe

Experiments on a scale model of an advanced unconventional subsonic transport concept, the Blended Wing Body (BWB), have demonstrated significant shielding of inlet-radiated noise. A computational model of the shielding mechanism has been developed using a combination of boundary integral equation method (BIEM) and equivalent source method (ESM). The computation models the incident sound from a point source in a nacelle and determines the scattered sound field. In this way the sound fields with and without the airfoil can be estimated for comparison to experiment. An experimental test bed using a simplified wedge-shape airfoil and a broadband point noise source in a simulated nacelle has been developed for the purposes of verifying the analytical model and also to study the effect of engine nacelle placement on shielding. The experimental study is conducted in the Anechoic Noise Research Facility at NASA Langley Research Center. The analytic and experimental results are compared at 6300 and 8000 Hz. These frequencies correspond to approximately 150 Hz on the full scale aircraft. Comparison between the experimental and analytic results is quite good, not only for the noise scattering by the airframe, but also for the total sound pressure in the far field. Many of the details of the sound field that the analytic model predicts are seen or indicated in the experiment, within the spatial resolution limitations of the experiment. Changing nacelle location produces comparable changes in noise shielding contours evaluated analytically and experimentally. Future work in the project will be enhancement of the analytic model to extend the analysis to higher frequencies corresponding to the blade passage frequency of the high bypass ratio ducted fan engines that are expected to power the BWB.

Gerhold, Carl H.↗

NASA NTRS2006

Investigation of Acoustical Shielding by a Wedge-Shaped Airframe

Gerhold, Carl H.↗

NASA NTRS1994

On the wavelet optimized finite difference method

When one considers the effect in the physical space, Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small scale structure exists. Adding a wavelet basis function at a given scale and location where one has a correspondingly large wavelet coefficient is, essentially, equivalent to adding a grid point, or two, at the same location and at a grid density which corresponds to the wavelet scale. This paper introduces a wavelet optimized finite difference method which is equivalent to a wavelet method in its multiresolution approach but which does not suffer from difficulties with nonlinear terms and boundary conditions, since all calculations are done in the physical space. With this method one can obtain an arbitrarily good approximation to a conservative difference method for solving nonlinear conservation laws.

Jameson, Leland↗

NASA NTRS1993

On the Daubechies-based wavelet differentiation matrix

The differentiation matrix for a Daubechies-based wavelet basis is constructed and superconvergence is proven. That is, it will be proven that under the assumption of periodic boundary conditions that the differentiation matrix is accurate of order 2M, even though the approximation subspace can represent exactly only polynomials up to degree M-1, where M is the number of vanishing moments of the associated wavelet. It is illustrated that Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small-scale structure is present.

Jameson, Leland↗

NASA NTRS1995

Spectral methods on arbitrary grids

Stable and spectrally accurate numerical methods are constructed on arbitrary grids for partial differential equations. These new methods are equivalent to conventional spectral methods but do not rely on specific grid distributions. Specifically, we show how to implement Legendre Galerkin, Legendre collocation, and Laguerre Galerkin methodology on arbitrary grids.

Carpenter, Mark H.↗

NASA NTRS2006

Reconstruction of the Acoustic Field Using a Conformal Array

Near-field acoustical holography (NAH) requires the measurement of the near-field pressure field over a conformal and closed surface in order to recover the acoustic field on a nearby surface. We are interested in the reconstruction of the acoustic field over the fuselage of a Boeing 757 airplane when pressure data is available over an array of microphones that are conformal to the fuselage surface. In this case the strict NAH theory does not hold, but still there are techniques used to overcome this difficulty. The best known is patch NAH, which has been used for planar surfaces. In this work we will discuss two new techniques used for surfaces with an arbitrarily shape: patch inverse boundary element methods (IBEM) and patch equivalent sources method (ESM). We will discuss the theoretical justification of the method and show reconstructions for in-flight data taken inside a Boeing 757 airplane.

Valdivia, Nichlas P.↗

NASA NTRS1987

A finite element large deflection random response analysis of beams and plates subjected to acoustic loading

A finite element formulation is presented for the analysis of beams and rectangular plates undergoing large deflections subjected to Gaussian white noise excitations. Single-mode response is assumed in the present formulation. Root-mean-square (RMS) maximum deflections for simply supported and clamped beams and plates at various sound spectrum levels are obtained and compared with solutions using the Fokker-Planck-Kolmogorov equation and the equivalent linearization methods. RMS maximum stains and equivalent linear frequencies are compared with the equivalent linearization results for assessment of the accuracy of the finite element method.

Mei, Chuh↗

NASA NTRS1987

A simple method to model truss-beams as equivalent continua

A new method is presented for obtaining stiffness constants for structures modeled as three-dimensional linear elastic beams. The three-dimensional lattice is comprised of multiple two-dimensional lattices. Matrix manipulation is used to determine the contribution of each two-dimensional substructure to the complete three dimensional lattice.

Barton, O., Jr.↗

NASA NTRS1993

The probabilistic neural network architecture for high speed classification of remotely sensed imagery

In this paper we discuss a neural network architecture (the Probabilistic Neural Net or the PNN) that, to the best of our knowledge, has not previously been applied to remotely sensed data. The PNN is a supervised non-parametric classification algorithm as opposed to the Gaussian maximum likelihood classifier (GMLC). The PNN works by fitting a Gaussian kernel to each training point. The width of the Gaussian is controlled by a tuning parameter called the window width. If very small widths are used, the method is equivalent to the nearest neighbor method. For large windows, the PNN behaves like the GMLC. The basic implementation of the PNN requires no training time at all. In this respect it is far better than the commonly used backpropagation neural network which can be shown to take O(N6) time for training where N is the dimensionality of the input vector. In addition the PNN can be implemented in a feed forward mode in hardware. The disadvantage of the PNN is that it requires all the training data to be stored. Some solutions to this problem are discussed in the paper. Finally, we discuss the accuracy of the PNN with respect to the GMLC and the backpropagation neural network (BPNN). The PNN is shown to be better than GMLC and not as good as the BPNN with regards to classification accuracy.

