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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.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

The equivalent angle-of-attack method for estimating the nonlinear aerodynamic characteristics of missile wings and control surfaces

A method has been developed for estimating the nonlinear aerodynamic characteristics of missile wing and control surfaces. The method is based on the following assumption: if a fin on a body has the same normal-force coefficient as a wing alone composed of two of the same fins joined together at their root chords, then the other force and moment coefficients of the fin and the wing alone are the same including the nonlinearities. The method can be used for deflected fins at arbitrary bank angles and at high angles of attack. In the paper, a full derivation of the method is given, its accuracy demonstrated and its use in extending missile data bases is shown.

Hemsch, M. J.↗
NASA NTRS1982

On ultrasonic factors and fracture toughness

Recent experimental and theoretical studies on ultrasonics have shown that the scattering of elastic waves by material defects yields data which characterize crack properties, such as size and orientation, and also the mechanical properties of the given material. In the present study, elastodynamic fields due to the presence of a pair of inhomogeneities in a material of plate geometry are investigated by the method of equivalent inclusions. The stress amplitude change of the plates during the passage of plane time-harmonic waves is found, and the relation between fracture toughness and ultrasonic factors is determined. The approach used does not assume the existence of a sharp crack in the material.

Fu, L. S.↗
NASA NTRS1982

Computation of transonic viscous-inviscid interacting flow

Transonic viscous-inviscid interaction is considered using the Euler and inverse compressible turbulent boundary-layer equations. Certain improvements in the inverse boundary-layer method are mentioned, along with experiences in using various Runge-Kutta schemes to solve the Euler equations. Numerical conditions imposed on the Euler equations at a surface for viscous-inviscid interaction using the method of equivalent sources are developed, and numerical solutions are presented and compared with experimental data to illustrate essential points.

Whitfield, D. L.↗
NASA NTRS1983

Computation of transonic viscous-inviscid interacting flow

Transonic viscous-inviscid interaction is considered using the Euler and inverse compressible turbulent boundary-layer equations. Certain improvements in the inverse boundary-layer method are mentioned, along with experiences in using various Runge-Kutta schemes to solve the Euler equations. Numerical conditions imposed on the Euler equations at a surface for viscous-inviscid interaction using the method of equivalent sources are developed, and numerical solutions are presented and compared with experimental data to illustrate essential points. Previously announced in STAR N83-17829

Whitfield, D. L.↗
NASA NTRS1983

The contribution of wedge scattering to the radar cross section of the ocean surface

This letter considers the contribution to the radar cross section of the ocean surface due to scattering from edges for which the local radius of curvature is small compared with the radar wavelength. An analytic expression based on the method of equivalent currents is given for such scattering and is evaluated for several assumed sets of parameters. This contribution is shown to augment the Bragg scattering cross section in regions where the latter underestimates the measured radar cross section, while remaining smaller than the Bragg component elsewhere.

Lyzenga, D.↗
NASA NTRS1987

Accuracy of the domain method for the material derivative approach to shape design sensitivities

Numerical accuracy for the boundary and domain methods of the material derivative approach to shape design sensitivities is investigated through the use of mesh refinement. The results show that the domain method is generally more accurate than the boundary method, using the finite element technique. It is also shown that the domain method is equivalent, under certain assumptions, to the implicit differentiation approach not only theoretically but also numerically.

Yang, R. J.↗
NASA NTRS1987

Effects of large deflection and transverse shear on response of rectangular symmetric composite laminates subjected to acoustic excitation

Nonlinear equations of motion of symmetrically laminated anisotropic plates are derived accounting for von Karman strains. The effect of transverse shear is included in the formulation. Using a single-mode Galerkin procedure, the nonlinear modal equation is obtained. The direct equivalent linearization method is employed for solution of this equation. The response to acoustic excitation of moderately thick composite panels is studied. Further, the effects of transverse shear on large deflection vibration of laminates under random excitation are studied. Mean-square deflections and mean-square inplane stresses are obtained for symmetric graphite-epoxy laminates. Using equilibrium equations and the continuity requirements, the mean-square transverse shear stresses are calculated. The results obtained will be useful in the sonic fatigue design of composite aircraft panels. The analysis is presented in detail for simply supported plates. The analogous equations for a clamped case are also obtained.

