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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Antenna pattern control using impedance surfaces

A hybrid numerical technique is developed for electrically large pyramidal horn antennas radiating in free space. A stepped-waveguide method is used to analyze the interior surfaces of the horn transition. The Electric Field Integral Equation (EFIE) is employed on the outer surfaces of the pyramidal horn including the radiating aperture. Meanwhile, the Magnetic Field Integral Equation (MFIE) is used on the aperture to relate the aperture fields and those in the horn transition. The resultant hybrid field integral equation (HFIE) is solved numerically by the method of moments. This formulation is both accurate and numerically stable so that high-gain microwave pyramidal horns can be analyzed rigorously. Far-field radiation patterns, both computed and measured, are presented for three electrically-large x-band horn antennas. The comparisons demonstrate that this method is accurate enough to predict the fine pattern structure at wide angles and in the back region. Computed far-field patterns and aperture field distribution of two smaller x-band horns are also presented along with a discussion on the validity of the approximate aperture field distributions routinely used in the analysis and design of pyramidal horns.

Balanis, Constantine A.↗
NASA NTRS1993

Analytical evaluation of a surface integral expressing the coupling between interior and exterior volumes in a FE-IE approach

Recently an approach which combines the finite element technique and an integral equation to determine the fields scattered by inhomogeneous bodies of complicated shape has been proposed. Basically, a mathematical surface which encloses the scatterers is introduced, thus dividing the space into an interior and an exterior volume, in which the finite element technique and an integral equation for EM scattering, respectively, are applied. The integral equation is set up for the tangential components of the fields at the surface, while the interior volume the unknowns are the total fields. Continuity of the tangential fields at the boundary, as required by Maxwell's equations, is imposed, thus coupling the two methods to obtain a consistent solution. The coupling term is expressed by a surface integral formed by the dot product of a FE basis function and an IE testing function, or viceversa. By choosing the boundary to be a surface of revolution and by making a convenient selection of IE basis (testing) functions, it is possible to evaluate the integrals analytically on surfaces such as curved triangles, curved quadrilaterals and curved pentagons. We will illustrate the salient steps involved in setting up and carrying out these integrals and discuss what class of basis (testing) functions and analytic surfaces of revolution they are applicable to. Analytic calculations offer the advantage of better accuracy than purely numerical ones, and, when combined with them, often shed light on issues of numerical convergence and limiting values. Furthermore, they may reduce computation time and storage requirements.

Zuffada, C.↗
NASA NTRS1974

Application of unsteady lifting surface theory to propellers in forward flight

Development of a theory for determining the aerodynamic forces for unsteady, compressible subsonic flow on a propeller in forward flight. The acceleration potential method is used in developing the basic downwash integral equation which governs the flow. This integral equation is solved by the doublet-lattice method, which consists of placing 'load' lines at certain locations on the chord and satisfying the downwash condition at other selected positions. The examples presented include the spanwise and chordwise loading on a rotating propeller for incompressible flow, an example of compressible flow calculations, and, finally, a calculation illustrating the loss of aerodynamic damping of a propeller blade due to the passage of the blade over its own wake.

Hammond, C. E.↗
NASA NTRS1973

Two bonded half planes with a crack going through the interface

The plane problem of two bonded elastic half planes containing a finite crack perpendicular to and going through the interface is considered. The problem is formulated as a system of singular integral equations with generalized Cauchy kernels. Even though the system has three irregular points, it is shown that the unknown functions are algebraically related at the irregular point on the interface and the integral equations can be solved by a method developed previously. The system of integral equations is shown to yield the same characteristic equation as that for two bonded quarter planes in the general case of the through crack, and the characteristic equation for a crack tip terminating at the interface in the special case. The numerical results given in the paper include the stress intensity factors at the crack tips, the normal and shear components of the stress intensity factors at the singular point on the interface, and the crack surface displacements.

