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NASA NTRS1987

Macroscale particle simulation of kinetic Alfven waves

Two types of simulations of the kinetic Alfven wave are presented using a macroscale particle simulation code (Tanaka and Sato, 1986) which enables individual particle dynamics to be followed in the MHD scales. In this code, low frequency electromagnetic fields are solved by eliminating high frequency oscillations such as the light modes, and the scalar potential electric field is solved by eliminating Lagrangian oscillations. The dependences of the frequency and the Landau damping on the perpendicular wavenumber were studied, and good agreement was found between simulation and theoretical predictions. Some fundamental nonlinear interactions of the kinetic Alfven wave with the particles (parallel acceleration of the electrons) were also noted.

Tanaka, Motohiko↗

NASA NTRS1989

Nonlinear evolution of oblique waves on compressible shear layers

The effects of critical-layer nonlinearity on spatially growing oblique instability waves on compressible shear layers between two parallel streams are considered. The analysis shows that mean temperature nonuniformities cause nonlinearity to occur at much smaller amplitudes than it does when the flow is isothermal. The nonlinear instability wave growth rate effects are described by an integrodifferential equation which bears some resemblance to the Landau equation, in that it involves a cubic-type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. Inviscid solutions always end in a singularity at a finite downstream distance, but viscosity can eliminate this singularity for certain parameter ranges.

Goldstein, M. E.↗

NASA NTRS2009

Ultra-Broad-Band Optical Parametric Amplifier or Oscillator

A concept for an ultra-broad-band optical parametric amplifier or oscillator has emerged as a by-product of a theoretical study in fundamental quantum optics. The study was originally intended to address the question of whether the two-photon temporal correlation function of light [in particular, light produced by spontaneous parametric down conversion (SPDC)] can be considerably narrower than the inverse of the spectral width (bandwidth) of the light. The answer to the question was found to be negative. More specifically, on the basis of the universal integral relations between the quantum two-photon temporal correlation and the classical spectrum of light, it was found that the lower limit of two-photon correlation time is set approximately by the inverse of the bandwidth. The mathematical solution for the minimum two-photon correlation time also provides the minimum relative frequency dispersion of the down-converted light components; in turn, the minimum relative frequency dispersion translates to the maximum bandwidth, which is important for the design of an ultra-broad-band optical parametric oscillator or amplifier. In the study, results of an analysis of the general integral relations were applied in the case of an optically nonlinear, frequency-dispersive crystal in which SPDC produces collinear photons. Equations were found for the crystal orientation and pump wavelength, specific for each parametric-down-converting crystal, that eliminate the relative frequency dispersion of collinear degenerate (equal-frequency) signal and idler components up to the fourth order in the frequency-detuning parameter

Strekalov, Dmitry↗

NASA NTRS1991

Effect of motor dynamics on nonlinear feedback robot arm control

A nonlinear feedback robot controller that incorporates the robot manipulator dynamics and the robot joint motor dynamics is proposed. The manipulator dynamics and the motor dynamics are coupled to obtain a third-order-dynamic model, and differential geometric control theory is applied to produce a linearized and decoupled robot controller. The derived robot controller operates in the robot task space, thus eliminating the need for decomposition of motion commands into robot joint space commands. Computer simulations are performed to verify the feasibility of the proposed robot controller. The controller is further experimentally evaluated on the PUMA 560 robot arm. The experiments show that the proposed controller produces good trajectory tracking performances and is robust in the presence of model inaccuracies. Compared with a nonlinear feedback robot controller based on the manipulator dynamics only, the proposed robot controller yields conspicuously improved performance.

Tarn, Tzyh-Jong↗

NASA NTRS1974

Computational procedures for mixed equations with shock waves

This paper discusses the procedures we have developed to treat a canonical problem involving a mixed nonlinear equation with boundary data that imply a discontinuous solution. This equation arises in various physical contexts and is basic to the description of the nonlinear acoustic behavior of a shock wave near a caustic. The numerical scheme developed is of second order, treats discontinuities as such by applying the appropriate jump conditions across them, and eliminates the numerical dissipation and dispersion associated with large gradients. Our results are compared with the results of a first-order scheme and with those of a second-order scheme we have developed. The algorithm used here can easily be generalized to more complicated problems, including transonic flows with imbedded shocks.

Yu, N. J.↗

NASA NTRS1982

Finite element analysis for bearingless rotor blade aeroelasticity

A conventional articulated rotor blade has mechanical flap and lag hinges, a lag damper, and a pitch bearing. In connection with an interest in designs of greater mechanical simplicity and increased maintainability, hingeless and bearingless rotors have been developed. A hingeless blade lacks the hinges and is cantilevered at the hub. It does have a pitch bearing for pitch control. A bearingless design eliminates the hinges and the pitch bearing as well. In the present investigation of bearingless rotor blade characteristics, finite element analysis has been successfully applied to determine the solutions of the nonlinear trim equations and the linearized flutter equations of multiple-load-path blades. The employed formulation is based on Hamilton's principle. The spatial dependence of the equations of motion is discretized by dividing the flexbeams, the torque tube, and the outboard into a number of elements.

