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All sourcesNASA NTRSDOE OSTI
NASA NTRS1961

Development of the Lunar and Solar Perturbations in the Motion of an Artificial Satellite

Problems relating to the influence of lunar and solar perturbations on the motion of artificial satellites are analyzed by an extension of Cayley's development of the perturbative function in the lunar theory. In addition, the results are modified for incorporation into the Hansen-type theory used by the NASA Space Computing Center. The theory is applied to the orbits of the Vanguard I and Explorer VI satellites, and the results of detailed computations for these satellites are given together with a physical description of the perturbations in terms of resonance effects.

Musen, P.↗
NASA NTRS1998

Some Comments on the Status of Shell Theory at the End of the 20th Century: Complaints and Correctives

This review is divided into complaints and correctives. Complaints are directed at: sloppy refereeing and editing; authors who fail to read or acknowledge what others have done; the mis-naming or mis-crediting of results; the misunderstanding and misuse of the Kirchhoff hypothesis; inflated claims of accuracy based on overly-simplified benchmark problems; the failure to appreciate the inherent errors in various shell models; the failure to appreciate that the physical response and mathematical structure of shell theory are fundamentally different from 3-dimensional elasticity; and the irrelevance of Cosserat-type theories. Correctives include a simple, straight-forward derivation of a general nonlinear dynamic shell theory with the following features: (1) the equations of motion and kinematics (and those of thermodynamics, if desired) are exact consequences of their 3-dimensional counterparts; (2) there are no asymptotic or series expansions through the thickness; (3) all approximations (including the Kirchhoff Hypothesis) occur in the constitutive relations; (4) in static problems, there is a mixed form of the governing equations involving a mixed-energy density and exhibiting remnants of the well-known static-geometric duality of linear theory which is numerically robust because the limiting cases of nonlinear membrane theory and inextensional bending theory fall out naturally. (These latter two special cases are known to produce numerical nightmares unless treated with great care); and (5) all equations may be expressed in coordinate-free form (although, sometimes, a hybrid form is shown to be superior).

Simmonds, James G.↗
NASA NTRS1989

Redistribution in astrophysically important hydrogen lines

Under typical solar chromospheric conditions for hydrogen radiators, strong collisions due to both electrons and ions are well separated in time, so that a binary collision theory for collisional redistribution is applicable. However, a simple impact approximation may not be used, but rather a unified type theory is required in which frequency dependent line shape parameters are used to describe both impact and quasi-static regions of the spectrum. In addition, correlated terms which describe absorption and emission during a collision are important, and, in fact, without correlated terms describing both transfer of excitation and emission during the same collision unphysical predictions (such as negative intensities) would be obtained. In this paper theory is specifically developed for the coupled Lyman-alpha, Lyman-beta, Hydrogen-alpha system, and equations of statistical equilibrium and absorption and emission coefficients are given. All correlated events are examined and emission during a collision is found to be important in the line wings. Stimulated emission and absorption is also included within a broadband approximation. The major approximation is to ignore lower state interaction. It is found that for Lyman-beta Raman-coupling with Hydrogen-alpha occurs and the overall scattering of radiation in the line wings is mostly coherent. In contrast, for Hydrogen-alpha, incoherent redistribution due to lower state radiative decay (which occurs even in the absence of collisions) is found to dominate the coherent scattering. Finally, in the Lyman series the dominant incoherent contribution is associated with cascade transitions and inelastic collisions between different principal quantum states.

Cooper, J.↗
NASA NTRS1990

A simplified orthotropic viscoplasticity theory based on overstress

The viscoplasticity theory based on overstress, a simplified version of Sutcu (1985) theory, is presented for the case of orthotropy. The theory permits asymptotic solutions for checking numerical experiments and for identification of material properties. It is applicable to materials with rate(time) dependence, hysteresis, and a permanent set, such as cubic crystals, directionally solidified alloys, and metal matrix composites. Though it is a unified type theory, with effects of creep and plasticity not separated, it allows to identify viscous and plastic contributions to the stress in the asymptotic state.

Sutcu, M.↗
NASA NTRS1987

Stress concentration around a part-through hole weakening a laminated plates

A quasi-three-dimensional-elasticity type theory, based on the assumptions of transverse inextensibility and layerwise constant shear-angle, is presented, in the context of an assumed quadratic displacement potential energy approach, for analyzing an edge-loaded laminated plate weakened by the presence of a part-through hole. Numerical results, obtained using the C-deg-type triangular finite element, indicate the existence of severe cross-sectional warping in the vicinity of the hole and plate boundaries. Furthermore, the three-dimensional nature of the stress concentration factor in the neighborhood of the hole boundary is clearly exhibited. Besides, very high stress concentration factors are found in the layer weakened by the part-through hole. The numerical results presented should serve as bench-mark solutions for future comparisons.

