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At least 1,135 records · Page 63
All sourcesNASA NTRSDOE OSTI
NASA NTRS1955

Simulator studies of the attack phase of an automatically controlled interceptor

The attack phase of the automatically controlled interceptor is studied in two parts. Part I is a limited simulation conducted to specify the lateral and longitudinal control systems for an automatic interceptor. The results are presented as Nyquist plots and time histories of the airplane variables. Part II uses the control systems developed in Part I, together with a dynamically perfect guidance system, to study the effect of the nonlinear terms in the complete equations of motion and nonlinear aerodynamics on the airplane response. The results are presented as time histories of the airplane and control surface motions.

CONTROL, LONGITUDINAL↗
NASA NTRS1976

Stability of elastic bending and torsion of uniform cantilever rotor blades in hover with variable structural coupling

The stability of elastic flap bending, lead-lag bending, and torsion of uniform, untwisted, cantilever rotor blades without chordwise offsets between the elastic, mass, tension, and areodynamic center axes is investigated for the hovering flight condition. The equations of motion are obtained by simplifying the general, nonlinear, partial differential equations of motion of an elastic rotating cantilever blade. The equations are adapted for a linearized stability analysis in the hovering flight condition by prescribing aerodynamic forces, applying Galerkin's method, and linearizing the resulting ordinary differential equations about the equilibrium operating condition. The aerodynamic forces are obtained from strip theory based on a quasi-steady approximation of two-dimensional unsteady airfoil theory. Six coupled mode shapes, calculated from free vibration about the equilibrium operating condition, are used in the linearized stability analysis. The study emphasizes the effects of two types of structural coupling that strongly influence the stability of hingeless rotor blades. The first structural coupling is the linear coupling between flap and lead-lag bending of the rotor blade. The second structural coupling is a nonlinear coupling between flap bending, lead-lag bending, and torsion deflections. Results are obtained for a wide variety of hingeless rotor configurations and operating conditions in order to provide a reasonably complete picture of hingeless rotor blade stability characteristics.

Hodges, D. H., Roberta.↗
NASA NTRS2002

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.

Jothiprasad, Giridhar↗
NASA NTRS1984

Comments on the Method of harmonic balance

The advantages and limitations of the harmonic-balance or describing-function approximation scheme for solving nonlinear ordinary differential equations of oscillatory motion are discussed. Advantages include appicability to equations of any order and with large degrees of nonlinearity, ease of determining limit-cycle behavior and its stability, and overall speed and efficiency; the limitation rules are essentially those described by Mickens (1983). It is pointed out that perturbation procedures provide better results when the degree of nonlinearity is small.

Mickens, R. E.↗
NASA NTRS1993

The soliton transform and a possible application to nonlinear Alfven waves in space

The inverse scattering transform (IST) based on the derivative nonlinear Schroedinger (DNLS) equation is applied to a complex time series of nonlinear Alfven wave data generated by numerical simulation. The IST describes the long-time evolution of quasi-parallel Alfven waves more efficiently than the Fourier transform, which is adapted to linear rather than nonlinear problems. When dissipation is added, so the conditions for the validity of the DNLS are not strictly satisfied, the IST continues to provide a compact description of the wavefield in terms of a small number of decaying envelope solitons.

Hada, T.↗
NASA NTRS1993

Direct time integration of Maxwell's equations in two-dimensional dielectric waveguides for propagation and scattering of femtosecond electromagnetic solitons

Solution of 2D vector nonlinear Maxwell's equations is described for material media with linear and nonlinear instantaneous and Lorentz dispersion effects in the electric polarization. Finite difference time domain method is used in the analysis. The method discussed here achieves robustness by enforcing vector-field boundary conditions at all interfaces of dissimilar media.

VECTOR FIELDS↗
NASA NTRS1991

Self adaptive solution strategies: Locally bound constrained Newton Raphson solution algorithms

A summary is given of strategies which enable the automatic adjustment of the constraint surfaces recently used to extend the range and numerical stability/efficiency of nonlinear finite element equation solvers. In addition to handling kinematic and material induced nonlinearity, both pre-and postbuckling behavior can be treated. The scheme employs localized bounds on various hierarchical partitions of the field variables. These are used to resize, shape, and orient the global constraint surface, thereby enabling essentially automatic load/deflection incrementation. Due to the generality of the approach taken, it can be implemented in conjunction with the constraints of an arbitrary functional type. To benchmark the method, several numerical experiments are presented. These include problems involving kinematic and material nonlinearity, as well as pre- and postbuckling characteristics. Also included is a list of papers published in the course of the work.

