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NASA NTRS1977

Dynamical response of the solar corona. III - Numerical simulation of the 1973 June 10 coronal transient

A spherically symmetric adiabatic single-fluid model is outlined for simulating the nonlinear time-dependent response of the corona to solar events that are simulated by perturbations in the appropriate physical variables from their steady-state values at the coronal base. Several observed features of the coronal transient that occurred on June 10, 1973, are simulated by using a particular steady-state solar wind, a specific combination of density and temperature perturbations, and a particular time dependence of the perturbations. A different steady-state solar wind, a perturbation of shorter duration, and other perturbation combinations are also employed to simulate the same transient so that the effect of each quantity can be determined. It is found that the model cannot adequately simulate all the observational results for the investigated transient, that the steady-state solar wind is relatively unimportant in such numerical simulations, and that studies which attempt only to reproduce observed shock trajectories may lead to erroneous conclusions regarding the physics of the solar event that produced the transient.

Steinolfson, R. S.↗

NASA NTRS1986

Mode II interlaminar fracture of graphite/epoxy and graphite/PEEK

The end notched flexure (ENF) specimen is employed in an investigation of the interlaminar fracture toughness in Mode II (skew symmetric shear) loading of unidirectional graphite/epoxy and graphite/PEEK composites. Important experimental parameters such as the influence of precracking and the data reduction scheme for the Mode II toughness are discussed. Nonlinear load-deflection response is significant for the tough thermoplastic resin composite but is also present for the brittle thermoset composite. The observed nonlinearities, which are highly rate dependent, are attributed to a combination of slow stable crack growth preceding unstable crack growth and material inelastic behavior in the process zone around the crack tip.

Carlsson, L. A.↗

NASA NTRS2003

Aeroservoelastic Model Validation and Test Data Analysis of the F/A-18 Active Aeroelastic Wing

Model validation and flight test data analysis require careful consideration of the effects of uncertainty, noise, and nonlinearity. Uncertainty prevails in the data analysis techniques and results in a composite model uncertainty from unmodeled dynamics, assumptions and mechanics of the estimation procedures, noise, and nonlinearity. A fundamental requirement for reliable and robust model development is an attempt to account for each of these sources of error, in particular, for model validation, robust stability prediction, and flight control system development. This paper is concerned with data processing procedures for uncertainty reduction in model validation for stability estimation and nonlinear identification. F/A-18 Active Aeroelastic Wing (AAW) aircraft data is used to demonstrate signal representation effects on uncertain model development, stability estimation, and nonlinear identification. Data is decomposed using adaptive orthonormal best-basis and wavelet-basis signal decompositions for signal denoising into linear and nonlinear identification algorithms. Nonlinear identification from a wavelet-based Volterra kernel procedure is used to extract nonlinear dynamics from aeroelastic responses, and to assist model development and uncertainty reduction for model validation and stability prediction by removing a class of nonlinearity from the uncertainty.

Brenner, Martin J.↗

NASA NTRS2006

A Numerical and Experimental Study of Compression-Loaded Composite Panels With Cutouts

Results from a numerical and experimental study on the effects of laminate orthotropy and circular cutout size on the response of compression-loaded composite curved panels are presented. Several 60-in-radius composite panels with four different laminate configurations were tested with cutout diameters that range from 10% to 60% of the panel width. Finite-element analyses were performed for each panel in order to identify the effects boundary conditions, measured initial geometric imperfections and thickness variations had on the nonlinear and buckling behavior of the panels. The compression-loaded panels considered herein exhibited two separate types of behavior depending on the laminate stacking sequence and cutout size. More specifically, some of the panels exhibited the classical snap-through type buckling response; however, some of the panels exhibited a monotonically increasing stable response and achieved compressive loads in excess of twice the predicted linear bifurcation buckling load. In general, the finite-element analyses were able to predict accurately the nonlinear response and buckling loads of the panels and the prebuckling and postbuckling out-of-plane deformations and strains.

Thornburgh, Robert P.↗

NASA NTRS1992

Nonlinear vibration and radiation from a panel with transition to chaos

The dynamic response of an aircraft panel forced at resonance and off-resonance by plane acoustic waves at normal incidence is investigated experimentally and numerically. Linear, nonlinear (period doubling), and chaotic responses are obtained by increasing the sound pressure level of the excitation. The response time history is sensitive to the input level and to the frequency of excitation. The change in response behavior is due to a change in input conditions, triggered either naturally or by modulation of the bandwidth of the incident waves. Off-resonance bifurcation is diffused and difficult to maintain; thus the panel response drifts into a linear behavior. The acoustic pressure emanated by the panel is either linear or nonlinear as is the vibration response. The nonlinear effects accumulate during the propagation with distance. Results are also obtained on the control of the panel response using damping tape on an aluminum panel and a graphite epoxy panel having the same size and weight. Good agreement is obtained betwen the experimental and numerical results.

