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At least 487 records · Page 27

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NASA NTRS1986

On the Nonlinearity of Modern Shock-Capturing Schemes

The development is reviewed of shock capturing methods, paying special attention to the increasing nonlinearity in the design of numerical schemes. The nature is studies of this nonlinearity and its relation to upwind differencing is examined. This nonlinearity of the modern shock capturing methods is essential, in the sense that linear analysis is not justified and may lead to wrong conclusions. Examples to demonstrate this point are given.

Harten, A.↗

NASA NTRS1987

Dynamics of trusses having nonlinear joints

The transient analysis of trusses having nonlinear joints can be accomplished using the residual force technique. The technique was applied a two degree of freedom spring mass system, a four bay planar truss, and an actual ten bay deployable truss. Joints chosen for analysis were the nonlinear gap joints and the linear Voigt joints. Results from the nonlinear gap analyses generally indicate that coupling between the modes can display some interesting effects during free vibration. One particularly interesting effect was that the damping of the structure appeared to be higher than could be accounted for from modal damping alone. Energy transferral from the lower to the higher modes was found to exist as a result of the modal coupling. The apparently increased damping was due to the fact that the energy transferred to the higher modes is inherently dissipated more quickly. Another interesting phenomenon was that the lower modes could drive the higher modes even during free vibration and that these modes could display a rather large quasi-steady state behavior even when modal damping was present. Gaps were also found to increase the amplitude and period of the free vibration response as expected.

Chapman, J. M.↗

NASA NTRS1987

Hamiltonian theory of nonlinear waves in planetary rings

The derivation of a Hamiltonian field theory for nonlinear density waves in Saturn's rings is discussed. Starting with a Hamiltonian for a discrete system of gravitating streamlines, an averaged Hamiltonian is obtained by successive applications of Lie transforms. The transformation may be carried out to any desired order in q, where q is the nonlinearity parameter defined in the work of Shu, et al (1985) and Borderies et al (1985). Subsequent application of the Wentzel-Kramer-Brillouin Method approximation yields an asymptotic field Hamiltonian. Both the nonlinear dispersion relation and the wave action transport equation are easily derived from the corresponding Lagrangian by the standard variational principle.

Stewart, G. R.↗

NASA NTRS1986

The evolution of nonlinear Alfven waves subject to growth and damping

The effects of wave amplification (by streaming particle distributions) and damping (by ion-cyclotron resonance absorption) on the nonlinear evolution of Alfven waves are investigated theoretically. The results of numerical simulations based on the derivative-Schroedinger-equation model of Spangler and Sheerin (1983 and 1985) are presented graphically and characterized in detail, with an emphasis on astrophysical applications. Three phases of wave-packet evolution (linear, nonlinear-saturation, and postsaturation quasi-steady) are identified, and nonlinearity is found to transfer wave energy from growing or amplified wavenumbers to wavenumbers affected by damping. It is pointed out that although there are similarities between the solitonlike pulses predicted by the simulations and short-wavelength shocklet structures observed in the earth bow shock, the model does not explain why low-frequency waves stop growing in the vicinity of the bow shock.

Spangler, S. R.↗

NASA NTRS1986

Multiply scaled constrained nonlinear equation solvers

To improve the numerical stability of nonlinear equation solvers, a partitioned multiply scaled constraint scheme is developed. This scheme enables hierarchical levels of control for nonlinear equation solvers. To complement the procedure, partitioned convergence checks are established along with self-adaptive partitioning schemes. Overall, such procedures greatly enhance the numerical stability of the original solvers. To demonstrate and motivate the development of the scheme, the problem of nonlinear heat conduction is considered. In this context the main emphasis is given to successive substitution-type schemes. To verify the improved numerical characteristics associated with partitioned multiply scaled solvers, results are presented for several benchmark examples.

