Almost symmetric spaces and gravitational radiation.
Killing fields applied to nonsymmetric spaces specify coordinate lines with slowest possible metric tensor variation and gravitational radiation
Matzner, R. A.↗
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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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On a nonlinear theory of elastic shells.
Elastic shell nonlinear theory, introducing nonsymmetric stress tensor and principles of virtual work and objectivity
Cohen, H.↗
A theoretical analysis of the free vibration of discretely stiffened cylindrical shells with arbitrary end conditions.
Free vibration of discretely stiffened cylindrical shells with arbitrary end conditions programmed for digital computer, considering flexure, extension, torsion and nonsymmetric stiffener cross section
Egle, D. M.↗
Studies of interface damping Final report, 25 Nov. 1966 - 10 Sep. 1969
Energy dissipation and damping effects on aluminum cantilever beams in air and vacuum vibration tests, and slip in cantilever beams with either nonsymmetric or multiple interfaces
Lindholm, U. S.↗
(p, 2p) reactions at 600 MeV on deuterium and helium-4
Cross sections measured for symmetric /p, 2p/ reactions on deuterium and He, discussing nonsymmetric /p, 2p/ events in He
Boschitz, E. T.↗
Optimum mass-strength analysis for orthotropic ring-stiffened cylinders under axial compression
An analysis was developed to calculate the minimum mass-strength curve for an orthotropic cylinder subjected to axial compressive loading. The analysis, which includes the effects of ring and stringer eccentricities, is in a general form so that various cylinder wall and stiffener geometries can be considered. Several different ring-stiffened orthotropic configurations were studied. The minimum mass-strength curves and the dimensions associated with these curves are presented for (in order of decreasing efficiency) a tubular double bead, a nonsymmetric double bead, a Z-stiffened skin, and a trapezoidal corrugation. A comparison of efficiencies of the configurations shows a tubular element cylinder to be more efficient than a 3-percent core-density honeycomb-sandwich cylinder. It was found that for an optimized Z-stiffened skin, the location of the Z-stiffeners (internal or external) made a negligible difference in efficiency.
Shideler, J. L.↗
Holographic measurement of wave propagation in axi-symmetric shells
The report deals with the use of pulsed, double-exposure holographic interferometry to record the propagation of transverse waves in thin-walled axi-symmetric shells. The report is subdivided into sections dealing with: (1) wave propagation in circular cylindrical shells, (2) wave propagation past cut-outs and stiffeners, and (3) wave propagation in conical shells. Several interferograms are presented herein which show the waves reflecting from the shell boundaries, from cut-outs, and from stiffening rings. The initial response of the shell was nearly axi-symmetric in all cases, but nonsymmetric modes soon appeared in the radial response. This result suggests that the axi-symmetric response of the shell may be dynamically unstable, and thus may preferentially excite certain circumferential harmonics through parametric excitation. Attempts were made throughout to correlate the experimental data with analysis. For the most part, good agreement between theory and experiment was obtained. Occasional differences were attributed primarily to simplifying assumptions used in the analysis. From the standpoint of engineering applications, it is clear that pulsed laser holography can be used to obtain quantitative engineering data. Areas of dynamic stress concentration, stress concentration factors, local anomalies, etc., can be readily determined by holography.
Evensen, D. A.↗
Governing equations for vibrating constrained-layer damping sandwich plates and beams.
A simple differential equation is derived to describe constrained-layer damping in nonsymmetric sandwich plates and beams composed of isotropic and homogeneous layers. The natural boundary conditions related to this equation are determined and some typical numerical results obtained by this equation are given. The equation is valid within the linear theories of elasticity and viscoelasticity in the absence of any constraints on thicknesses, positions, symmetries, and densities of the layers.
Yan, M.-J.↗
The motion and stability of a dual-spin satellite during the momentum wheel spin-up maneuver.
The stability of a dual-spin satellite system during the momentum wheel spin-up maneuver is treated both analytically and numerically. The dual-spin system consists of a slowly rotating or despun main body, a momentum wheel (or rotor) which is accelerated by a torque motor to change its initial angular velocity relative to the main part to some high terminal value, and a nutation damper. A closed-form solution for the case of a symmetrical satellite indicates that when the nutation damper is physically constrained from movement (i.e., by use of a mechanical clamp) the magnitude of the vector sum of the transverse angular velocity components remains bounded during the wheel spin-up under the influence of a constant motor torque. The analysis is extended to consider such effects as the motion of the nutation damper during spin-up, and the effect of a nonsymmetrical mass distribution.
Sen, S.↗
Asperity lubrication and cavitation in face seals
The basic aspect of parallel-surface lubrication that distinguishes it from other areas of lubrication technology is that classical lubrication theory does not predict the existence of a stable hydrodynamic film for steady-state, isothermal, incompressible flow between smooth, parallel surfaces. Hydrodynamic films between apparently parallel surfaces have been observed in practice and are often essential for the reliable performance of thrust bearings and seals. In order to account for this fortunate discrepancy between classical theory and experiment, load-support mechanisms relating to accidential features characteristic of seal performance, which relax one or more of the assumptions in the classical theory and permit the theoretical prediction of load support are proposed. Some of the features that have been analyzed are vibratory effects such as wobble and bounce, surface waviness, nonsymmetric rotation resulting from various types of misalignment, lubricant density change, non-Newtonian lubricant effects, and surface roughness.
