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At least 1,477 records · Page 82
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

A quasi-analytical method for non-iterative computation of nonlinear controls

An optimal control solution process was developed for a general class of nonlinear dynamical systems. The method combines control theory, perturbation methods, and Van Loan's recent matrix exponential results. A variety of applications support the practical utility of this method. Nonlinear rigid body optimal maneuvers are routinely solved. Flexible body dynamical systems of an order greater than 40 were solved. The method fails occasionally due to poor convergence of the perturbation expansion or numerical difficulties associated with computing the matrix exponential. The method is attractive because it appears to be a good candidate for semi-automation; no initial guess is required, and it usually converges at 2nd or 3rd order in minutes of machine time.

Junkins, J. L.↗
NASA NTRS1987

Selection principles and pattern formation in fluid mechanics and nonlinear shell theory

Research accomplishments are summarized and publications generated under the contract are listed. The general purpose of the research was to investigate various symmetry breaking problems in fluid mechanics by the use of structure parameters and selection principles. Although all of the nonlinear problems studied involved systems of partial differential equations, many of these problems led to the study of a single nonlinear operator equation of the form F(w, lambda, gamma) = 0, (w is an element of H), (lambda is an element of R1), (gamma is an element of R1). Instead of varying only the load parameter lambda, as is often done in the study of such equations, one of the main ideas used was to vary the structure parameter gamma in such a way that stable solutions were obtained. In this way one determines detailed stability results by making use of the structure of the model equations and the known physical parameters of the problem. The approach was carried out successfully for Benard-type convection problems, Taylor-like problems for short cylinders, rotating Couette-Poiseuille channel flows, and plane Couette flows. The main focus of the research was on wave theory of vortex breakdown in a tube. A number of preliminary results for inviscid axisymmetric flows were obtained.

Sather, Duane P.↗
NASA NTRS1987

Component mode synthesis and large deflection vibration of complex structures. Volume 3: Multiple-mode nonlinear free and forced vibrations of beams using finite element method

Multiple-mode nonlinear forced vibration of a beam was analyzed by the finite element method. Inplane (longitudinal) displacement and inertia (IDI) are considered in the formulation. By combining the finite element method and nonlinear theory, more realistic models of structural response are obtained more easily and faster.

Mei, Chuh↗
NASA NTRS1987

The convergence of spectral methods for nonlinear conservation laws

The convergence of the Fourier method for scalar nonlinear conservation laws which exhibit spontaneous shock discontinuities is discussed. Numerical tests indicate that the convergence may (and in fact in some cases must) fail, with or without post-processing of the numerical solution. Instead, a new kind of spectrally accurate vanishing viscosity is introduced to augment the Fourier approximation of such nonlinear conservation laws. Using compensated compactness arguments, it is shown that this spectral viscosity prevents oscillations, and convergence to the unique entropy solution follows.

Tadmor, Eitan↗
NASA NTRS1987

A hybrid transfinite element approach for nonlinear transient thermal analysis

A new computational approach for transient nonlinear thermal analysis of structures is proposed. It is a hybrid approach which combines the modeling versatility of contemporary finite elements in conjunction with transform methods and classical Bubnov-Galerkin schemes. The present study is limited to nonlinearities due to temperature-dependent thermophysical properties. Numerical test cases attest to the basic capabilities and therein validate the transfinite element approach by means of comparisons with conventional finite element schemes and/or available solutions.

Tamma, Kumar K.↗
NASA NTRS1986

Paneling methods with vorticity effects and corrections for nonlinear compressibility

The prediction of missile aerodynamic characteristics is presently undertaken through the application of supersonic paneling methods and nonlinear corrections to the prediction of missile aerodynamic characteristics. Attention is given to supersonic panel methods and line-singularity methods for the modeling of axisymmetric bodies, in combination with corrections for nonlinear flow phenomena, which are applied to complete missile, inlets, and wing-body combinations. The LRCDM2 computer program is used as an example of the methods presented.