Padovan, Joe↗

NASA NTRS1987

Ultrasonic characterization of the nonlinear elastic properties of unidirectional graphite/epoxy composites

The theoretical treatment of linear and nonlinear elasticity in a unidirectionally fiber reinforced composite as well as measurements for a unidirectional graphite/epoxy composite (T300/5208) are presented. Linear elastic properties were measured by both ultrasonic and strain gage measurements. The nonlinear properties were determined by measuring changes in ultrasonic natural phase velocity with a pulsed phase locked loop interferometer as a function of stress and temperature. These measurements provide the basis for further investigations into the relationship between nonlinear elastic properties and other important properties such as strength and fiber-matrix interfacial stength in graphite/epoxy composites.

Prosser, William H.↗

NASA NTRS1988

A nonlinear filtering process diagnostic system for the Space Station

A nonlinear filtering process diagnostic system, terrestrial simulation and real time implementation studies is presented. Possible applications to Space Station subsystem elements are discussed. A process diagnostic system using model based nonlinear filtering for systems with random structure was shown to provide improvements in stability, robustness, and overall performance in comparison to linear filter based systems. A suboptimal version of the nonlinear filter (zero order approximation filter, or ZOA filter) was used in simulation studies, initially, with a pressurized water reactor model and then with water/steam heat exchanger models. Finally, a real time implementation for leak detection in a water/steam heat exchanger was conducted using the ZOA filter and heat exchanger models.

Yoel, Raymond R.↗

NASA NTRS1988

Convergence of Galerkin approximations for operator Riccati equations: A nonlinear evolution equation approach

An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.

Rosen, I. G.↗

NASA NTRS1987

Integrating nonlinear aerodynamic and structural analysis for a complete fighter configuration

The coupling of a nonlinear aerodynamics program with a structural analysis program to include the effects of static aeroelasticity in early preliminary design studies is described. A nonlinear, full potential aerodynamics method with capability to model geometric details of a complete aircraft in supersonic flow is used. The deflections of the lifting surfaces are calculated using an equivalent plate structural representation which can readily accommodate the changes in stiffness and geometric properties required during the preliminary design process. An iterative solution procedure is used to obtain consistent aerodynamic loads and structural deflections at the specified flight conditions. The volume of data transmitted between programs is minimized. The procedure is applied to a complete aircraft and the numerical results illustrate the aeroelastic effects on pressure distribution as well as total forces and moments. During this design study, the thickness distribution of the wing cover skins was initially sized based on rigid loads and subsequently resized under aeroelastic loads. Comparisons are made between these nonlinear aeroelastic results and results obtained from linear aerodynamic methods applied to a rigid shape during conceptual design studies.

Tatum, Kenneth E.↗

NASA NTRS1986

Variable structure control of nonlinear systems through simplified uncertain models

A variable structure control approach is presented for the robust stabilization of feedback equivalent nonlinear systems whose proposed model lies in the same structural orbit of a linear system in Brunovsky's canonical form. An attempt to linearize exactly the nonlinear plant on the basis of the feedback control law derived for the available model results in a nonlinearly perturbed canonical system for the expanded class of possible equivalent control functions. Conservatism tends to grow as modeling errors become larger. In order to preserve the internal controllability structure of the plant, it is proposed that model simplification be carried out on the open-loop-transformed system. As an example, a controller is developed for a single link manipulator with an elastic joint.

Sira-Ramirez, Hebertt↗

NASA NTRS1986

Approximating linearizations for nonlinear systems

The following problem is examined: given a nonlinear control system dot-x(t) = f(x/t/) + the sum to m terms (i = 1) u sub i (t)g sub i (x/t/) on R(n) and a point x(0) in R(n), approximate the system near x(0) by a linear system. One approach is to use the usual Taylor series linearization. However, the controllability properties of both the nonlinear and linear systems depend on certain Lie brackets of the vector field under consideration. This suggests that a linear approximation based on Lie bracket matching should be constructed at x(0). In general, the linearizations based on the Taylor method and the Lie bracket approach are different. However, under certain mild assumptions, it is shown that there is a coordinate system for R(n) near x(0) in which these two types of linearizations agree. The importance of this agreement is indicated by examining the time responses of the nonlinear system and its linear approximation and comparing the lower order kernels in Volterra expansions of each.

