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At least 919 records · Page 51
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NASA NTRS1972

Application of multivariable search techniques to structural design optimization

Multivariable optimization techniques are applied to a particular class of minimum weight structural design problems: the design of an axially loaded, pressurized, stiffened cylinder. Minimum weight designs are obtained by a variety of search algorithms: first- and second-order, elemental perturbation, and randomized techniques. An exterior penalty function approach to constrained minimization is employed. Some comparisons are made with solutions obtained by an interior penalty function procedure. In general, it would appear that an interior penalty function approach may not be as well suited to the class of design problems considered as the exterior penalty function approach. It is also shown that a combination of search algorithms will tend to arrive at an extremal design in a more reliable manner than a single algorithm. The effect of incorporating realistic geometrical constraints on stiffener cross-sections is investigated. A limited comparison is made between minimum weight cylinders designed on the basis of a linear stability analysis and cylinders designed on the basis of empirical buckling data. Finally, a technique for locating more than one extremal is demonstrated.

Jones, R. T.↗
NASA NTRS1972

Overview of technology relative to the pogo instability on space shuttle

The prediction of pogo contains a major source of uncertainty in the difficulty of defining the dynamic characteristics of certain components. An overview of the space shuttle technology with respect to each the following pogo problem areas is presented: structure, tank-liquid interaction, feedline, engine (pump), pogo-loop/control-loop interaction, and stability analysis.

Pinson, L. D.↗
NASA NTRS1972

Low-frequency macroscopic instabilities of fully ionized magnetoplasma

Studies are described of low-frequency quasi-static instabilities in a fully ionized plasma. The plasma is assumed to be immersed in a uniform magnetic field, and is either uniform or has a number density gradient perpendicular to the magnetic field. A moment equation description of the ion and electron dynamics is used; collisions are assumed to have a strong effect on electron motion along the magnetic field. Before considering specific modes, a stability analysis is developed which allows a classification of wave growth characteristics to be made for a bounded system from solutions to the dispersion relation for an infinite system. Also, a method is given for calculating the normal mode frequencies and wave profiles by using the reflection coefficients at the boundaries. For wave propagation perpendicular to the magnetic field, the flute wave is studied in cylindrical geometry. The destabilizing effect of a radial electric field is considered by solving a differential equation.

Rognlien, T. D.↗
NASA NTRS1973

Dynamics and control of advanced space vehicles, volume 1

The following studies are reported: (1) Modal analyses of elastic continua for Liapunov stability analysis of flexible spacecraft; (2) development of general purpose simulation equations for arbitrary spacecraft; (3) evaluation of alternative mathematical models for elastic components of spacecraft; and (4) examination of the influence of vehicle flexibility on spacecraft attitude control system performance.

Likins, P. W.↗
NASA NTRS1973

Energy-like Liapunov functionals for linear elastic systems on a Hilbert space.

An approach is presented for generating energy-like functionals for linear elastic dynamic systems on a Hilbert space. The objective is to obtain a family of functionals which may be used for stability analysis of the equilibrium, i.e., Liapunov functionals. Although the energy functional, when one exists, is always a member of this family, the family is shown to exist even when an energy functional does not. Several discrete and distributed-parameter examples are presented, as are certain specific techniques for utilizing this approach.

Walker, J. A.↗
NASA NTRS1972

On the initiation of melt fracture.

Discussion of a problem encountered in the processing of viscoelastic materials that is caused by the presence of a hydrodynamic instability in the extrusion of polymer melts. The importance of the so-called Weissenberg number in determining the onset of the melt fracture is examined using classical linearized hydrodynamic stability analysis. It is shown that the simple shearing flow of a viscoelastic fluid becomes unstable at a critical value of the Weissenberg number. Implications for the extrusion processing of polymers are reviewed.

Mcintire, L. V.↗
NASA NTRS1952

Experimental Study of Isothermal Wake-Flow Characteristics of Various Flame-Holder Shapes

An investigation of the isothermal wake-flow characteristics of several flame-holder shapes was carried out in a 4- by 4-inch flow chamber. The effects of flame-holder-shape changes on the characteristics of the Karman vortices and thus on the recirculation zones to which experimenters have related the combustion process were obtained for several flame holders. The results may furnish a basis of correlation, of combustion efficiency and stability for similarly shaped flame holders in combustion studies. Values of the spacing ratio-(ratio of lateral spacing to longitudinal spacing of vortices] obtained for the various shapes approximated the theoretical value of 0.36 given by the Karman stability analysis. Variations in vortex strength of more than 200 percent and in frequency of more than 60 percent were accomplished by varying flame-holder shape. A maximum increase in the recirculation parameter of 56 percent over that for a conventional V-gutter was also obtained. Varying flameholder shape and size enables the designer to select many schedules of variations in vortex strength and frequency- not obtainable by changing size only and may make it possible to approach theoretical maximum vortex strength for any given frequency.

Younger, G. G.↗
NASA NTRS1974

Enhancing simulation of efficiency with analytical tools

Some means of combining both computer simulation and anlytical techniques are indicated in order to mutually enhance their efficiency as design tools and to motivate those involved in engineering design to consider using such combinations. While the idea is not new, heavy reliance on computers often seems to overshadow the potential utility of analytical tools. Although the example used is drawn from the area of dynamics and control, the principles espoused are applicable to other fields. In the example the parameter plane stability analysis technique is described briefly and extended beyond that reported in the literature to increase its utility (through a simple set of recursive formulas) and its applicability (through the portrayal of the effect of varying the sampling period of the computer). The numerical values that were rapidly selected by analysis were found to be correct for the hybrid computer simulation for which they were needed. This obviated the need for cut-and-try methods to choose the numerical values, thereby saving both time and computer utilization.

