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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 613 records · Page 34
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Explicit modeling of composite plates and beams in the dynamics of multibody systems

The state of the art dynamic response analysis of flexible multibody systems is currently restricted to elastic bodies with homogeneous materials. The requirements for high speed operation has made it necessary to use lightweight multi layered composite bodies in robotic systems and space structure applications. Dynamic modeling and analysis of such systems are particularly important since the effects of body flexibility to the performance are likely to be more pronounced. The eight-noded isoperimetric quadrilateral element with independent rotational and displacement degrees of freedom is extended to laminated composite elements. The element includes an arbitrary number of bonded layers, each of which may have a different thickness. The transverse shear deformation which is a predominant factor in the analysis of laminated composite structures is taken into account in developing the stiffness and mass matrices. The corresponding 3-D mode shapes are then incorporated to the multibody system dynamical equations. Floating body reference frames allow the selection of different boundary conditions, and the dynamical equations contain all the nonlinear interactions between the rigid and elastic motion. Example simulations are presented to illustrate the methods proposed.

Amirouche, F. M. L.↗
NASA NTRS1993

On the Prediction of the Number of Solitons Excited by an Arbitrary Potential: An Observation from Inverse Scattering

A heuristic estimate for the soliton production rate by a pulse is verified for the Korteweg - de Vries equation using inverse scattering. An observation from this result, which is shown to hold for some other nonlinear equations and for the case of the 'forced' nonlinear Schroedinger equation, is that production is determined by quantities that are invariant under rescaling of the original nonlinear equations. We speculate that this result may be useful to the development of an inverse scattering theory for 'forced' nonlinear systems.

Hansen, P. J.↗
NASA NTRS2005

Stochastic Representation of Chaos using Terminal Attractors

A nonlinear version of the Liouville equation based upon terminal attractors is proposed for describing post-instability motions of dynamical systems with exponential divergence of trajectories such as those leading to chaos and turbulence. As a result, the post-instability motions are represented by expectations, variances, and higher moments of the state variables as functions of time. The proposed approach can be applied to conservative chaos, and in particular, to n-bodies problem, as well as to dissipative systems, and in particular, to chaotic attractors and turbulence.

stochastic processes↗
NASA NTRS1991

Nonlinear dynamic analysis of flexible multibody systems

Two approaches are developed to analyze the dynamic behavior of flexible multibody systems. In the first approach each body is modeled with a modal methodology in a local non-inertial frame of reference, whereas in the second approach, each body is modeled with a finite element methodology in the inertial frame. In both cases, the interaction among the various elastic bodies is represented by constraint equations. The two approaches were compared for accuracy and efficiency: the first approach is preferable when the nonlinearities are not too strong but it becomes cumbersome and expensive to use when many modes must be used. The second approach is more general and easier to implement but could result in high computation costs for a large system. The constraints should be enforced in a time derivative fashion for better accuracy and stability.

Bauchau, Olivier A.↗
NASA NTRS1993

Nonlinear modes of the tensor Dirac equation and CPT violation

Recently, it has been shown that Dirac's bispinor equation can be expressed, in an equivalent tensor form, as a constrained Yang-Mills equation in the limit of an infinitely large coupling constant. It was also shown that the free tensor Dirac equation is a completely integrable Hamiltonian system with Lie algebra type Poisson brackets, from which Fermi quantization can be derived directly without using bispinors. The Yang-Mills equation for a finite coupling constant is investigated. It is shown that the nonlinear Yang-Mills equation has exact plane wave solutions in one-to-one correspondence with the plane wave solutions of Dirac's bispinor equation. The theory of nonlinear dispersive waves is applied to establish the existence of wave packets. The CPT violation of these nonlinear wave packets, which could lead to new observable effects consistent with current experimental bounds, is investigated.

Reifler, Frank J.↗
NASA NTRS1989

Application of numerical optimization techniques to control system design for nonlinear dynamic models of aircraft

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. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.