Maestrello, Lucio↗

NASA NTRS1986

Dynamic response and stability of a composite prop-fan model

Results are presented for blade response and stability during wind tunnel tests of a 62.2 cm diameter model of a prop-fan, advanced turboprop, with swept graphite/epoxy composite blades. Measurements of dynamic response were made with the rotor mounted on an isolated nacelle, with varying tilt for nonuniform inflow, at flow speeds from 0.36 to 0.9 Mach number. The blade displayed no instabilities over the operating range tested, up to 0.9 Mach number and 10,000 RPM. Measurements are compared with those for other prop-fan models of both solid metal and graphite composite construction. The swept composite blade had less response than an unswept composite blade. Composite blades had more response than metal blades. Measurements are compared with theoretically based predictions. The 1-P blade response was significantly overpredicted using unimproved methods and somewhat overpredicted using improved methods. Unexpectedly high 2-P strain levels were measured and suggest the presence of nonlinear effects on blade response.

Smith, A. F.↗

NASA NTRS1960

The Design of Feedback Control Systems Containing a Saturation Type Nonlinearity

A derivation of the optimum response for a step input for plant transfer functions which have an unstable pole and further data on plants with a single zero in the left half of the s plane. The calculated data are presented tabulated in normalized form. Optimum control systems are considered. The optimum system is defined as one which keeps the error as small as possible regardless of the input, under the constraint that the input to the plant (or controlled system) is limited. Intuitive arguments show that in the case where only the error can be sensed directly, the optimum system is obtained from the optimum relay or on-off solution. References to known solutions are presented. For the case when the system is of the sampled-data type, arguments are presented which indicate the optimum sampled-data system may be extremely difficult if not impossible to realize practically except for very simple plant transfer functions. Two examples of aircraft attitude autopilots are presented, one for a statically stable and the other for a statically unstable airframe. The rate of change of elevator motion is assumed limited for these examples. It is shown that by use of nonlinear design techniques described in NASA TN D-20 one can obtain near optimum response for step inputs and reason- able response to sine wave inputs for either case. Also, the nonlinear design prevents inputs from driving the system unstable for either case.

Schmidt, Stanley F.↗

NASA NTRS1975

Vaporization response of evaporating drops with finite thermal conductivity

A numerical computing procedure was developed for calculating vaporization histories of evaporating drops in a combustor in which travelling transverse oscillations occurred. The liquid drop was assumed to have a finite thermal conductivity. The system of equations was solved by using a finite difference method programmed for solution on a high speed digital computer. Oscillations in the ratio of vaporization of an array of repetitivity injected drops in the combustor were obtained from summation of individual drop histories. A nonlinear in-phase frequency response factor for the entire vaporization process to oscillations in pressure was evaluated. A nonlinear out-of-phase response factor, in-phase and out-of-phase harmonic response factors, and a Princeton type 'n' and 'tau' were determined. The resulting data was correlated and is presented in graphical format. Qualitative agreement with the open literature is obtained in the behavior of the in-phase response factor. Quantitatively the results of the present finite conductivity spray analysis do not correlate with the results of a single drop model.

Agosta, V. D.↗

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 NTRS1992

Response characteristics of the human torsional vestibuloocular reflex

The characteristics of the response dynamics of the human torsional vestibuloocular reflex were studied during controlled rotations about an earth-horizontal axis. The results extended the frequency range to 2 Hz and identified the nonlinearity of the amplitude response.

Peterka, Robert J.↗

NASA NTRS1992

Investigation of the flight mechanics simulation of a hovering helicopter

The flight mechanics simulation of a hovering helicopter is investigated by comparing the results of two different numerical models with flight test data for a hovering AH-64 Apache. The two models are the U.S. Army BEMAP and the Technion model. These nonlinear models are linearized by applying a numerical linearization procedure. The results of the linear models are compared with identification results in terms of eigenvalues, stability and control derivatives, and frequency responses. Detailed time histories of the responses of the complete nonlinear models, as a result of various pilots' inputs, are compared with flight test results. In addition the sensitivity of the models to various effects are also investigated. The results are discussed and problematic aspects of the simulation are identified.

Chaimovich, M.↗

NASA NTRS2003

An Intrinsic Baldwin Effect in the H Beta Broad Emission Line in the Spectrum of NGC 5548

We investigate the possibility of an intrinsic Baldwin effect (i.e., nonlinear emission-line response to continuum variations) in the broad HP emission line of the active galaxy NGC 5548 using crosscorrelation techniques to remove light-travel time effects from the data. We find a nonlinear relationship between the HP emission line and continuum fluxes that is in good agreement with theoretical predictions. We suggest that similar analysis of multiple lines might provide a useful diagnostic of physical conditions in the broad-line region.