Seltzer, S. M.↗
NASA NTRS1974

Comparison of approximate and numerical analyses of nonlinear combustion instability

At the present time, there are three general analytical techniques available to study problems of unsteady motions in rocket motors: linear stability analysis; approximate nonlinear analysis, founded on examining the behavior of coupled normal modes; and numerical calculations based on the conservation equations for one-dimensional flows. The last two yield the linear results as a limit. It is the main purpose of this paper to check the accuracy of the approximate analysis against the numerical analysis for some special cases. The results provide some justification for using the approximate analysis to study three-dimensional problems.

Culick, F. E. C.↗
NASA NTRS1973

Partial implicitization

The steady-state solution to the full Navier-Stokes equations for complicated flows is generally difficult to obtain. The Burgers (1948) equation is used as a model of the Navier-Stokes equations. The steady-state solution is obtained by a one-step explicit technique resulting from a partial implicitization of the difference equation. Stability analysis shows that the technique is unconditionally stable, and numerical tests show the technique to be accurate.

Graves, R. A., Jr.↗
NASA NTRS1974

Exponential stability of large-scale discrete systems

The concept of vector Liapunov functions is used to obtain conditions for the exponential stability of large-scale discrete systems which can be decomposed into a number of interconnected subsystems with the same stability property. Both the structurally invariant composite systems and the large-scale systems under structural perturbations are considered. Connective absolute stability of a large-scale system composed of the interconnected Lur'e-type subsystems is defined and resolved in this context, resulting in a computationally and conceptually attractive alternative to a straightforward stability analysis of the system by frequency-domain criteria.

Grujic, L. T.↗
NASA NTRS1974

Peak pool boiling heat flux in viscous liquids

The stability of a gas jet in a surrounding viscous liquid is studied. An expression is developed for the critical velocity at which the jet becomes unstable in a returning viscous liquid. The stability analysis is made to correspond with the geometrical configuration of gas jets and liquid columns similar to those observed near the peak pool boiling heat flux. The critical velocity of the gas jet is then used to obtain the functional form of the peak heat flux on flat plates and cylindrical heaters. The expressions are compared with original observations of the peak heat flux in very viscous liquids on flat plate, and cylindrical, heaters at both earth-normal, and elevated, gravities.

Dhir, V. K.↗
NASA NTRS1975

Large-scale systems: Complexity, stability, reliability

After showing that a complex dynamic system with a competitive structure has highly reliable stability, a class of noncompetitive dynamic systems for which competitive models can be constructed is defined. It is shown that such a construction is possible in the context of the hierarchic stability analysis. The scheme is based on the comparison principle and vector Liapunov functions.

Siljak, D. D.↗
NASA NTRS1975

Analytical stability and simulation response study for a coupled two-body system

An analytical stability study and a digital simulation response study of two connected rigid bodies are documented. Relative rotation of the bodies at the connection is allowed, thereby providing a model suitable for studying system stability and response during a soft-dock regime. Provisions are made of a docking port axes alignment torque and a despin torque capability for encountering spinning payloads. Although the stability analysis is based on linearized equations, the digital simulation is based on nonlinear models.

Tao, K. M.↗
NASA NTRS1975

The Cepheid mode problem

The modal behavior of RR Lyrae stars and low mass Cepheids has been investigated using a nonlinear relaxation technique and stability analysis. The advantages of this type of numerical approach in investigations of preferred mode of pulsation are discussed. The results obtained for both classes of variable stars are quite similar: first harmonic pulsation toward the blue, fundamental pulsation toward the red, and mixed-mode behavior at the extreme red edge of the instability strip. In addition, stars near the center of the strip can pulsate in either the fundamental or the first harmonic mode. Possible implications for observational results, including the Oosterhoff dichotomy of globular clusters and the beat Cepheids, are discussed.

Stellingwerf, R. F.↗
NASA NTRS1975

Forward marching procedure for separated boundary-layer flows

A forward-marching procedure for separated boundary-layer flows which permits the rapid and accurate solution of flows of limited extent is presented. The streamwise convection of vorticity in the reversed flow region is neglected, and this approximation is incorporated into a previously developed (Carter, 1974) inverse boundary-layer procedure. The equations are solved by the Crank-Nicolson finite-difference scheme in which column iteration is carried out at each streamwise station. Instabilities encountered in the column iterations are removed by introducing timelike terms in the finite-difference equations. This provides both unconditional diagonal dominance and a column iterative scheme, found to be stable using the von Neumann stability analysis.

Carter, J. E.↗
NASA NTRS1976

Climate stability for a Sellers-type model

We study a diffusive energy-balance climate model governed by a nonlinear parabolic partial differential equation. Three positive steady-state solutions of this equation are found; they correspond to three possible climates of our planet: an interglacial (nearly identical to the present climate), a glacial, and a completely ice-covered earth. We consider also models similar to the main one studied, and determine the number of their steady states. All the models have albedo continuously varying with latitude and temperature, and entirely diffusive horizontal heat transfer. The diffusion is taken to be nonlinear as well as linear. We investigate the stability under small perturbations of the main model's climates. A stability criterion is derived, and its application shows that the 'present climate' and the 'deep freeze' are stable, whereas the model's glacial is unstable. A variational principle is introduced to confirm the results of this stability analysis. For a sufficient decrease in solar radiation (about 2%) the glacial and interglacial solutions disappear, leaving the ice-covered earth as the only possible climate.

Ghil, M.↗