Sivaneri, N. T.↗

NASA NTRS1976

Derivatives of a statically reduced stiffness matrix with respect to sizing variables

An expression is obtained for the first derivatives with respect to the sizing variables of a statically reduced stiffness matrix that is a nonlinear function of the sizing variables, where the unreduced stiffness matrix is a linear function of the sizing variables. An accepted procedure to reduce the number of degrees of freedom is to eliminate a number of nodal displacements from the degrees of freedom such that the accuracy of the flutter analysis is not significantly affected. In a typical optimization procedure with flutter constraints, the derivative of the stiffness matrix may be used in a form that contains the characteristic vector of the flutter matrix equation and the transpose of the characteristic vector of the adjoint flutter matrix equation corresponding to a particular solution of the flutter equation.

Oconnell, R. F.↗

NASA NTRS1974

Nutation control during precession of a spin-stabilized spacecraft

Precession maneuver control laws for single-spin spacecraft are investigated so that nutation is concurrently controlled. Analysis has led to the development of two types of control laws employing precession modulation for concurrent nutation control. Results were verified through digital simulation of a Synchronous Meteorological Satellite (SMS) configuration. An addition research effort was undertaken to investigate the cause and elimination of nutation anomalies in dual-spin spacecraft. A literature search was conducted and a dual-spin configuration was simulated to verify that nutational anomalies are not predicted by the existing nonlinear model. No conclusions were drawn as to the cause of the observed nutational anomalies in dual-spin spacecraft.

Source record↗

NASA NTRS1976

Nonlinear motion analysis of flexible satellites

The article reviews research on pointing accuracies of flexible satellites with regard to derived equations of motion of individual elements and composite bodies. The solution of these equations may be achieved through the formulation of a set of singularly perturbed equations by eliminating the generalized position vector. These equations are generally solved by a method of asymptotic expansions if certain convergence criteria are satisfied. The analysis may be applied to dual-spin flexible satellites.

Huang, T. C.↗

NASA NTRS1984

Variational objective analyses for cyclone studies

The basic analysis equations, i.e., the two horizontal momentum equations, the hydrostatic equation, and the integrated continuity equation were derived for the nonlinear vertical coordinate, nondimensionalized, and expressed in finite differences on a staggered grid. Special care was taken to transform the hydrostatic equation and the pressure gradient terms of the horizontal momentum equations to nearly eliminate truncation error over steeply sloping terrain. This formulation also eliminated explicit reference to orographically induced variations in the thermodynamic variables so that the variational adjustments are on the scale of the meteorological perturbations. The analysis equations were subjected to the Euler-Lagrange operations as expressed for finite differences and an additional set of five partial differential equations was derived, bringing to nine the number of equations in Model I. Higher order terms, terms containing observed quantities, and terms containing none of the variables to be adjusted were grouped into forcing functions and the equations were solved for the zero order terms. Zero order variables were eliminated between these equations and there resulted two diagnostic equations which take the form of general linear second order partial differential equations with nonconstant coefficients.

Achtemeier, G. L.↗

NASA NTRS1976

Effects of modifications to the space shuttle entry guidance and control systems

A nonlinear six degree of freedom entry simulation study was conducted to identify space shuttle guidance and control system software modifications which reduce the control system sensitivity to the guidance system sampling frequency. Several modifications which eliminated the control system sensitivity and associated control limit cycling were examined. The result of the modifications was a reduction in required reaction control system fuel.

Powell, R. W.↗

NASA NTRS2004

Instrument Attitude Precision Control

A novel approach is presented in this paper to analyze attitude precision and control for an instrument gimbaled to a spacecraft subject to an internal disturbance caused by a moving component inside the instrument. Nonlinear differential equations of motion for some sample cases are derived and solved analytically to gain insight into the influence of the disturbance on the attitude pointing error. A simple control law is developed to eliminate the instrument pointing error caused by the internal disturbance. Several cases are presented to demonstrate and verify the concept presented in this paper.

Juang, Jer-Nan↗

NASA NTRS2004

Buckling Behavior of Compression-Loaded Composite Cylindrical Shells With Reinforced Cutouts

Results from a numerical study of the response of thin-walled compression-loaded quasi-isotropic laminated composite cylindrical shells with unreinforced and reinforced square cutouts are presented. The effects of cutout reinforcement orthotropy, size, and thickness on the nonlinear response of the shells are described. A nonlinear analysis procedure has been used to predict the nonlinear response of the shells. The results indicate that a local buckling response occurs in the shell near the cutout when subjected to load and is caused by a nonlinear coupling between local shell-wall deformations and in-plane destabilizing compression stresses near the cutout. In general, reinforcement around a cutout in a compression-loaded shell is shown to retard or eliminate the local buckling response near the cutout and increase the buckling load of the shell. However, some results show that certain reinforcement configurations can cause an unexpected increase in the magnitude of local deformations and stresses in the shell and cause a reduction in the buckling load. Specific cases are presented that suggest that the orthotropy, thickness, and size of a cutout reinforcement in a shell can be tailored to achieve improved buckling response characteristics.

