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At least 1,495 records · Page 83
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NASA NTRS1988

Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems

An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.

Banks, H. T.↗
NASA NTRS1988

The strong nonlinear interaction of Tollmien-Schlichting waves and Taylor-Goertler vortices in curved channel flow

Viscous fluid flows with curved streamlines can support both centrifugal and viscous traveling wave instabilities. Here the interaction of these instabilities in the context of the fully developed flow in a curved channel is discussed. The viscous (Tollmein-Schlichting) instability is described asymptotically at high Reynolds numbers and it is found that it can induce a Taylor-Goertler flow even at extremely small amplitudes. In this interaction, the Tollmein-Schlichting wave can drive a vortex state with wavelength either comparable with the channel width or the wavelength of lower branch viscous modes. The nonlinear equations which describe these interactions are solved for nonlinear equilibrium states.

Bennett, J.↗
NASA NTRS1987

Stochasticity in numerical solutions of the nonlinear Schroedinger equation

The cubically nonlinear Schroedinger equation is an important model of nonlinear phenomena in fluids and plasmas. Numerical solutions in a spatially periodic system commonly involve truncation to a finite number of Fourier modes. These solutions are found to be stochastic in the sense that the largest Liapunov exponent is positive. As the number of modes is increased, the size of this exponent appears to converge to zero, in agreement with the recent demonstration of the integrability of the spatially periodic case.

Shen, Mei-Mei↗
NASA NTRS1987

Nonlinear effects in coplanar GaAs/InGaAs strained-layer superlattice directional couplers

The performance characteristics of InGaAs/GaAs strained-layer superlattice coplanar ridge-type directional couplers realized by molecular beam epitaxy are reported. The measured power transfer characteristics with 1.15 micron incident photoexcitation demonstrate nonlinear coupling due to absorption associated with the tails of the excitonic resonances in the quantum wells. From a theoretical fit of the measured data, the nonlinear refractive index coefficient, n2, of the multiquantum well is found to be 2.25 x 10 to the -7th sq cm/W. This agrees very well with a value of n2 = 1.9 x 10 to the-7th sq cm/W obtained independently on the same material from interferometric measurents.

Das, Utpal↗
NASA NTRS1987

Nonlinear acoustic wave propagation in atmosphere TLSP - Final report

In this paper a model problem is considered that simulates an atmospheric acoustic wave propagation situation that is nonlinear. The model is derived from the basic Euler equations for the atmospheric flow and from the regular perturbations for the acoustic part. The nonlinear effects are studied by obtaining two successive linear problems in which the second one involves the solution of the first problem. Well-posedness of these problems is discussed and approximations of the radiation boundary conditions that can be used in numerical simulations are presented.

Hariharan, S. I.↗
NASA NTRS1988

Nonlinear aerodynamics of two-dimensional airfoils in severe maneuver

This paper presents a nonlinear theory of forces and moment acting on a two-dimensional airfoil in unsteady potential flow. Results are obtained for cases of both large and small amplitude motion. The analysis, which is based on an extension of Wagner's integral equation to the nonlinear regime, takes full advantage of the trailing wake's tendency to deform under local velocities. Interactive computational results are presented that show examples of wake-induced lift and moment augmentation on the order of 20 percent of quasi-static values. The expandability and flexibility of the present computational method are noted, as well as the relative speed with which solutions are obtained.

Scott, Matthew T.↗
NASA NTRS1988

Hybrid transfinite element modeling/analysis of nonlinear heat conduction problems involving phase change

The present paper describes the applicability of hybrid transfinite element modeling/analysis formulations for nonlinear heat conduction problems involving phase change. The methodology is based on application of transform approaches and classical Galerkin schemes with finite element formulations to maintain the modeling versatility and numerical features for computational analysis. In addition, in conjunction with the above, the effects due to latent heat are modeled using enthalpy formulations to enable a physically realistic approximation to be dealt computationally for materials exhibiting phase change within a narrow band of temperatures. Pertinent details of the approach and computational scheme adapted are described in technical detail. Numerical test cases of comparative nature are presented to demonstrate the applicability of the proposed formulations for numerical modeling/analysis of nonlinear heat conduction problems involving phase change.