Dillenius, Marnix F. E.↗
NASA NTRS1987

Nonlinear flight test trajectory controllers for aircraft

Flight test trajectory control systems are designed to enable the pilot to follow complex trajectories for evaluating an aircraft within its known flight envelope and to explore the boundaries of its capabilities. Previous design approaches were baed on linearized aircraft models necessitating a large amount of data storage along with gain schedules. In this paper, the synthesis of nonlinear flight test trajectory controllers for a fixed-wing aircraft is described. This approach uses singular perturbation theory and the recently developed theory of prelinearizing transformations. These controllers do not require gain scheduling for satisfactory operation, can be used in arbitrarily nonlinear maneuvers, and are mechanized with a direct, noniterative analytic solution.

Menon, P. K. A.↗
NASA NTRS1987

Nonlinear evolution of radiation-driven thermally unstable fluids

The nonlinear evolution of a radiation-driven thermally unstable planar fluid is simulated numerically using a semiimplicit finite-difference algorithm. When the equilibrium state of the fluid is perturbed by random initial excitation of the velocity field, dense, cool, two-dimensional structures are found to form in a rarer, warmer surrounding medium. The nonlinear phase of evolution is characterized by the turbulent contraction of the condensed region, accompanied by a significant increase in the amount of energy radiated. It is found that, if the random velocity perturbation has a sufficiently large amplitude, the fluid will not form condensed structures. Finally, the relationship of these results to observations of the solar chromosphere, transition region, and corona is discussed.

Dahlburg, R. B.↗
NASA NTRS1986

Solution of nonlinear finite difference ocean models by optimization methods with sensitivity and observational strategy analysis

The paper studies with finite difference nonlinear circulation models the uncertainties in interesting flow properties, such as western boundary current transport, potential and kinetic energy, owing to the uncertainty in the driving surface boundary condition. The procedure is based upon nonlinear optimization methods. The same calculations permit quantitative study of the importance of new information as a function of type, region of measurement and accuracy, providing a method to study various observing strategies. Uncertainty in a model parameter, the bottom friction coefficient, is studied in conjunction with uncertain measurements. The model is free to adjust the bottom friction coefficient such that an objective function is minimized while fitting a set of data to within prescribed bounds. The relative importance of the accuracy of the knowledge about the friction coefficient with respect to various kinds of observations is then quantified, and the possible range of the friction coefficients is calculated.

Schroeter, Jens↗
NASA NTRS1987

Solar oscillations - A method for deriving nonlinear effects

The frequencies of solar oscillations are so closely spaced that nonlinear interactions among modes are probable. The rate of interaction is proportional to an integral involving the eigenfunctions of the interacting modes, which usually are known only numerically. An approximation in which the eigenfunctions are strictly sinusoidal functions of a suitably defined radial variable, and the numerical details of stellar structure are banished to a coefficient in the integrand, are here explored. The physical assumptions are the same as in the asymptotic approximation of p- or g-modes. This method should allow a general investigation as to likely nonlinear interactions and which modes may participate in such interactions. The coupling of two p-modes by possible large-scale internal magnetic fields is introduced as an anisotropic pressure response to a displacement. Pairs of modes differing in frequency by less than the fraction magnetic/thermal pressure are strongly coupled, and energy appears to oscillate slowly between the two associated spherical harmonics. Potentially, upper limits may be derived for internal magnetic fields.

Wentzel, Donat G.↗
NASA NTRS1987

Nonlinear radiative condensation in a sheared magnetic field

A well-resolved two-dimensional nonlinear numerical simulation of the radiative/thermal instability in a sheared magnetic field is described which leads to filament formation. The condensation is initiated by a linearly unstable mode and widens until it is slowed by thermal conduction parallel to B. During the nonlinear evolution, the minimum temperature falls from 10 to the 6th K to 10 to the 4th K and eventually reaches a state of local thermal equilibrium in about five e-folding times.

Van Hoven, G.↗
NASA NTRS1987

The thermal stability of coronal loops by nonlinear diffusion asymptotics

A nonlinear reaction-diffusion equation and some additional constraints are derived which describe the time-dependent behavior of the temperature structure of the plasma in coronal loops. The equation is analyzed using nonlinear diffusion asymptotics, in particular singular perturbation techniques, and the results are interpreted in the context of the physical problem of the thermal stability and temporal behavior of the plasma. The results are consistent with the possibility of cyclic thermal behavior of the plasma, as suggested by Kuin and Martens (1982).