Hilburger, Mark W.↗

NASA NTRS1994

Growth of thin films of dicyanovinylanisole on quartz and teflon-coated quartz by physical vapor transport

Organic compounds offer the possibility of molecular engineering in order to optimize the nonlinearity and minimize damage due to the high-power lasers used in nonlinear optical devices. Recently dicyanovinylanisole (DIVA), ((2-methoxyphenyl) methylenepropanedinitrile) has been shown to have a second order nonlinearity 40 times that of alpha-quartz. Debe et. al. have shown that a high degree of orientational order exists for thin films of phthalocyanine grown by physical vapor transport in microgravity. The microgravity environment eliminates convective flow and was critical to the formation of highly ordered dense continuous films in these samples. This work seeks to discover the parameters necessary for the production of thin continuous films of high optical quality in Earth gravity. These parameters must be known before the experiment can be planned for growing DIVA in a microgravity environment. The microgravity grown films are expected to be denser and of better optical quality than the unit gravity films as was observed in the phthalocyanine films.

Pearson, Earl F.↗

NASA NTRS2002

Buckling Behavior of Compression-Loaded Composite Cylindrical Shells with Reinforced Cutouts

Results from a numerical study of the response of thin-wall compression-loaded quasi-isotropic laminated composite cylindrical shells with reinforced and unreinforced square cutouts are presented. The effects of cutout reinforcement orthotropy, size, and thickness on the nonlinear response of the shells are described. A high-fidelity nonlinear analysis procedure has been used to predict the nonlinear response of the shells. The analysis procedure includes a nonlinear static analysis that predicts stable response characteristics of the shells and a nonlinear transient analysis that predicts unstable dynamic buckling response characteristics. The results illustrate how a compression-loaded shell with an unreinforced cutout can exhibit a complex nonlinear response. In particular, a local buckling response occurs in the shell near the cutout and is caused by a complex nonlinear coupling between local shell-wall deformations and in-plane destabilizing compression stresses near the cutout. In general, the addition of reinforcement around a cutout in a compression-loaded shell can retard or eliminate the local buckling response near the cutout and increase the buckling load of the shell, as expected. However, results are presented that show how certain reinforcement configurations can actually cause an unexpected increase in the magnitude of local deformations and stresses in the shell and cause a reduction in the buckling load. Specific cases are presented that suggest that the orthotropy, thickness, and size of a cutout reinforcement in a shell can be tailored to achieve improved response characteristics.

Hilburger, Mark W.↗

NASA NTRS1987

Automating the parallel processing of fluid and structural dynamics calculations

The NASA Lewis Research Center is actively involved in the development of expert system technology to assist users in applying parallel processing to computational fluid and structural dynamic analysis. The goal of this effort is to eliminate the necessity for the physical scientist to become a computer scientist in order to effectively use the computer as a research tool. Programming and operating software utilities have previously been developed to solve systems of ordinary nonlinear differential equations on parallel scalar processors. Current efforts are aimed at extending these capabilities to systems of partial differential equations, that describe the complex behavior of fluids and structures within aerospace propulsion systems. This paper presents some important considerations in the redesign, in particular, the need for algorithms and software utilities that can automatically identify data flow patterns in the application program and partition and allocate calculations to the parallel processors. A library-oriented multiprocessing concept for integrating the hardware and software functions is described.

Arpasi, Dale J.↗

NASA NTRS1987

Automating the parallel processing of fluid and structural dynamics calculations

The NASA Lewis Research Center is actively involved in the development of expert system technology to assist users in applying parallel processing to computational fluid and structural dynamic analysis. The goal of this effort is to eliminate the necessity for the physical scientist to become a computer scientist in order to effectively use the computer as a research tool. Programming and operating software utilities have previously been developed to solve systems of ordinary nonlinear differential equations on parallel scalar processors. Current efforts are aimed at extending these capabilties to systems of partial differential equations, that describe the complex behavior of fluids and structures within aerospace propulsion systems. This paper presents some important considerations in the redesign, in particular, the need for algorithms and software utilities that can automatically identify data flow patterns in the application program and partition and allocate calculations to the parallel processors. A library-oriented multiprocessing concept for integrating the hardware and software functions is described.

Arpasi, Dale J.↗

NASA NTRS1977

Composite methods for hyperbolic equations

A composite approximation procedure combining the properties of the Lax-Wendroff and leapfrog algorithms is proposed for solving hyperbolic equations. For a one-dimensional equation, a three-step approximation consisting of a two-step Richtmeyer method followed by a leapfrog step is considered. This is a two-level scheme, so all difficulties, including storage requirements, associated with the three-level leapfrog are eliminated. For two-dimensional problems a generalization of the preceding method is used consisting of a rotated Richtmeyer method followed by a modified leapfrog step. It is found that the composite schemes are effective in reducing oscillations and nonlinear instabilities that affect the leapfrog method. The dissipation in the composite schemes is much less than in the Richtmeyer algorithm, and hence can be used for long term integrations.

Turkel, E.↗