Vibrations of a hollow elastic cylinder bonded to a thin casing of a different material
Exact solutions for vibrations of hollow elastic cylinder bonded to thin casing of different material
ELASTIC CYLINDER↗
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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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A nonuniform shock wave subjected to an oblique magnetic field.
Nonuniform shock wave subject to oblique magnetic field in gas at rest with nonuniform density studied using exact solutions of conducting fluid flow
Gundersen, R. M.↗
On the kinetic equation for resonant three-wave coupling.
Exact solution to kinetic equation for resonant three wave coupling in weakly turbulent plasmas, assuming only single triplet of modes interaction
Davidson, R. C.↗
Role of potential curve crossing in subexcitation molecular collisions - Exact /two-state/ computations vs decoupling approximations for resonance positions.
Exact solutions for two state potential curve crossing in subexcitation molecular collisions in terms of various decoupling schemes
Bernstein, R. B.↗
Analytical method for steady state heat transfer in two-dimensional porous media
Analytical method for obtaining exact solutions for steady state heat transfer behavior of two dimensional porous cooled media
Goldstein, M. E.↗
On certain approximations in the finite- element method
Finite element method approximations outside variational principle in elasticity problems, examining convergence to exact solution
Mclay, R. W.↗
Analysis of solar ultraviolet lines
The formation of the strongest ultra-violet emission lines of Mg II, O I, C II, and C III in the solar atmosphere is studied in detail. The equations of statistical equilibrium and radiative transfer for each ion are solved using a general computer program that is capable of solving non-LTE line-formation problems for arbitrary atmospheric and atomic models. Interpreting the results in terms of the structure of the solar atmosphere, it is concluded that the HSRA atmosphere has a temperature too low by about 500 K near h = 1100 km and that a temperature plateau with T sub e approximately = 18,000 K and width close to 60 km exists in the upper chromosphere. The structure of the solar atmosphere in the range 20,000 to 100,000 K and the effects of microturbulence on the formation of lines are also investigated. Approximate analytic line-formation problems are solved, and more exact solutions are derived later. An attempt is made to make the best possible fit to the Ca II K line center-to-limb profiles with a one-component atmosphere, with an assumed source function and microturbulent velocity.
Chipman, E.↗
Finite element analysis of large transient elastic-plastic deformations of simple structures, with application to the engine rotor fragment containment/deflection problem
Assumed-displacement versions of the finite-element method are developed to predict large-deformation elastic-plastic transient deformations of structures. Both the conventional and a new improved finite-element variational formulation are derived. These formulations are then developed in detail for straight-beam and curved-beam elements undergoing (1) Bernoulli-Euler-Kirchhoff or (2) Timoshenko deformation behavior, in one plane. For each of these categories, several types of assumed-displacement finite elements are developed, and transient response predictions are compared with available exact solutions for small-deflection, linear-elastic transient responses. The present finite-element predictions for large-deflection elastic-plastic transient responses are evaluated via several beam and ring examples for which experimental measurements of transient strains and large transient deformations and independent finite-difference predictions are available.
Wu, R. W.↗
Curved characteristics behind blast waves.
The behavior of nonisentropic flow behind a propagating blast wave is theoretically studied. Exact solutions, expressed in closed form in terms of elementary functions, are presented for three sets of curved characteristicseind a self-similar, strong blast wave.
Laporte, O.↗
Approximate estimation for systems with quantized data.
Estimation of the state of a nonlinear discrete-time system using quantized data is considered. An exact solution for the maximum likelihood estimate is expressed as the solution of a nonlinear two-point boundary-value problem. Approximate recursive solutions for both the maximum likelihood and the conditional-mean estimates are obtained. The results of Monte-Carlo simulations are presented in which the performance of these two algorithms is compared with that of a Kalman filter in which the quantization error is approximated by white noise.-
Clements, K. A.↗
Sonic-boom calculation in a stratified atmosphere.
For a lifting body of revolution, the exact solutions to the gas dynamical equation are given for the flow field in a stratified atmosphere. The boundary condition is satisfied by using the (linearized) slender-body theory. The solution allows one to make a prediction of the magnitude and the location of the sonic boom in a stratified atmosphere as well as to handle cutoff effects.
Schorling, M.↗
Optimization of self-acting step thrust bearings for load capacity and stiffness.