Chaudhuri, Reaz A.↗
NASA NTRS1981

Gortler vortices and transition in wall boundary layers of two Mach 5 nozzles

The onset of transition in the wall boundary layers of two axisymmetric Mach 5 wind-tunnel nozzles has been measured under conditions of extremely low incident disturbance levels. The range of test unit Reynolds numbers, based on conditions at the nozzle exit, was from 6 x 10 to the 6th power m to 2.5 x 10 to the 7th power m. When the nozzle walls were maintained in a polished and clean condition, transition moved gradually upstream as the test Reynolds number was increased. When transition occurred in the supersonic concave wall region, the values of the local Gortler parameter at transition varied from about 5 to 6, whereas the momentum thickness Reynolds number varied from about 750 to 1050. Oil flow patterns obtained near the exit of the nozzles indicated that Gortler vortices were always present when the wall boundary layers were laminar. Calculations for the growth of Gortler vortices based on new results from linear theory for supersonic flat-plate profiles gave amplification ratios to transition from e to the 4th power to e to the 15th power. Possible reasons for this wide range in amplification ratios are discussed, but no definite conclusions are yet possible regarding the values of n in a simple e to the nth power type theory for the assumed linear amplification of Gortler vortices to transition in supersonic nozzles.

Beckwith, I. E.↗
NASA NTRS1994

General analytic results for nonlinear waves and solitons in molecular clouds

We study nonlinear wave phenomena in self-gravitating fluid systems, with a particular emphasis on applications to molecular clouds. This paper presents analytical results for one spatial dimension. We show that a large class of physical systems can be described by theories with a 'charge density' q(rho); this quantity replaces the density on the right-hand side of the Poisson equation for the gravitational potential. We use this formulation to prove general results about nonlinear wave motions in self-gravitating systems. We show that in order for stationary waves to exist, the total charge (the integral of the charge density over the wave profile) must vanish. This 'no-charge' property for solitary waves is related to the capability of a system to be stable to gravitational perturbations for arbitrarily long wavelengths. We find necessary and sufficient conditions on the charge density for the existence of solitary waves and stationary waves. We study nonlinear wave motions for Jeans-type theories (where q(rho) = rho-rho(sub 0)) and find that nonlinear waves of large amplitude are confined to a rather narrow range of wavelengths. We also study wave motions for molecular clouds threaded by magnetic fields and show how the allowed range of wavelengths is affected by the field strength. Since the gravitational force in one spatial dimension does not fall off with distance, we consider two classes of models with more realistic gravity: Yukawa potentials and a pseudo two-dimensional treatment. We study the allowed types of wave behavior for these models. Finally, we discuss the implications of this work for molecular cloud structure. We argue that molecular clouds can support a wide variety of wave motions and suggest that stationary waves (such as those considered in this paper) may have already been observed.

Adams, Fred C.↗
NASA NTRS1981

Application of the line-spring model to a cylindrical shell containing a circumferential or axial part-through crack

An approximate solution was obtained for a cylindrical shell containing a part-through surface crack. It was assumed that the shell contains a circumferential or axial semi-elliptic internal or external surface crack and was subjected to a uniform membrane loading or a uniform bending moment away from the crack region. A Reissner type theory was used to account for the effects of the transverse shear deformations. The stress intensity factor at the deepest penetration point of the crack was tabulated for bending and membrane loading by varying three dimensionless length parameters of the problem formed from the shell radius, the shell thickness, the crack length, and the crack depth. The upper bounds of the stress intensity factors are provided by the results of the elasticity solution obtained from the axisymmetric crack problem for the circumferential crack, and that found from the plane strain problem for a circular ring having a radial crack for the axial crack. The line-spring model gives the expected results in comparison with the elasticity solutions. Results also compare well with the existing finite element solution of the pressurized cylinder containing an internal semi-elliptic surface crack.

Delale, F.↗
NASA NTRS1982

Application of the line-spring model to a cylindrical shell containing a circumferential or axial part-through crack

The line-spring model developed by Rice and Levy (1972) is used to obtain an approximate solution for a cylindrical shell containing a part-through surface crack. A Reissner type theory is used to account for the effects of the transverse shear deformations, and the stress intensity factor at the deepest penetration point of the crack is tabulated for bending and membrane loading by varying three-dimensionless length parameters of the problem formed from the shell radius, the shell thickness, the crack length, and the crack depth. The upper bounds of the stress intensity factors are provided, and qualitatively the line-spring model gives the expected results in comparison with elasticity solutions.

Delale, F.↗
NASA NTRS1984

Simple theoretical models for composite rotor blades

The development of theoretical rotor blade structural models for designs based upon composite construction is discussed. Care was exercised to include a member of nonclassical effects that previous experience indicated would be potentially important to account for. A model, representative of the size of a main rotor blade, is analyzed in order to assess the importance of various influences. The findings of this model study suggest that for the slenderness and closed cell construction considered, the refinements are of little importance and a classical type theory is adequate. The potential of elastic tailoring is dramatically demonstrated, so the generality of arbitrary ply layup in the cell wall is needed to exploit this opportunity.