Tamma, Kumar K.↗
NASA NTRS1987

Spacecraft attitude determination using a second-order nonlinear filter

The stringent attitude determination accuracy and faster slew maneuver requirements demanded by present-day spacecraft control systems motivate the development of recursive nonlinear filters for attitude estimation. This paper presents the second-order filter development for the estimation of attitude quaternion using three-axis gyro and star tracker measurement data. Performance comparisons have been made by computer simulation of system models and filter mechanization. It is shown that the second-order filter consistently performs better than the extended Kalman filter when the performance index of the root sum square estimation error of the quaternion vector is compared. The second-order filter identifies the gyro drift rates faster than the extended Kalman filter. The uniqueness of this algorithm is the online generation of the time-varying process and measurement noise covariance matrices, derived as a function or the process and measurement nonlinearity, respectively.

Vathsal, S.↗
NASA NTRS1987

Effect of nonlinear instability on gravity-wave momentum transport

This paper investigates the nonlinear instability of internal gravity waves and the effects of their nonlinear interaction on momentum flux, using simple theoretical and numerical models. From the result of an analysis of parametric instability of a two-dimensional internal gravity wave as discussed by Yeh and Liu (1981) and Klostermeyer (1982), a group trajectory length scale for a gravity wave packet was determined, expressed in terms of the dominant vertical wavelenght and the degree of convective saturation. It is shown that this analysis justifies the Eikonal saturation method for relatively transient packets, that are well below the saturation amplitude, propagating in a slowly varying mean flow. Conversely, linear theory fails for persistent disturbances and trasient wave packets near convective saturation.

Dunkerton, Timothy J.↗
NASA NTRS1988

Nonlinear evolution of longitudinal plasma waves

Long-time nonlinear behavior of single-mode longitudinal plasma waves is studied on the basis of the Vlasov equation with Fokker-Planck collision terms. The resonant layer, trapped island, collisional sublayers, and X-point neighborhoods are analyzed. A nonlinear evolution equation is obtained and the wave-generated current is also evaluated.

Pao, Young-Ping↗
NASA NTRS1988

Magnetic fields interacting with nonlinear compressible convection

Two-dimensional numerical simulations are used to study fully compressible convection in the presence of an imposed magnetic field. Highly nonlinear flows are considered that span multiple density scale heights. The convection tends to sweep the initially uniform vertical magnetic field into concentrated flux sheets with significant magnetic pressures. These flux sheets are partially evacuated, and effects of buoyancy and Lorentz forces there can serve to suppress motions. The flux sheets can be surrounded by a sheath of descending flow. If the imposed magnetic field is sufficiently strong, the convection can become oscillatory. The unstably stratified fluid layer has an initial density ratio (bottom to top of layer) of 11. Surveys of solutions at fixed Rayleigh number sample Chandrasekhar numbers from 1 to 1000 and magnetic Prandtl numbers from 1/16 to 1. These nonlinear simulations utilize a two-dimensional numerical scheme based on a modified two-step Lax-Wendroff method.

Hulburt, Neal E.↗
NASA NTRS1988

Influence of geometric nonlinearities on skin-stiffener interface stresses

A method for computing skin-stiffener interface stresses in stiffened composite panels is developed. Both geometrically linear and nonlinear analyses are considered. Particular attention is given to the flange termination region where stresses are expected to exhibit unbounded characteristics. The method is based on a finite-element analysis and an elasticity solution. The results indicate that the inclusion of geometric nonlinearities is very important for an accurate determination of the interface stresses. Membrane flattening of the panel tends to reduce the tendency of the stiffener to separate.