Erdogan, F.↗
NASA NTRS1986

The crack problem in a reinforced cylindrical shell

In this paper a partially reinforced cylinder containing an axial through crack is considered. The reinforcement is assumed to be fully bonded to the main cylinder. The composite cylinder is thus modelled by a nonhomogeneous shell having a step change in the elastic properties at the z=0 plane, z being the axial coordinate. Using a Reissner type transverse shear theory the problem is reduced to a pair of singular integral equations. In the special case of a crack tip touching the bimaterial interface it is shown that the dominant parts of the kernels of the integral equations associated with both membrane loading and bending of the shell reduce to the generalized Cauchy kernel obtained for the corresponding plane stress case. The integral equations are solved and the stress intensity factors are given for various crack and shell dimensions. A bonded fiberglass reinforcement which may serve as a crack arrestor is used as an example.

Yahsi, O. S.↗
NASA NTRS1986

The crack problem in a reinforced cylindrical shell

A partially reinforced cylinder containing an axial through crack is considered. The reinforcement is assumed to be fully bonded to the main cylinder. The composite cylinder is thus modelled by a nonhomogeneous shell having a step change in the elastic properties at the z = 0 plane, z being the axial coordinate. Using a Reissner type transverse shear theory the problem is reduced to a pair of singular integral equations. In the special case of a crack tip touching the bimaterial interface it is shown that the dominant parts of the kernels of the integral equations associated with both membrane loading and bending of the shell reduce to the generalized Cauchy kernel obtained for the corresponding plane stress case. The integral equations are solved and the stress intensity factors are given for various crack and shell dimensions. A bonded fiberglass reinforcement which may serve as a crack arrestor is used as an example.

Yahsi, O. S.↗
NASA NTRS1976

A nonlinear finite-element analysis of wings in steady incompressible flows with wake roll-up

The problem of lifting surfaces and complex aircraft configurations in steady incompressible flow is considered. For lifting surfaces the problem is formulated in terms of an integral equation relating the potential discontinuity on wing and wake to the normal derivative of the potential on the lifting surface. For complex configurations the problem is formulated in terms of an integral equation relating the potential to its normal derivative on the surface of the aircraft. The integral equation is approximated by a system of linear algebraic equations obtained by dividing the surfaces into small quadrilateral elements and by assuming the potential (or the potential discontinuity) and its normal derivative to be constant within each element. The wake geometry is obtained by iteration by satisfying the condition that the velocity be tangent to the surface of the wake and that the potential discontinuity be constant along the streamlines.

Suciu, E. O.↗
NASA NTRS1992

Wavelets and electromagnetics

Wavelets are an exciting new topic in applied mathematics and signal processing. This paper will provide a brief review of wavelets which are also known as families of functions with an emphasis on interpretation rather than rigor. We will derive an indirect use of wavelets for the solution of integral equations based techniques adapted from image processing. Examples for resistive strips will be given illustrating the effect of these techniques as well as their promise in reducing dramatically the requirement in order to solve an integral equation for large bodies. We also will present a direct implementation of wavelets to solve an integral equation. Both methods suggest future research topics and may hold promise for a variety of uses in computational electromagnetics.

Kempel, Leo C.↗
NASA NTRS1973

The problem of edge cracks in an infinite strip

The elastostatic plane problem of an infinite strip containing two symmetrically located internal cracks perpendicular to the boundary is formulated in terms of a singular integraL equation with the derivative of the crack surface displacement as the density function. The solution of the problem is obtained for various crack geometries and for uniaxial tension applied to the strip away from the crack region. The limiting case of the edge cracks is then considered in some detail. The fundamental function of the integral equation is obtained and a numerical technique for solving the singular integral equations with this particular type of fundamental function which is characteristic of the edge cracks is described. The stress intensity factor for the complete range of net ligament-to-width ratio is calculated. The results also include the solution of the edge crack problem in an elastic half plane.

Gupta, G. D.↗
NASA NTRS1974

The problem of edge cracks in an infinite strip

The elastostatic plane problem of an infinite strip containing two symmetrically located internal cracks perpendicular to the boundary is formulated in terms of a singular integral equation with the derivative of the crack surface displacement as the density function. The solution of the problem is obtained for various crack geometries and for uniaxial tension applied to the strip away from the crack region. The limiting case of the edge cracks is then considered in some detail. The fundamental function of the integral equation is obtained and a numerical technique for solving the singular integral equations with this particular type of fundamental function which is characteristic of the edge cracks is described. The stress-intensity factor for the complete range of net ligament-to-width ratio is calculated. The results also include the solution of the edge crack problem in an elastic half plane.