Lan, C. Edward↗
NASA NTRS1984

Intermittency and solitons in the driven dissipative nonlinear Schroedinger equation

The cubic nonlinear Schroedinger equation, in the presence of driving and Landau damping, is studied numerically. As the pump intensity is increased, the system exhibits a transition from intermittency to a two-torus to chaos. The laminar phase of the intermittency is also a two-torus motion which corresponds in physical space to two identical solitons of amplitude determined by a power-balance equation.

Moon, H. T.↗
NASA NTRS1987

Extrapolation methods for vector sequences

This paper derives, describes, and compares five extrapolation methods for accelerating convergence of vector sequences or transforming divergent vector sequences to convergent ones. These methods are the scalar epsilon algorithm (SEA), vector epsilon algorithm (VEA), topological epsilon algorithm (TEA), minimal polynomial extrapolation (MPE), and reduced rank extrapolation (RRE). MPE and RRE are first derived and proven to give the exact solution for the right 'essential degree' k. Then, Brezinski's (1975) generalization of the Shanks-Schmidt transform is presented; the generalized form leads from systems of equations to TEA. The necessary connections are then made with SEA and VEA. The algorithms are extended to the nonlinear case by cycling, the error analysis for MPE and VEA is sketched, and the theoretical support for quadratic convergence is discussed. Strategies for practical implementation of the methods are considered.

Smith, David A.↗
NASA NTRS1988

Minimum-Time Control For Robotic Manipulators

Existence theorem proved for nonlinear systems. Report discusses mathematical requirements for existence of solution to minimum-time control problem for robotic manipulator that obeys nonlinear equations of motion.

Wen, John T.↗
NASA NTRS1990

Output model-following control synthesis for an oblique-wing aircraft

Recent interest in oblique-wing aircraft has focused on the potential aerodynamic performance advantage of a variable-skew oblique wing over a conventional or symmetric sweep wing. Unfortunately, the resulting asymmetric configuration has significant aerodynamic and inertial cross-coupling between the aircraft longitudinal and lateral-directional axes. Presented here is a decoupling control law synthesis technique that integrates stability augmentation, decoupling, and the direct incorporation of desired handling qualities into an output feedback controller. The proposed design technique uses linear quadratic regulator concepts in the framework of explicit model following. The output feedback strategy used is a suboptimal projection from the state space to the output space. Dynamics are then introduced into the controller to improve steady-state performance and increase system robustness. Closed-loop performance is shown by application of the control laws to the linearized equations of motion and nonlinear simulation of an oblique-wing aircraft.

Pahle, Joseph W.↗
NASA NTRS1990

Parameter identification for nonlinear aerodynamic systems

Parameter identification for nonlinear aerodynamic systems is examined. It is presumed that the underlying model can be arranged into an input/output (I/O) differential operator equation of a generic form. The algorithm estimation is especially efficient since the equation error can be integrated exactly given any I/O pair to obtain an algebraic function of the parameters. The algorithm for parameter identification was extended to the order determination problem for linear differential system. The degeneracy in a least squares estimate caused by feedback was addressed. A method of frequency analysis for determining the transfer function G(j omega) from transient I/O data was formulated using complex valued Fourier based modulating functions in contrast with the trigonometric modulating functions for the parameter estimation problem. A simulation result of applying the algorithm is given under noise-free conditions for a system with a low pass transfer function.

Pearson, Allan E.↗
NASA NTRS1992

Self-focusing of whistler waves

The theory of axially symmetric self-focusing of whistler waves, based on the full system of Maxwell equations, is developed. The plasma is described by the magnetohydrodynamic equations including the ponderomotive force from RF field. The nonlinear Schrodinger equations (NSE) for arbitrary azimuthal modes of whistler waves are derived. It is shown that they differ from the NSE for a scalar field; this is connected with an intrinsic angular momentum due to the rotating polarization of whistlers. It is shown that the self-focusing, as described by the NSE, differs in its final stage from the results following the full set of Maxwell equations. The latter gives defocusing after sufficient narrowing of the initial wave beam, due to transformation of the trapped wave into a nontrapped branch which is not contained in the NSE description. The oscillatory character of the defocusing is demonstrated.

