Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Perturbative methods”

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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1948

On similarity rules for transonic flows

A method used by Tsien to derive similarity rules for hypersonic flows is utilized to derive Von Karman's similarity rules for transonic flows. At the lower limit of the transonic region of flow the theory yields a formula for the critical stream Mach numbers of a given family of symmetrical profiles. It is further shown that this formula can also be obtained by means of the Prandtl-Glauert small-perturbation method. Investigation of the behavior of the similarity parameter in the region where the thickness coefficient approaches zero and the critical stream Mach number approaches unity shows that it possesses a limiting value characteristic of the prescribed family of shapes.

Kaplan, Carl↗
NASA NTRS1992

Backscattering from a randomly rough dielectric surface

A backscattering model for scattering from a randomly rough dielectric surface is developed based on an approximate solution of a pair of integral equations for the tangential surface fields. Both like and cross-polarized scattering coefficients are obtained. It is found that the like polarized scattering coefficients contain two types of terms: single scattering terms and multiple scattering terms. The single scattering terms in like polarized scattering are shown to reduce the first-order solutions derived from the small perturbation method when the roughness parameters satisfy the slightly rough conditions. When surface roughnesses are large but the surface slope is small, only a single scattering term corresponding to the standard Kirchhoff model is significant. If the surface slope is large, the multiple scattering term will also be significant. The cross-polarized backscattering coefficients satisfy reciprocity and contain only multiple scattering terms. The difference between vertical and horizontal scattering coefficients is found to increase with the dielectric constant and is generally smaller than that predicted by the first-order small perturbation model. Good agreements are obtained between this model and measurements from statistically known surfaces.

Fung, Adrian K.↗
NASA NTRS1996

A Numerical Simulation of Scattering from One-Dimensional Inhomogeneous Dielectric Random Surfaces

In this paper, an efficient numerical solution for the scattering problem of inhomogeneous dielectric rough surfaces is presented. The inhomogeneous dielectric random surface represents a bare soil surface and is considered to be comprised of a large number of randomly positioned dielectric humps of different sizes, shapes, and dielectric constants above an impedance surface. Clods with nonuniform moisture content and rocks are modeled by inhomogeneous dielectric humps and the underlying smooth wet soil surface is modeled by an impedance surface. In this technique, an efficient numerical solution for the constituent dielectric humps over an impedance surface is obtained using Green's function derived by the exact image theory in conjunction with the method of moments. The scattered field from a sample of the rough surface is obtained by summing the scattered fields from all the individual humps of the surface coherently ignoring the effect of multiple scattering between the humps. The statistical behavior of the scattering coefficient sigma(sup 0) is obtained from the calculation of scattered fields of many different realizations of the surface. Numerical results are presented for several different roughnesses and dielectric constants of the random surfaces. The numerical technique is verified by comparing the numerical solution with the solution based on the small perturbation method and the physical optics model for homogeneous rough surfaces. This technique can be used to study the behavior of scattering coefficient and phase difference statistics of rough soil surfaces for which no analytical solution exists.

Sarabandi, Kamal↗
NASA NTRS2001

A Study of Green's Function Methods Applied to Space Radiation Protection

The purpose of this research was to study the propagation of galactic ions through various materials. Galactic light ions result from the break up of heavy ion particles and their propagation through materials is modeled using the one-dimensional Boltzmann equation. When ions enter materials there can occur (i) the interaction of ions with orbital electrons which causes ionization within the material and (ii) ions collide with atoms causing production of secondary particles which penetrate deeper within the material. These processes are modeled by a continuum model. The basic idea is to place a control volume within the material and examine the change in ion flux across this control volume. In this way on can derive the basic equations for the transport of light and heavy ions in matter. Green's function perturbation methods can then be employed to solve the resulting equations using energy dependent nuclear cross sections.

Heinbockel, John H.↗
NASA NTRS1984

Rational approach for assumed stress finite elements

A new method for the formulation of hybrid elements by the Hellinger-Reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element. The equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co-ordinates. The resulting element possesses all the ideal qualities, i.e. it is invariant, it is less sensitive to geometric distortion, it contains a minimum number of stress parameters and it provides accurate stress calculations. For the formulation of a 4-node plane stress element, a small perturbation method is used to determine the equilibrium constraint equations. The element has been proved to be always rank sufficient.

Pian, T. H. H.↗
NASA NTRS2010

Technique for Performing Dielectric Property Measurements at Microwave Frequencies

A paper discusses the need to perform accurate dielectric property measurements on larger sized samples, particularly liquids at microwave frequencies. These types of measurements cannot be obtained using conventional cavity perturbation methods, particularly for liquids or powdered or granulated solids that require a surrounding container. To solve this problem, a model has been developed for the resonant frequency and quality factor of a cylindrical microwave cavity containing concentric cylindrical samples. This model can then be inverted to obtain the real and imaginary dielectric constants of the material of interest. This approach is based on using exact solutions to Maxwell s equations for the resonant properties of a cylindrical microwave cavity and also using the effective electrical conductivity of the cavity walls that is estimated from the measured empty cavity quality factor. This new approach calculates the complex resonant frequency and associated electromagnetic fields for a cylindrical microwave cavity with lossy walls that is loaded with concentric, axially aligned, lossy dielectric cylindrical samples. In this approach, the calculated complex resonant frequency, consisting of real and imaginary parts, is related to the experimentally measured quantities. Because this approach uses Maxwell's equations to determine the perturbed electromagnetic fields in the cavity with the material(s) inserted, one can calculate the expected wall losses using the fields for the loaded cavity rather than just depending on the value of the fields obtained from the empty cavity quality factor. These additional calculations provide a more accurate determination of the complex dielectric constant of the material being studied. The improved approach will be particularly important when working with larger samples or samples with larger dielectric constants that will further perturb the cavity electromagnetic fields. Also, this approach enables the ability to have a larger sample of interest, such as a liquid or powdered or granulated solid, inside a cylindrical container.

Barmatz, Martin B.↗
NASA NTRS1972

Perturbation and harmonic balance methods for nonlinear panel flutter.

A systematic way of applying both perturbation methods and harmonic balance methods to nonlinear panel flutter problems is developed here. Results obtained by both these methods for two-dimensional simply supported and three-dimensional clamped-clamped plates with six modes agree well with those obtained by the straightforward direct integration method, yet require less computer time and provide better insight into the solutions. Effects of viscoelastic structural damping on the flutter stability boundary are generally found to be destabilizing and the postflutter behavior becomes more explosive. The methods developed here may be of interest in related vibration problems.

Kuo, C.-C.↗