Gupta, G. D.↗
NASA NTRS1987

Full potential integral solution for transonic flows with and without embedded Euler domains

Two methods are presented to solve for the transonic airfoil flow problems. The first method is based on the integral equation solution of the full-potential equation in terms of the velocity field, and a Shock Capturing-Shock Fitting (SCSF) scheme has been developed. The SCSF-scheme consists of a shock-capturing part and a shock-fitting part in which shock panels are introduced at the shock location. The sock panels are fitted and crossed by using the Rankine-Hugoniot relations. The second method is based on coupling the integral equation of the full-potential equation with the pseudo time integration of Euler equations in a small embedded region around the shock. The integral solution provides the initial and boundary conditions for the Euler domain. This scheme is named as the Integral Equation-Embedded Euler (IEEE) scheme. The two methods are applied to NACA 0012 and NACA 64A010A over a wide range of Mach numbers, and the reults are in good agreement with the experimental data and other computational results. The schemes converge within a number of iterations which is one-order of magnitude less than the finite-difference schemes.

Kandil, Osama A.↗
NASA NTRS1995

Electromagnetic Scattering From a Rectangular Cavity Recessed in a 3-D Conducting Surface

The problem of electromagnetic (EM) scattering from an aperture backed by a rectangular cavity recessed in a three-dimensional conducting body is analyzed using the coupled field integral equation approach. Using the free-space Green's function, EM fields scattered outside the cavity are determined in terms of (1) an equivalent electric surface current density flowing on the three-dimensional conducting surface of the object including the cavity aperture and (2) an equivalent magnetic surface current density flowing over the aperture only. The EM fields inside the cavity are determined using the waveguide modal expansion functions. Making the total tangential electric and magnetic fields across the aperture continuous and subjecting the total tangential electric field on the outer conducting three-dimensional surface of the object to zero, a set of coupled integral equations is obtained. The equivalent electric and magnetic surface currents are then obtained by solving the coupled integral equation using the Method of Moments. The numerical results on scattering from rectangular cavities embedded in various three-dimensional objects are compared with the results obtained by other numerical techniques.

Deshpande, M. D.↗
NASA NTRS1997

Electromagnetic Scattering from Arbitrarily Shaped Aperture Backed by Rectangular Cavity Recessed in Infinite Ground Plane

The electromagnetic scattering from an arbitrarily shaped aperture backed by a rectangular cavity recessed in an infinite ground plane is analyzed by the integral equation approach. In this approach, the problem is split into two parts: exterior and interior. The electromagnetic fields in the exterior part are obtained from an equivalent magnetic surface current density assumed to be flowing over the aperture and backed by an infinite ground plane. The electromagnetic fields in the interior part are obtained in terms of rectangular cavity modal expansion functions. The modal amplitudes of cavity modes are determined by enforcing the continuity of the electric field across the aperture. The integral equation with the aperture magnetic current density as an unknown is obtained by enforcing the continuity of magnetic fields across the aperture. The integral equation is then solved for the magnetic current density by the method of moments. The electromagnetic scattering properties of an aperture backed by a rectangular cavity are determined from the magnetic current density. Numerical results on the backscatter radar cross-section (RCS) patterns of rectangular apertures backed by rectangular cavities are compared with earlier published results. Also numerical results on the backscatter RCS patterns of a circular aperture backed by a rectangular cavity are presented.

Cockrell, C. R.↗
NASA NTRS1971

The spectrum of steady state turbulent convection.

Based on Heisenberg's statistical theory of turbulence, a model for steady state turbulent convection is herein proposed, and on the basis of this model, equations for the energy spectrum for steady state turbulent convection are derived. The spectrum is obtained from the solution of a nonlinear integral equation. After the integral equation is brought into a universally valid nondimensional form, it is transformed into a nonlinear first order differential equation to be solved numerically, with the Rayleigh number appearing as the only parameter. The energy spectrum has a substantial deviation from the Kolmogoroff law, as a result of the buoyancy force acting on the rising and falling eddies. The presented theory may be applicable to convection in planetary and stellar atmospheres wherein the radiative heat transport is small.