Karpman, V. I.↗
NASA NTRS1956

Effect of interaction on landing-gear behavior and dynamic loads in a flexible airplane structure

The effects of interaction between a landing gear and a flexible airplane structure on the behavior of the landing gear and the loads in the structure have been studied by treating the equations of motion of the airplane and the landing gear as a coupled system. The landing gear is considered to have nonlinear characteristics typical of conventional gears, namely, velocity-squared damping, polytropic air-compression springing, and exponential tire force-deflection characteristics. For the case where only two modes of the structure are considered, an equivalent three-mass system is derived for representing the airplane and landing-gear combination, which may be used to simulate the effects of structural flexibility in jig drop tests of landing gears. As examples to illustrate the effects of interaction, numerical calculations, based on the structural properties of two large airplanes having considerably different mass and flexibility characteristics, are presented.

Cook, Francis E↗
NASA NTRS2001

Applications of the Hilbert-Huang Transform

A new method, the Hilbert-Huang Transform, has been developed for analyzing nonlinear and nonstationary data. The key part of the method is the Empirical Mode Decomposition with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An M is defined as any function having the same numbers of zero-crossing and extrema, and also having symmetric envelopes defined by the local maxima and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and nonstationary processes. With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous frequencies'as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. With this technique we can examine the detailed dynamics characteristics of a nonlinear system through the instantaneous frequency rather than harmonics. Thus it constitutes a new view of the nonlinear dynamics. Examples of classic nonlinear equations and other nonlinear and nonstationary data sets will be used as examples to illustrate the advantage of the application of this new data analysis method.

Huang, Norden E.↗
NASA NTRS2006

A Nonlinear Reduced Order Method for Prediction of Acoustic Fatigue

The goal of this investigation is to assess the quality of high-cycle-fatigue life estimation via a reduced order method, for structures undergoing geometrically nonlinear random vibrations. Modal reduction is performed with several different suites of basis functions. After numerically solving the reduced order system equations of motion, the physical displacement time history is obtained by an inverse transformation and stresses are recovered. Stress ranges obtained through the rainflow counting procedure are used in a linear damage accumulation method to yield fatigue estimates. Fatigue life estimates obtained using various basis functions in the reduced order method are compared with those obtained from numerical simulation in physical degrees-of-freedom.

Przekop, Adam↗
NASA NTRS1980

A mathematical representation of an advanced helicopter for piloted simulator investigations of control system and display variations

A mathematical model of an advanced helicopter is described. The model is suitable for use in control/display research involving piloted simulation. The general design approach for the six degree of freedom equations of motion is to use the full set of nonlinear gravitational and inertial terms of the equations and to express the aerodynamic forces and moments as the reference values and first order terms of a Taylor series expansion about a reference trajectory defined as a function of longitudinal airspeed. Provisions for several different specific and generic flight control systems are included in the model. The logic required to drive various flight control and weapon delivery symbols on a pilot's electronic display is also provided. Finally, the model includes a simplified representation of low altitude wind and turbulence effects. This model was used in a piloted simulator investigation of the effects of control system and display variations for an attack helicopter mission.

Aiken, E. W.↗
NASA NTRS1982

Evaluation of automated decisionmaking methodologies and development of an integrated robotic system simulation. Volume 1: Study results

A variety of artificial intelligence techniques which could be used with regard to NASA space applications and robotics were evaluated. The techniques studied were decision tree manipulators, problem solvers, rule based systems, logic programming languages, representation language languages, and expert systems. The overall structure of a robotic simulation tool was defined and a framework for that tool developed. Nonlinear and linearized dynamics equations were formulated for n link manipulator configurations. A framework for the robotic simulation was established which uses validated manipulator component models connected according to a user defined configuration.

Lowrie, J. W.↗
NASA NTRS1983

Joint state and parameter estimation

Recent results are described concerning the problem of state reconstruction for a class of nonlinear distributed systems. The methods are then applied to the problem of joint state and parameter estimation. An example with the wave equation is presented.

Carmichael, N.↗