Valisetty, R. R.↗
NASA NTRS1987

Thermochemical erosion

A quasi-steady multidimensional Stefan problem is treated by means of similarity, asymptotic methods, and numerical analysis. The continuous wearing away of a solid 'erodee' is effected by gradual consumption of a solid 'eroder'. In the process under study, the erodee melts and the (liquid) melt diffuses to the eroder, where an exothermic, indefinitely rapid, diffusion-controlled surface reaction occurs. The products of reaction convey some of the chemically-generated heat to the surface of the erodee, so that further melting may occur, and the process may proceed. The analysis seeks to estimate the quasi-steady rates of consumption of the erodee and eroder, for the (convenient) self-similar case of confocal parabolas defining the boundaries of the melt layer. The analysis is simplified by observing that the flow is of lubrication-theory type: creeping, primarily unidirectional motion owing to the thinness of the melt layer between the erodee and eroder, with diffusion of heat and mass predominantly perpendicular to the principal motion. The analysis is completed by consideration of the force balance on the eroder.

Butler, Gerald↗
NASA NTRS1990

Charged polymers in high dimensions

A Monte Carlo study of charged polymers with either homogeneously distributed frozen charges or with mobile charges has been performed in four and five space dimensions. The results are consistent with the renormalization-group predictions and contradict the predictions of Flory-type theory. Introduction of charge mobility does not modify the behavior of the polymers.

Kantor, Yacov↗
NASA NTRS1998

Analysis of Curved Sandwich Panels Subjected to Combined Temperature Gradient and Mechanical Loads

The results of a detailed study of the nonlinear response of curved sandwich panels with composite face sheets and subjected to a temperature gradient through-the-thickness combined with mechanical loadings are presented. The analysis is based on a first-order shear-deformation Sanders-Budiansky type theory with the effects of large displacements, moderate rotations, transverse shear deformation and laminated anisotropic material behavior included. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, principal strains, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the nonlinear response to variations in the panel parameters, the effective properties of the face sheet layers and the core, and the micromechanical parameters. Numerical results are presented for cylindrical panels subjected to combined pressure loading, edge shortening or extension, edge shear and a temperature gradient through the thickness. The results show the effects of variations in the loading and the panel aspect ratio, on the nonlinear response and its sensitivity to changes in the various panel, effective layer and micromechanical parameters.

Noor, Ahmed K.↗
NASA NTRS2004

The 90 deg Acoustic Spectrum of a High Speed Air Jet

Tam and Auriault successfully predicted the acoustic spectrum at 90deg to the axis of a high speed air jet by using an acoustic equation derived from ad hoc kinetic theory-type arguments. The present paper shows that similar predictions can be obtained by using a rigorous acoustic analogy approach together with actual measurements of the relevant acoustic source correlations. This puts the result on a firmer basis and enables its extension to new situations and to the prediction of sound at other observation angles.

Goldstein, Marvin E.↗
NASA NTRS1997

In situ wave phenomena in the upstream and downstream regions of interplanetary shocks: Implications for type 2 burst theories

The results are presented of in situ waves observed by the Ulyssess unified radio and plasma wave experiment (URAP) in the upstream and downstream regions of a large number of interplanetary shocks. The Langmuir waves which are the most essential ingredients for the type 2 radio emission are observed only in the upstream regions of a limited number of shocks. On the other hand, the ion-acoustic-like waves (0.5 to 5 kHz) are observed near most of the interplanetary shocks. Implications of observations made for the electron acceleration mechanisms at the collisionless shocks and for type 2 burst theories are presented.

Thejappa, G.↗
NASA NTRS1976

On the theory of the type III burst exciter

In situ satellite observations of type III burst exciters at 1 AU show that the beam does not evolve into a plateau in velocity space, contrary to the prediction of quasilinear theory. The observations can be explained by a theory that includes mode coupling effects due to excitation of the parametric oscillating two-stream instability and its saturation by anomalous resistivity. The time evolution of the beam velocity distribution is included in the analysis.

Smith, R. A.↗
NASA NTRS1979

A theory of solar type 3 radio bursts

Energetic electrons propagating through the interplanetary medium are shown to excite the one dimensional oscillating two stream instability (OTSI). The OTSI is in turn stabilized by anomalous resistivity which completes the transfer of long wavelength Langmuir waves to short wavelengths, out of resonance with the electrons. The theory explains the small energy losses suffered by the electrons in propagating to 1 AU, the predominance of second harmonic radiation, and the observed correlation between radio and electron fluxes.

Goldstein, M. L.↗