Linearized analysis of a finite-width rectangular step thrust bearing. Dimensionless load capacity and stiffness are expressed in terms of a Fourier cosine series. The dimensionless load capacity and stiffness were found to be a function of the dimensionless bearing number, the pad length-to-width ratio, the film thickness ratio, the step location parameter, and the feed groove parameter. The equations obtained in the analysis were verified. The assumptions imposed were substantiated by comparing the results with an existing exact solution for the infinite width bearing. A digital computer program was developed which determines optimal bearing configuration for maximum load capacity or stiffness. Simple design curves are presented. Results are shown for both compressible and incompressible lubrication. Through a parameter transformation the results are directly usable in designing optimal step sector thrust bearings.
Hamrock, B. J.↗
Closed anisotropic cosmological models.
Derivation of a new exact solution to Einstein's equations representing homogeneous nonisotropic cosmological models of a closed universe containing electromagnetic and scalar fields. This solution reduces to a generalization of Brill's electromagnetic universe when the scalar field vanishes, and to the Taub-NUT-M space when both these fields vanish. The solutions also satisfy the scalar tensor equations and represent a universe containing electromagnetic fields and a source-free solution to the scalar-tensor equations representing a closed universe.
Batakis, N.↗
Coronal magnetic fields and the solar wind
Current information is presented on coronal magnetic fields as they bear on problems of the solar wind. Both steady state fields and coronal transient events are considered. A brief critique is given of the methods of calculating coronal magnetic fields including the potential (current free) models, exact solutions for the solar wind and field interaction, and source surface models. These solutions are compared with the meager quantitative observations which are available at this time. Qualitative comparisons between the shapes of calculated magnetic field lines and the forms visible in the solar corona at several recent eclipses are displayed. These suggest that: (1) coronal streamers develop above extended magnetic arcades which connect unipolar regions of opposite polarity; and (2) loops, arches, and rays in the corona correspond to preferentially filled magnetic tubes in the approximately potential field.
Newkirk, G., Jr.↗
A Numerical Analysis of the Transient Response of an Ablation System Including Effects of Thermal Nonequilibrium, Mass Transfer and Chemical Kinetics
The differential equations governing the transient response of a one-dimensional ablative thermal protection system undergoing stagnation ablation are derived. These equations are for thermal nonequilibrium effects between the pyrolysis gases and the char layer and kinetically controlled chemical reactions and mass transfer between the pyrolysis gases and the char layer. The boundary conditions are written for the particular case of stagnation heating with surface removal by oxidation or sublimation and pyrolysis of the uncharred layer occurring in a plane. The governing equations and boundary conditions are solved numerically using the modified implicit method (Crank-Nicolson method). Numerical results are compared with exact solutions for a number of simplified cases. The comparison is favorable in each instance.
Clark, R. K.↗
A study of the properties of beryllium doped silicon with particular emphasis on diffusion mechanisms: Profiles of depth dependent conductivity as determined by electrical surface probes
Very large diffusion coefficients were encountered and required the determination of impurity profiles for samples approximately 1 cm thick. Since conductivity values are readily converted into concentrations of electrically active impurities, the major problem became that of accurately determining the conductivity profiles of beryllium diffused silicon samples. Four-point probe measurements on samples having depth conductivities are interpreted in terms of conductivity profiles, based on an exact solution of the problem of exponentially depth dependent conductivity. Applications include surface conductivity determination where the form of the conductivity profile is known, and conductivity profile determination from probe measurements taken as the sample surface is progressively lapped away. The application is limited to samples having conductivity monotonically decreasing with depth from the probed surface.
Franks, R. K.↗
A method for predicting shock shapes and pressure distributions on two dimensional airfoils at large angles of attack
A method is presented for determining shock envelopes and pressure distributions for two-dimensional airfoils at angles of attack sufficiently large to cause shock detachment and subsonic flow over the windward surface of the airfoil. Correlation functions obtained from exact solutions are used to relate the shock standoff distance at the stagnation and sonic points of the body through a suitable choice for the shock shape. The necessary correlation functions were obtained from perfect gas solutions but may be extended to any gas flow for which the normal shock-density ratio can be specified.
Kaattari, G. E.↗
A nonlinear theory for sonic-boom calculations in a stratified atmosphere
The exact solutions to the equations of gas dynamics are given with respect to the axis of slender lifting bodies in a stratified atmosphere. The boundary condition is satisfied by using slender-body theory. The solution predicts the magnitude of the pressure rise of the sonic boom and estimates the nonlinear effects in the vicinity of the cutoff point.
Schorling, M.↗