Padovan, Joe↗
NASA NTRS1992

Computational modeling of nonlinear electromagnetic phenomena

A new algorithm has been developed that permits, for the first time, the direct time integration of the full-vector nonlinear Maxwell's equations. This new capability permits the modeling of linear and nonlinear, instantaneous and dispersive effects in the electric polarization material media. Results are presented of first-time calculations in 1D of the propagation and collision of femtosecond electromagnetic solitons that retain the optical carrier.

Goorjian, Peter M.↗
NASA NTRS1993

The block adaptive multigrid method applied to the solution of the Euler equations

In the present study, a scheme capable of solving very fast and robust complex nonlinear systems of equations is presented. The Block Adaptive Multigrid (BAM) solution method offers multigrid acceleration and adaptive grid refinement based on the prediction of the solution error. The proposed solution method was used with an implicit upwind Euler solver for the solution of complex transonic flows around airfoils. Very fast results were obtained (18-fold acceleration of the solution) using one fourth of the volumes of a global grid with the same solution accuracy for two test cases.

Pantelelis, Nikos↗
NASA NTRS1972

Procedure for estimating stability and control parameters from flight test data by using maximum likelihood methods employing a real-time digital system

A maximum likelihood parameter estimation procedure and program were developed for the extraction of the stability and control derivatives of aircraft from flight test data. Nonlinear six-degree-of-freedom equations describing aircraft dynamics were used to derive sensitivity equations for quasilinearization. The maximum likelihood function with quasilinearization was used to derive the parameter change equations, the covariance matrices for the parameters and measurement noise, and the performance index function. The maximum likelihood estimator was mechanized into an iterative estimation procedure utilizing a real time digital computer and graphic display system. This program was developed for 8 measured state variables and 40 parameters. Test cases were conducted with simulated data for validation of the estimation procedure and program. The program was applied to a V/STOL tilt wing aircraft, a military fighter airplane, and a light single engine airplane. The particular nonlinear equations of motion, derivation of the sensitivity equations, addition of accelerations into the algorithm, operational features of the real time digital system, and test cases are described.

Grove, R. D.↗
NASA NTRS1985

Nonlinear rotordynamics analysis

The special nonlinearities of the Jeffcott equations in rotordynamics are examined. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot firing ground testing. Deadband, side force and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency is defined and used to develop the solutions of the nonlinear Jeffcott equations as asympotic expansions. This nonlinear natural frequency which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies. Numerical solutions are included for comparison with the analysis. Also, nonlinear frequency-response tables are made for a typical range of values.

Day, W. B.↗
NASA NTRS1987

Asymptotic expansions in nonlinear rotordynamics

This paper is an examination of special nonlinearities of the Jeffcott equations in rotordynamics. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot-firing ground testing. Deadband, side force, and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency, is defined and used to develop the solutions of the nonlinear Jeffcott equations as singular asymptotic expansions. This nonlinear natural frequency, which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies.

Day, William B.↗
NASA NTRS2019

On the Calculation of Exact Cumulative Distribution Statistics for Burgers Equation

A mathematical procedure is presented for the calculation of exact cumulative distribution statistics for a viscosity-free variant of Burgers nonlinear partial differential equation (PDE) in one space dimension and time subject to sinusoidal initial data with uncertain (random variable) amplitude or phase shift. Analytical solutions of nonlinear PDEs with uncertain initial and/or boundary data are invaluable benchmarks in assessing approximate uncertainty quantification techniques. The Burgers equation solution with uncertain initial data results in nonsmooth solution behavior in both physical and random variable dimensions which provides a severe test for approximate uncertainty quantification techniques. Mathematical proofs are provided to verify that exact cumulative distribution statistics can be systematically and robustly obtained for all forward time.

Burgers↗
NASA NTRS1990

Optimal design of control systems for prevention of aircraft flight departure

Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. In the analysis, the general nonlinear flight dynamic equations with nonlinear aerodynamics are numerically integrated; and the dynamic characteristics needed in the optimization process are then identified from the dynamic response. To assure a reasonable solution, the initial input values of the design variables are estimated through a sensitivity analysis. To demonstrate the method, the pitch departure prevention for an F-16 configuration is demonstrated.

Lan, C. Edward↗
NASA NTRS1984

On the development of hierarchical solution strategies for nonlinear finite element formulations

This paper develops a hierarchical type solution scheme which can handle the field equations associated with nonlinear finite element simulations. The overall procedure possesses various levels of application namely degree of freedom, nodal, elemental, substructural as well as global. In particular iteration, updating, assembly and solution control occurs at the various hierarchical levels. Due to the manner of formulation, the degree of matrix inversion depends on the size of the various hierarchical partitioned groups. In this context, degree of freedom partitioning requires no inversion. To benchmark the overall scheme, the results of several numerical examples are presented.

Padovan, J.↗