Mei, Chuh↗
NASA NTRS1987

Higher order diffractions from a circular disk

The backscattering from a circular disk is analyzed using the geometrical theory of diffraction. First-, second-, and third-order diffractions are included in the hard polarization analysis, while first-, second-, and third-order slope diffractions are included for soft polarization. Improvements in the prediction of the monostatic radar cross section over previous works are noted. For hard polarization, an excellent agreement is exhibited between experimental and theoretical results, while a very good agreement is noted for soft polarization. To further improve the soft polarization results for wide angles, a model for the creeping wave or circulating current on the edge of the disk is obtained and used to find an additional component of the backscattered field. The addition of this component significantly improves the results for wide angles, leading to excellent agreement for soft polarization also. An axial-caustic correction method using equivalent currents is also included in the analysis.

Marsland, Diane P.↗
NASA NTRS1989

Effects of transverse shear on large deflection random response of symmetric composite laminates with mixed boundary conditions

Nonlinear equations of motion of symmetrically laminated anisotropic plates are derived considering von Karman strains and transverse shear effects. Using a single-mode Galerkin procedure, the nonlinear modal equation is obtained. The direct equivalent linearization method is employed for solution of this equation. The effects of transverse shear on large deflection vibration of laminated plates with mixed boundary support conditions under random excitation are studied. Mean-square deflections and mean-square inplane strains are obtained for symmetric graphite-epoxy laminates. Using equilibrium equations and the continuity requirements, the mean-square transverse shear stresses are calculated. The results obtained will be useful in the sonic fatigue design of composite aircraft panels. The analysis is presented in detail for plates with two opposing edges simply supported and the remaining edges clamped.

Prasad, C. B.↗
NASA NTRS1989

A finite element formulation for the large deflection random response of thermally buckled plates

By using the linear mode shapes of a thermally buckled structure, a governing system of finite element equations for large-deflection random vibrations is reduced to a system of nonlinear modal equations. This system is then solved using the method of equivalent linearization. The methodology developed in this study is applicable to the design of aerospace vehicles subjected to combined thermal/acoustic loads.

Locke, James↗
NASA NTRS1989

Ray analysis of modal reflection for three-dimensional open-ended waveguides

An efficient high-frequency ray analysis, which combines the geometrical theory of diffraction (GTD) with the equivalent current method, is used for evaluating modal reflection at the open ends of three-dimensional waveguides. After reviewing a method used for the two-dimensional case and introducing some extensions necessary for evaluating modal reflection of open-ended three-dimensional waveguides, the modal reflection coefficients are then given for open-ended circular and rectangular waveguides. Numerical results calculated using these expressions agree favorably with those obtained by a different analytical technique and by experiment.

Chuang, C. W.↗
NASA NTRS1990

Mutual coupling between circular apertures on an infinite conducting ground plane and radiating into a finite width slab

The problem of electromagnetic coupling between two horns is of interest for the Microwave Reflectometer Ionization Sensor (MRIS) that will be used in the Aeroassist Flight Experiment (AFE). Laboratory measurements of mutual coupling between conical horns (using a flat metallic reflector to simulate a critically dense plasma outside) have shown a strong dependence on the finite dimensions of the shuttle tile over the apertures. Since both, the dielectric tile and the plasma outside the tile reflect microwaves, a study should be done to isolate the two mechanisms so that the MRIS reentry flight data can be interpreted correctly. Once the coupling due to the tile itself is determined then the location of the critial electron number density layers can be determined. As a first attempt to tackle this problem the Geometrical Theory of Diffraction was used to modify the existing solution to mutual coupling between apertures with infinite dielectric sheets. By using the equivalent current method, aperture theory to determine the radiated fields inside the dielectric tiles, and ray tracing the contributions to mutual coupling were determined. Results from two cases with different tile thicknesses have indicated that the main contribution to mutual coupling is due to diffraction from the bottom and top (back and front) wedges.