Cohen, D.↗
NASA NTRS1988

The theoretical and experimental study of the nonlinear and chaotic response of curved panels to intense acoustic excitation

Assuming a single-mode transverse displacement, a simple formula is derived for the transverse load-displacement relationship of a plate under in-plane compression. The formula is used to derive a simple analytical expression for the nonlinear dynamic response of postbuckled plates under sinusoidal or random excitation. The highly nonlinear motion of snap-through can be easily interpreted using the single-mode formula. Experimental results are obtained using buckled and cylindrical aluminum panels using discrete frequency and broadband excitation of mechanical and acoustic forces.

Ng, C. F.↗
NASA NTRS1988

The nonlinear behavior of a passive zero-spring-rate suspension system

Various concepts for advanced syspension systems have been proposed for counteracting gravity loads in ground vibration testing of large space structures. Approximating the flight modes of a low-frequency flexible structure in a ground test requires a very soft suspension system. The dynamic behavior of a passive zero-spring-rate mechanism, sometimes used for such ground testing, is analyzed. This mechanism reduces the stiffness inherent in suspending a test specimen by cables. However, the mechanism is shown to be sensitive to imperfections. Imperfections can initiate nonlinear behavior which becomes more pronounced at lower operating frequencies. Furthermore, large pendular motion of the suspension system couples with the vertical motion, producing additional nonlinearity.

Woodard, Stanley E.↗
NASA NTRS1988

Integrated nonlinear structural analysis and design

An integrated approach to the design optimization of structures which require nonlinear analysis is proposed. The optimization process begins with a linearized structural response and the amount of nonlinearity is increased as the optimum design becomes closer. The proposed approach has the potential of reducing substantially the computational cost of the optimization. Two truss examples are used for demonstration.

Haftka, Raphael T.↗
NASA NTRS1988

Effect of joint damping and joint nonlinearity on the dynamics of space structures

Analyses of the effect of linear joint characteristics on the vibrations of a free-free, three-joint beam model show that increasing joint damping increases resonant frequencies and increases modal damping but only to the point where the joint gets 'locked up' by damping. This behavior is different from that predicted by modeling joint damping as proportional damping. Nonlinear analyses of the three-joint model with cubic springs at the joints show all the classical single DOF nonlinear response behavior at each resonance of the multiple DOF system: nondoubling of response for a doubling of forcing amplitude, multiple solutions, jump behavior, and resonant frequency shifts. These properties can be concisely quantified by characteristic backbone curves, which show the locus of resonant peaks for increasing forcing amplitude.

Bowden, Mary↗
NASA NTRS1988

The topology of large-scale structure. II - Nonlinear evolution of Gaussian models

The evolution of non-Gaussian behavior in the large-scale universe from Gaussian initial conditions is studied. Topology measures developed in previous papers are applied to the smoothed initial, final, and biased matter distributions of cold dark matter, white noise, and massive neutrino simulations. When the smoothing length is approximately twice the mass correlation length or larger, the evolved models look like the initial conditions, suggesting that random phase hypotheses in cosmology can be tested with adequate data sets. When a smaller smoothing length is used, nonlinear effects are recovered, so nonlinear effects on topology can be detected in redshift surveys after smoothing at the mean intergalaxy separation. Hot dark matter models develop manifestly non-Gaussian behavior attributable to phase correlations, with a topology reminiscent of bubble or sheet distributions. Cold dark matter models remain Gaussian, and biasing does not disguise this.

Melott, Adrian L.↗
NASA NTRS1987

Nonlinear plants, factorizations and stable feedback systems

For nonlinear plants represented by causal maps defined over extended spaces, right factorization and normalized right-coprime factorization concepts are discussed in terms of well-posed stable feedback systems. This setup covers continuous-time, discrete-time, time-invariant or time-varying input-output maps. The nonlinear maps are factored in terms of causal bounded-input bounded-output stable maps. In factored form, all instabilities of the original map are represented by the inverse of a causal stable `denominator' map. The existence of maps with right factorizations and normalized right-coprime factorizations is shown using a well-posed stable unity-feedback system. In the case where one of the subsystems has a normalized right-coprime factorization, the stability of the feedback system is equivalent to the stability of the pseudostate map.

Desoer, Charles A.↗