Pakkert, J. W.↗
NASA NTRS1987

A spectral view of nonlinear fluxes and stationary-transient interaction in the atmosphere

Nonlinear spectral transfers of kinetic energy and enstrophy, and stationary-transient interaction, are studied using global FGGE data for January 1979. The spectral transfers are found to be dominated by two dynamically distinct components, one due to nonlinear self-interactions within the transient flow and the other arising from coupled interactions between the stationary and transient parts of the flow. The former seems to be attributable to two-dimensional homogeneous turbulence, while the second cannot be understood within that theory. It is argued that the mixed stationary-transient interactions can be understood physically as a process of shear-induced spectral transfer of transient enstrophy along lines of constant zonal wavenumber. The transients act mainly to strengthen the stationary flow, and this 'forcing' operates on a timescale comparable to presumed viscous timescales.

Shepherd, Theodore G.↗
NASA NTRS1985

Nonlinear aerodynamic wing design

The applicability of new nonlinear theoretical techniques is demonstrated for supersonic wing design. The new technology was utilized to define outboard panels for an existing advanced tactical fighter model. Mach 1.6 maneuver point design and multi-operating point compromise surfaces were developed and tested. High aerodynamic efficiency was achieved at the design conditions. A corollary result was that only modest supersonic penalties were incurred to meet multiple aerodynamic requirements. The nonlinear potential analysis of a practical configuration arrangement correlated well with experimental data.

Bonner, Ellwood↗
NASA NTRS1987

The nonlinear thermodynamics of meteors, noctilucent clouds, enhanced airglow and global atmospheric circulation

Two types of fundamental topological junctions of elements are deduced from a nonlinear thermodynamical model. Using this scheme, the possibility of a causal relation between fireballs and faint meteors as nonlinear sources on the one hand, and noctilucent clouds (NC) and Hoffmeister's enhanced airglow (EA) as complementary formative processes in the middle atmosphere and ionosphere, on the other hand, is examined. The principal role of the global atmospheric circulation in this relation is demonstrated. Such circulation in the mesosphere appears to prevent the neutral dust dissipated by fireballs from becoming an efficient agent in NLC generation. In this case, the behavior of ionized material deposited by both the bright and faint meteors is more probably controlled, as shown from the annual variation of the E sub s layer by the darkness of lunar eclipses and the global circulation of the lower thermosphere. The role of fireballs and neutral dust might be more significant as a source of EA phenomenon.

Rajchl, J.↗
NASA NTRS1987

Numerical solution of turbulent flow past a backward facing step using a nonlinear K-epsilon model

The problem of turbulent flow past a backward facing step is important in many technological applications and has been used as a standard test case to evaluate the performance of turbulence models in the prediction of separated flows. It is well known that the commonly used kappa-epsilon (and K-l) models of turbulence yield inaccurate predictions for the reattachment points in this problem. By an analysis of the mean vorticity transport equation, it will be argued that the intrinsically inaccurate prediction of normal Reynolds stress differences by the Kappa-epsilon and K-l models is a major contributor to this problem. Computations using a new nonlinear kappa-epsilon model (which alleviates this deficiency) are made with the TEACH program. Comparisons are made between the improved results predicted by this nonlinear kappa-epsilon model and those obtained from the linear kappa-epsilon model as well as from second-order closure models.

Speziale, C. G.↗
NASA NTRS1988

Applications of nonlinear systems theory to control design

For most applications in the control area, the standard practice is to approximate a nonlinear mathematical model by a linear system. Since the feedback linearizable systems contain linear systems as a subclass, the procedure of approximating a nonlinear system by a feedback linearizable one is examined. Because many physical plants (e.g., aircraft at the NASA Ames Research Center) have mathematical models which are close to feedback linearizable systems, such approximations are certainly justified. Results and techniques are introduced for measuring the gap between the model and its truncated linearizable part. The topic of pure feedback systems is important to the study.

Hunt, L. R.↗
NASA NTRS1988

Nonlinear Constitutive Relations for High Temperature Applications, 1986

The purpose of the symposium was to review the state-of-the-art in nonlinear constitutive modeling of high temperature materials for aeronautics applications and to identify the need for future research and development efforts in this area. Through this symposium, it was recognized that considerable research efforts are urgently needed in the development of nonlinear constitutive relations for high temperature applications. In the aerospace industry this need is further prompted by recent advances in high temperature materials technology and new demands on material and component performance.

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