Christodoulou, Christos↗
NASA NTRS1991

High-frequency techniques for RCS prediction of plate geometries

Several different high-frequency methods for modeling the radar cross sections (RCSs) of plate geometries are examined. The Method of Equivalent Currents and a numerically derived corner diffraction coefficient are used to model the RCS of a rectangular, perfectly conducting plate in nonprincipal planes. The Uniform Theory of Diffraction is used to model the RCS of a rectangular, perfectly conducting plate in principal planes. For the soft polarization case, first-order and slope-diffraction terms are included. For the hard polarization case, up to four orders of diffraction are included. Finally, the Uniform Theory of Diffraction for impedance wedges and the Impedance Boundary Condition are used to model the RCS of a coated, rectangular plate in principal planes. In most of the cases considered, comparisons are made between theoretical and experimental results.

Balanis, Constantine A.↗
NASA NTRS1991

High-frequency techniques for RCS prediction of plate geometries

Radar cross section (RCS) prediction of several rectangular plate geometries is discussed using high-frequency techniques such as the Uniform Theory of Diffraction (UTD) for perfectly conducting and impedance wedges and the Method of Equivalent Currents (MEC). Previous reports have presented detailed solutions to the principal-plane scattering by a perfectly conducting and a coated rectangular plate and nonprincipal-plane scattering by a perfectly conducting plate. These solutions are briefly reviewed and a modified model is presented for the coated plate. Theoretical and experimental data are presented for the perfectly conducting geometries. Agreement between theory and experiment is very good near and at normal incidence. In regions near and at grazing incidence, the disagreement between the data vary according to diffraction distances and angles involved. It is these areas of disagreement which are of extreme interest as an explanation for the disagreement will yield invaluable insight into scattering mechanisms which are not yet identified as major contributors near and at grazing incidence. Areas of disagreement between theory and experiment are identified and examined in an attempt to better understand and predict near-grazing incidence, grazing incidence, and nonprincipal-plane diffractions.

Balanis, Constantine A.↗
NASA NTRS1992

Schroedinger's radial equation - Solution by extrapolation

A high-accuracy numerical method for the solution of a 1D Schroedinger equation that is suitable for a diatomic molecule, obtained by combining a finite-difference method with iterative extrapolation to the limit, is presently shown to have several advantages over more conventional methods. Initial guesses for the term values are obviated, and implementation of the algorithm is straightforward. The method is both less sensitive to round-off error, and faster than conventional methods for equivalent accuracy. These advantages are illustrated through the solution of Schroedinger's equation for a Morse potential function suited for HCl and a numerically derived Rydberg-Klein-Rees potential function for the X 1Sigma(+) state of CO.

Goorvitch, D.↗
NASA NTRS1993

On the cross-stream spectral method for the Orr-Sommerfeld equation

Cross-stream models are defined as solutions to the Orr-Sommerfeld equation which are propagating normal to the flow direction. These models are utilized as a basis for a Hilbert space to approximate the spectrum of the Orr-Sommerfeld equation with plane Poiseuille flow. The cross-stream basis leads to a standard eigenvalue problem for the frequencies of Poiseuille flow instability waves. The coefficient matrix in the eigenvalue problem is shown to be the sum of a real matrix and a negative-imaginary diagonal matrix which represents the frequencies of the cross-stream modes. The real coefficient matrix is shown to approach a Toeplitz matrix when the row and column indices are large. The Toeplitz matrix is diagonally dominant, and the diagonal elements vary inversely in magnitude with diagonal position. The Poiseuille flow eigenvalues are shown to lie within Gersgorin disks with radii bounded by the product of the average flow speed and the axial wavenumber. It is shown that the eigenvalues approach the Gersgorin disk centers when the mode index is large, so that the method may be used to compute spectra with an essentially unlimited number of elements. When the mode index is large, the real part of the eigenvalue is the product of the axial wavenumber and the average flow speed, and the imaginary part of the eigen value is identical to the corresponding cross-stream mode frequency. The cross-stream method is numerically well-conditioned in comparison to Chebyshev based methods, providing equivalent accuracy for small mode indices and superior accuracy for large indices.

Zorumski, William E.↗