Walowitt, J. A.↗
Shell deformation studies using holographic interferometry
The buckling of shallow spherical shells under pressure has been the subject of many theoretical and experimental papers. Experimental data above the theoretical buckling load of Huang have given rise to speculation that shallow shell theory may not adequately predict the stability of nonsymmetric modes in higher-rise shells which are normally classified as shallow by the Reissner criterion. This article considers holographic interferometry as a noncontact, high-resolution method of measuring prebuckling deformations. Prebuckling deformations of a lambda = 9, h/b = 0.038 shell are Fourier-analyzed. Buckling is found to occur in an N = 5 mode as predicted by Huang's theory. The N = 4 mode was unusually stable, suggesting that even at this low value of h/b, stabilizing effects may be at work.
Parmerter, R. R.↗
Reduced backscattering cross section (Sigma degree) data from the Skylab S-193 radar altimeter
Backscattering cross section per unit scattering area data, reduced from measurements made by the Skylab S-193 radar altimeter over the ocean surface are presented. Descriptions of the altimeter are given where applicable to the measurement process. Analytical solutions are obtained for the flat surface impulse response for the case of a nonsymmetrical antenna pattern. Formulations are developed for converting altimeter AGC outputs into values for the backscattering cross section. Reduced data are presented for Missions SL-2, 3 and 4 for all modes of the altimeter where sufficient calibration existed. The problem of interpreting land scatter data is also discussed. Finally, a comprehensive error analysis of the measurement is presented and worst case random and bias errors are estimated.
Brown, G. S.↗
Analytical displacements and vibrations of cantilevered unsymmetric fiber composite laminates
A fiber composite flat cantilever plate that has symmetric and nonsymmetric laminate configurations is theoretically investigated to determine its static and dynamic structural response. The finite element analysis method used includes a unique triangular finite element developed at Lewis for the analysis of fiber composite airfoils. The various responses investigated include tip displacements, natural frequencies, and fundamental mode shapes. The results show that laminate configurations may be selected for a cantilever such that when the tip at the leading edge is loaded normal to the plane of the plate, the tip at the trailing edge can (1) deflect in the opposite direction, (2) deflect about the same, or (3) deflect more than the tip at the leading edge. This variation in response can be utilized to provide built-in structural damping to resist flutter.
Minich, M. D.↗
Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations
A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.
Cooke, C. H.↗
A new formulation for anisotropic radiative transfer problems. I - Solution with a variational technique
The equations of radiative transfer in anisotropically scattering media are reformulated as linear operator equations in a single independent variable. The resulting equations are suitable for solution by a variety of standard mathematical techniques. The operators appearing in the resulting equations are in general nonsymmetric; however, it is shown that every bounded linear operator equation can be embedded in a symmetric linear operator equation and a variational solution can be obtained in a straightforward way. For purposes of demonstration, a Rayleigh-Ritz variational method is applied to three problems involving simple phase functions. It is to be noted that the variational technique demonstrated is of general applicability and permits simple solutions for a wide range of otherwise difficult mathematical problems in physics.
Cheyney, H., III↗
A NASTRAN implementation of the doubly asymptotic approximation for underwater shock response
A detailed description is given of how the decoupling approximation known as the doubly asymptotic approximation is implemented with NASTRAN to solve shock problems for submerged structures. The general approach involves locating the nonsymmetric terms (which couple structural and fluid variables) on the right hand side of the equations. This approach results in coefficient matrices of acceptable bandwidth but degrades numerical stability, requiring a smaller time step size than would otherwise be used. It is also shown how the structure's added (virtual) mass matrix, is calculated with NASTRAN.
Everstine, G. C.↗
Pure field theories and MACSYMA algorithms
A pure field theory attempts to describe physical phenomena through singularity-free solutions of field equations resulting from an action principle. The physics goes into forming the action principle and interpreting specific results. Algorithms for the intervening mathematical steps are sketched. Vacuum general relativity is a pure field theory, serving as model and providing checks for generalizations. The fields of general relativity are the 10 components of a symmetric Riemannian metric tensor; those of the Einstein-Straus generalization are the 16 components of a nonsymmetric. Algebraic properties are exploited in top level MACSYMA commands toward performing some of the algorithms of that generalization. The light cone for the theory as left by Einstein and Straus is found and simplifications of that theory are discussed.
Ament, W. S.↗
NASTRAN analysis of Tokamak vacuum vessel using interactive graphics
Isoparametric quadrilateral and triangular elements were used to represent the vacuum vessel shell structure. For toroidally symmetric loadings, MPCs were employed across model boundaries and rigid format 24 was invoked. Nonsymmetric loadings required the use of the cyclic symmetry analysis available with rigid format 49. NASTRAN served as an important analysis tool in the Tokamak design effort by providing a reliable means for assessing structural integrity. Interactive graphics were employed in the finite element model generation and in the post-processing of results. It was felt that model generation and checkout with interactive graphics reduced the modelling effort and debugging man-hours significantly.
Miller, A.↗