Winterberg, F.↗
NASA NTRS1972

Profiles of emission lines in Be stars.

Study of the broadening functions resulting from a gaseous ring in circular motion around a star according to Kepler's law. When the distribution in the gaseous ring has a circular symmetry in the equatorial plane, the broadening profile is related to the surface density distribution along the radius by an integral equation which can be transformed into the Abel integral equation and solved analytically. Profiles corresponding to gaseous rings with a uniform density distribution but different widths are used to illustrate the general properties of the profile broadened by the gaseous ring in circular motion. The emission profile has also been studied for cases in which the circular motion does not follow Kepler's law.

Huang, S. S.↗
NASA NTRS1989

Resonance in cylindrical-rectangular and wraparound microstrip structures

A rigorous analysis of the resonance frequency problem of both the cylindrical-rectangular and the wraparound microstrip structure is presented. The problem is formulated in terms of a set of vector integral equations. Using Galerkin's method to solve the integral equations, the complex resonance frequencies are studied with sinusoidal basis functions which incorporate the edge singularity. The complex resonance frequencies are computed using a perturbation approach. Modes suitable for resonator or antenna applications are investigated. The edge singularity of the patch current is shown to have no significant effect on the accuracy of the results. It is shown that the HE10 modes of the cylindrical-rectangular and wraparound patches are more appropriate for resonator applications. The HE01 and TE01 modes of the cylindrical-rectangular and wraparound patches, respectively, are efficient radiating modes.

Ali, Sami M.↗
NASA NTRS1996

A Hybrid Boundary Element-Finite Volume Method for Unsteady Transonic Airfoil Flows

A hybrid boundary element finite volume method for unsteady transonic flow computation has been developed. In this method, the unsteady Euler equations in a moving frame of reference are solved in a small embedded domain (inner domain) around the airfoil using an implicit finite volume scheme. The unsteady full-potential equation, written in the same frame of reference and in the form of the Poisson equation. is solved in the outer domain using the integral equation boundary element method to provide the boundary conditions for the inner Euler domain. The solution procedure is a time-accurate stepping procedure, where the outer boundary conditions for the inner domain are updated using the integral equation -- boundary element solution over the outer domain. The method is applied to unsteady transonic flows around the NACA0012 airfoil undergoing pitching oscillation and ramp motion. The results are compared with those of an implicit Euler equation solver, which is used throughout a large computational domain, and experimental data.

Hu, Hong↗
NASA NTRS2011

Excitation of a Parallel Plate Waveguide by an Array of Rectangular Waveguides

This work addresses the problem of excitation of a parallel plate waveguide by an array of rectangular waveguides that arises in applications such as the continuous transverse stub (CTS) antenna and dual-polarized parabolic cylindrical reflector antennas excited by a scanning line source. In order to design the junction region between the parallel plate waveguide and the linear array of rectangular waveguides, waveguide sizes have to be chosen so that the input match is adequate for the range of scan angles for both polarizations. Electromagnetic wave scattered by the junction of a parallel plate waveguide by an array of rectangular waveguides is analyzed by formulating coupled integral equations for the aperture electric field at the junction. The integral equations are solved by the method of moments. In order to make the computational process efficient and accurate, the method of weighted averaging was used to evaluate rapidly oscillating integrals encountered in the moment matrix. In addition, the real axis spectral integral is evaluated in a deformed contour for speed and accuracy. The MoM results for a large finite array have been validated by comparing its reflection coefficients with corresponding results for an infinite array generated by the commercial finite element code, HFSS. Once the aperture electric field is determined by MoM, the input reflection coefficients at each waveguide port, and coupling for each polarization over the range of useful scan angles, are easily obtained. Results for the input impedance and coupling characteristics for both the vertical and horizontal polarizations are presented over a range of scan angles. It is shown that the scan range is limited to about 35 for both polarizations and therefore the optimum waveguide is a square of size equal to about 0.62 free space wavelength.

Rengarajan, Sembiam↗