Chettri, Samir R.↗

NASA NTRS2011

Collocation and Galerkin Time-Stepping Methods

We study the numerical solutions of ordinary differential equations by one-step methods where the solution at tn is known and that at t(sub n+1) is to be calculated. The approaches employed are collocation, continuous Galerkin (CG) and discontinuous Galerkin (DG). Relations among these three approaches are established. A quadrature formula using s evaluation points is employed for the Galerkin formulations. We show that with such a quadrature, the CG method is identical to the collocation method using quadrature points as collocation points. Furthermore, if the quadrature formula is the right Radau one (including t(sub n+1)), then the DG and CG methods also become identical, and they reduce to the Radau IIA collocation method. In addition, we present a generalization of DG that yields a method identical to CG and collocation with arbitrary collocation points. Thus, the collocation, CG, and generalized DG methods are equivalent, and the latter two methods can be formulated using the differential instead of integral equation. Finally, all schemes discussed can be cast as s-stage implicit Runge-Kutta methods.

Huynh, H. T.↗

NASA NTRS1988

Equivalent linearization for fatigue life estimates of a nonlinear structure

An adaptation of the method of equivalent linearization is developed in order to estimate the fatigue life of a nonlinear structure excited by Gaussian white noise. While conventional equivalent linearization has been successfully applied to approximate the mean square responses of the variety of complex nonlinear systems, it has not been possible to apply the method for fatigue predictions. This limitation results from the assumption that the probability density of the response of the nonlinear system is Gaussian, which is not generally true. In the present effort, a modification of equivalent linearization, developed by the author, is employed which has been shown in recent studies to provide a much more accurate description of the random response of a nonlinear structure than provided by conventional equivalent linearization. A method is presented for estimating fatigue life based on this approach and results are compared with those obtained using both numerical simulation and the classical method. The fatigue life is estimated for a nonlinear plate vibrating in a single resonant mode with random white noise excitation. Excellent agreement is found between all three methods. These results indicate that equivalent linearization may be extended to predict the fatigue life of more complex nonlinear systems than can be analyzed at present.

Miles, R. N.↗

NASA NTRS1985

Distribution of Snow and Maximum Snow Water Equivalent Obtained by LANDSAT Data and Degree Day Method

Maximum snow water equivalence and snowcover distribution are estimated using several LANDSAT data taken in snowmelting season over a four year period. The test site is Okutadami-gawa Basin located in the central position of Tohoku-Kanto-Chubu District. The year to year normalization for snowmelt volume computation on the snow line is conducted by year to year correction of degree days using the snowcover percentage within the test basin obtained from LANDSAT data. The maximum snow water equivalent map in the test basin is generated based on the normalized snowmelt volume on the snow line extracted from four LANDSAT data taken in a different year. The snowcover distribution on an arbitrary day in snowmelting of 1982 is estimated from the maximum snow water equivalent map. The estimated snowcover is compared with the snowcover area extracted from NOAA-AVHRR data taken on the same day. The applicability of the snow estimation using LANDSAT data is discussed.

Takeda, K.↗

NASA NTRS2002

Constitutive Modeling of Nanotube/Polymer Composites with Various Nanotube Orientations

In this study, a technique has been proposed for developing constitutive models for polymer composite systems reinforced with single-walled carbon nanotubes (SWNT) with various orientations with respect to the bulk material coordinates. A nanotube, the local polymer adjacent to the nanotube, and the nanotube/polymer interface have been modeled as an equivalent-continuum fiber by using an equivalent-continuum modeling method. The equivalent-continuum fiber accounts for the local molecular structure and bonding information and serves as a means for incorporating micromechanical analyses for the prediction of bulk mechanical properties of SWNT/polymer composite. As an example, the proposed approach is used for the constitutive modeling of a SWNT/LaRC-SI (with a PmPV interface) composite system, with aligned nanotubes, three-dimensionally randomly oriented nanotubes, and nanotubes oriented with varying degrees of axisymmetry. It is shown that the Young s modulus is highly dependent on the SWNT orientation distribution.

Odegard, Gregory M.↗

NASA NTRS1977

A critical study of higher-order numerical methods for solving the boundary-layer equations

A fourth-order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations. The efficiency of the present method is compared with other two-point and three-point higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, and the three-point spline methods. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.

Wornom, S. F.↗

NASA NTRS1978

Application of higher-order numerical methods to the boundary-layer equations

A fourth-order method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations for both attached and separated flows. The efficiency of the present method is compared with other higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, the three-point spline methods, and a modified finite-element method. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.

Wornom, S. F.↗

NASA NTRS1978

Critical study of higher order numerical methods for solving the boundary-layer equations

A fourth order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method, which is the natural extension of the second order box scheme to fourth order, was demonstrated with application to the incompressible, laminar and turbulent, boundary layer equations. The efficiency of the present method is compared with two point and three point higher order methods, namely, the Keller box scheme with Richardson extrapolation, the method of deferred corrections, a three point spline method, and a modified finite element method. For equivalent accuracy, numerical results show the present method to be more efficient than higher order methods for both laminar and turbulent flows.

Wornom, S. F.↗