Hunt, L. R.↗

NASA NTRS1988

A brief review on the identification of nonlinear mechanical systems

This paper presents a brief review of the disciplines used in the identification of nonlinear mechanical systems, including the detection of nonlinearities and their quantification, and parameter estimation. Techniques for determining the parameters of nonlinear system models with assumed model form are described and briefly discussed. Recent developments in identifying system models which may contain the actual model forms as well as incorrect forms is also briefly described. A list of representative references from structures and control disciplines is given.

Natke, H. G.↗

NASA NTRS1988

A nonlinear analysis of an equilibrium craze. I - Problem formulation and solution. II - Simulations of craze and crack growth

A numerical method is developed for the determinations of the equilibrium shape of a craze in an infinite elastic plane whose fibrils exhibit very general nonlinear force-displacement behavior. The problem formulation is based on the superposition of the relevant elasticity Green's function; the solution of the resulting nonlinear problem is obtained by using Picard's successive approximation scheme. The model is used to investigate the effect of nonlinear fibril behavior on the mechanics of craze and crack growth, and the results are compared with the Dugdale model.

Ungsuwarungsri, T.↗

NASA NTRS1987

Nonlinear system approximations

The approximation of a nonlinear system by a feedback linearizable system instead of a linear system is considered. Two approaches presently exist in the literature. One involves the concept of involutivity to a certain order, and the other considers a canonical expansion and pure feedback approximation. The relationship between these two methods is shown. This provides insight into lower-order invariants in the equivalence problem for two nonlinear systems. The output time responses for a nonlinear system and its feedback linearizable approximation are outlined.

Goldthwait, Richard G.↗

NASA NTRS1988

Nonlinear photorefractive response at high modulation depths

The response of photorefractive materials to sinusoidal intensity patterns of high modulation depths is considered. It is shown that the induced refractive-index response in this regime is highly nonlinear. Concise analytic expressions for the various nonlinear harmonics of the photorefractive response field are developed and compared with exact numerical solutions of the underlying charge-transport equations as well as with the results of previous theoretical models over a broad range of physical parameters. We show that the nonlinear response characteristics are strongly dependent on both the magnitude of applied electric fields and the relative concentrations of charge donor and acceptor sites in the material. For drift dominated recording, in particular, we determine analytically that in the limit of a minimal acceptor/donor ratio, the amplitudes of higher spatial harmonics of the response reach a maximum and eventually decay as functions of increasing applied field, whereas these amplitudes reach a nonzero limit in the case of a near-unity acceptor/donor ratio. Finally, we generalize our results to account for diffusion effects in an appended derivation.

Vachss, Frederick↗

NASA NTRS1987

Ultrasonic characterization of the nonlinear elastic properties of unidirectional graphite/epoxy composites

Prosser, William H.↗

NASA NTRS1988

Nonlinear roll-up of externally excited free shear layers

The effects of strong critical-layer nonlinearity on the spatially growing instabilities of a shear layer between two parallel streams are considered. A composite expansion technique is used to obtain a single formula that accounts for both shear-layer spreading and nonlinear critical-layer effects. Nonlinearity causes the instability to saturate well upstream of the linear neutral stability point. It also produces vorticity roll-up that cannot be predicted by linear theory.

Goldstein, M. E.↗

NASA NTRS1988

Survey of optimization techniques for nonlinear spacecraft trajectory searches

Mathematical analysis of the optimal search of a nonlinear spacecraft trajectory to arrive at a set of desired targets is presented. A high precision integrated trajectory program and several optimization software libraries are used to search for a converged nonlinear spacecraft trajectory. Several examples for the Galileo Jupiter Orbiter and the Ocean Topography Experiment (TOPEX) are presented that illustrate a variety of the optimization methods used in nonlinear spacecraft trajectory searches.

Wang, Tseng-Chan↗