Gilbert, Karoline M.↗

NASA NTRS1981

Theoretical and lidar studies of the density response of the mesospheric sodium layer to gravity wave perturbations

The density response of atmospheric layers to gravity waves is developed in two forms, an exact solution and a perturbation series solution. The degree of nonlinearity in the layer density response is described by the series solution whereas the exact solution gives insight into the nature of the responses. Density perturbation in an atmospheric layer are shown to be substantially greater than the atmospheric density perturbation associated with the propagation of a gravity wave. Because of the density gradients present in atmospheric layers, interesting effects were observed such as a phase reversal in the linear layer response which occurs near the layer peak. Once the layer response is understood, the sodium layer can be used as a tracer of atmospheric wave motions. A two dimensional digital signal processing technique was developed. Both spatial and temporal filtering are utilized to enhance the resolution by decreasing shot noise by more han 10 dB. Many of the features associated with a layer density response to gravity waves were observed in high resolution density profiles of the mesospheric sodium layer. These include nonlinearities as well as the phase reversal in the linear layer response.

Shelton, J. D.↗

NASA NTRS1993

Compression strength failure mechanisms in unidirectional composite laminates containing a hole

Experiments on graphite-epoxy laminated plates containing unloaded small holes show that these laminates are notch insensitive. That is, the uniaxial strength of these laminates with small holes exceeds the strength predicted by a point stress criterion using the stress concentration factor for the in-plane stress field. Laminates containing large holes exhibit notch sensitive behavior and consequently their strength is reasonably well predicted by the stress concentration effect. This hole size effect is manifested both in tension and in compression. Apparently, some mechanism must cause in-plane stress relief for laminates containing small holes. The purpose of this research was to study the influence of geometric nonlinearity on the micromechanical response of a filamentary composite material in the presence of a strain gradient caused by a discontinuity such as a hole. A mathematical model was developed at the micromechanical level to investigate this geometrically nonlinear effect.

Johnson, Eric R.↗

NASA NTRS2002

A Nonlinear Viscoelastic Model for Ceramics at High Temperatures

High-temperature creep behavior of ceramics is characterized by nonlinear time-dependent responses, asymmetric behavior in tension and compression, and nucleation and coalescence of voids leading to creep rupture. Moreover, creep rupture experiments show considerable scatter or randomness in fatigue lives of nominally equal specimens. To capture the nonlinear, asymmetric time-dependent behavior, the standard linear viscoelastic solid model is modified. Nonlinearity and asymmetry are introduced in the volumetric components by using a nonlinear function similar to a hyperbolic sine function but modified to model asymmetry. The nonlinear viscoelastic model is implemented in an ABAQUS user material subroutine. To model the random formation and coalescence of voids, each element is assigned a failure strain sampled from a lognormal distribution. An element is deleted when its volumetric strain exceeds its failure strain. Element deletion has been implemented within ABAQUS. Temporal increases in strains produce a sequential loss of elements (a model for void nucleation and growth), which in turn leads to failure. Nonlinear viscoelastic model parameters are determined from uniaxial tensile and compressive creep experiments on silicon nitride. The model is then used to predict the deformation of four-point bending and ball-on-ring specimens. Simulation is used to predict statistical moments of creep rupture lives. Numerical simulation results compare well with results of experiments of four-point bending specimens. The analytical model is intended to be used to predict the creep rupture lives of ceramic parts in arbitrary stress conditions.

Powers, Lynn M.↗

NASA NTRS1984

Analysis of aircraft control strategies for microburst encounter

Analyses have indicated that improved control strategies could reduce the threat posed by the presence of microburst-type wind shear during aircraft takeoffs and landings. The attenuation of flight path response to microburst inputs by feedback control to elevators and throttle was studied for the cases of a jet transport and a general aviation aircraft, using longitudinal equations of motion, root locus analysis, Bode plots of altitude response to wind inputs, and nonlinear numerical simulation. Energy management relative to the airmass, a pitch-up response to the decreasing airspeed, increased phugoid mode damping, and decreased phugoid natural frequency, are found to improve microburst penetration aircraft behavior. Aircraft stall, and throttle saturation, are limiting factors in an aircraft's ability to maintain a given flight path during a microburst encounter.

Stengel, R. F.↗

NASA NTRS1980

Turbine blade structural dynamic analysis

The paper presents structural dynamic analysis and test results for the Space Shuttle Main Engine turbine blades. Athough these blades are designed to avoid coincidence of natural frequencies with harmonic excitation forces, the complexity of the turbine hardware, its nonlinearities and lack of information regarding the forcing function have led to fatigue failures. A comparison of single-blade analysis and test modal frequencies, shapes, and stresses is given; analysis techniques to describe the forcing function, compute dynamic responses, and incorporate the nonlinearities of Coulomb-friction dampers are presented. Recommendations are made for new research to improve forcing function computations and structural damping estimates used in the analysis.

Dickerson, E. O.↗

NASA NTRS1993

Semi-analytical static nonlinear structural sensitivity analysis

The paper discusses two uses of the semianalytical methods for nonlinear sensitivity analysis. First, the application to noncritical response is analyzed. It is shown that the semianalytical method is equivalent to a particular form of the overall finite difference approach. It is concluded that the difference between overall finite differences and the semianalytical approach is blurred for the case of nonlinear static response. Next, the application of the semianalytical method to calculating sensitivities of limit loads is discussed. A formulation that is easy to implement in general purpose finite element programs is derived. Three examples are used to demonstrate the application of the formulation and to explore its accuracy.

Haftka, Raphael T.↗