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At least 253 records · Page 14

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NASA NTRS1982

The effect of non-linear propagation in jet noise

An experimental investigation of the nonlinear propagation effects which occur in the noise radiated from low and moderate Reynolds number supersonic jets has been performed. An array of three condenser microphones was used to measure the waveforms propagated by axisymmetric, cold model jets of Mach numbers 2.1 and 2.5. Relatively low Reynolds numbers were obtained by exhausting the jets into a low pressure anechoic test chamber. The results show that phenomena normally associated with nonlinear acoustic propagation, such as wave steepening, harmonic generation and wave merging, are measurable in the high speed model jets.

Gallagher, J. A.↗

NASA NTRS1982

Second order non-linear equations of motion for spinning highly flexible line elements

The second order nonlinear equations of motion are formulated for spinning line elements having little or no intrinsic structural stiffness. The derivation is based on the extended Hamilton's principle and includes the effect of initial geometric imperfections (axial, curvature, and twist) on the line element dynamics. For comparison with previous work, the nonlinear equations are reduced to a linearized form frequently found in the literature. The comparison revealed several new spin-stiffening terms that have not been previously identified and/or retained. They combine geometric imperfections, rotary inertia, Coriolis, and gyroscopic terms.

Salama, M.↗

NASA NTRS1982

Response control for fatigue testing of non-linear systems

A signal conditioner which ensures that peak and low values during vibration testing are not lost during nonlinear or asymmetric vibration testing on small structures is described. The trapped signals may be for acceleration, velocity, or displacement. The test signal is sent through an analog circuit to a multiplexer, which resets to zero each time a zero-line is crossed by another incoming signal. Peak positive and negative amplitude and frequency are retained and nonsymmetric responses are thus detected, rather than averaged out.

Gowdey, J. C.↗

NASA NTRS1982

PROGRAM VSAERO: A computer program for calculating the non-linear aerodynamic characteristics of arbitrary configurations: User's manual

VSAERO is a computer program used to predict the nonlinear aerodynamic characteristics of arbitrary three-dimensional configurations in subsonic flow. Nonlinear effects of vortex separation and vortex surface interaction are treated in an iterative wake-shape calculation procedure, while the effects of viscosity are treated in an iterative loop coupling potential-flow and integral boundary-layer calculations. The program employs a surface singularity panel method using quadrilateral panels on which doublet and source singularities are distributed in a piecewise constant form. This user's manual provides a brief overview of the mathematical model, instructions for configuration modeling and a description of the input and output data. A listing of a sample case is included.

Maskew, B.↗

NASA NTRS1985

Modeling taper charge with a non-linear equation

Work aimed at modeling the charge voltage and current characteristics of nickel-cadmium cells subject to taper charge is presented. Work reported at previous NASA Battery Workshops has shown that the voltage of cells subject to constant current charge and discharge can be modeled very accurately with the equation: voltage = A + (B/(C-X)) + De to the -Ex where A, B, D, and E are fit parameters and x is amp-hr of charge removed during discharge or returned during charge. In a constant current regime, x is also equivalent to time on charge or discharge.

Mcdermott, P. P.↗

NASA NTRS1985

The HEAO-2 Guest Investigator Program: Non-linear growth of instabilities in line-driven stellar winds

The linear instability of line-driven stellar winds to take proper account of the dynamical effect of scattered radiation were analyzed. It is found that: (1) the drag effect of the mean scattered radiation does greatly reduce the contribution of scattering lines to the instability at the very base of the wind, but the instability growth rate associated with such lines rapidly increases as the flow moves outward from the base, reaching more than 50% of the growth rate for pure absorption lines within a stellar radius of the surface, and eventually reaching 80% of that rate at large radii; (2) perturbations in the scattered radiation field may be important for the propagation of wind disturbances, but they have little effect on the wind instability; and (3) the contribution of strongly shadowed lines to the wind instability is often reduced compared to that of unshadowed lines, but their overall effect is not one of damping in the outer parts of the wind. It is concluded that, even when all scattering effects are taken into account, the bulk of the flow in a line-driven stellar wind is still highly unstable.

Rybicki, G. B.↗

NASA NTRS1984

Approximate analytic solutions for singular non-linear oscillators

Mickens (1981, 1984) has considered analytic techniques for obtaining approximate solutions to one-dimensional nonlinear oscillatory systems x(double-dot) + x = lambda f(x, x/dot/, lambda) where lambda is a small positive parameter and f is a nonlinear polynomial function of its arguments. However, in certain cases there is interest in the analysis of physical systems for which the nonlinear function f(x, x/dot/, lambda) is singular for finite values of x or x(dot). The present investigation is concerned with the use of existing approximate analytic schemes to obtain solutions to singular nonlinear oscillatory differential equations.

Bota, K. B.↗

NASA NTRS1983

A non-linear viscoelastic characterisation method for matrix resin composites

Lifetime prediction of matrix resin composites is an important problem because of their viscoelastic character. If the Time-Temperature-Stress-Superposition principle is valid, results from short time tests at high stress levels can give the necessary information for the prediction of long time behavior. At such stress levels the viscoelastic response is nonlinear. In this contribution the basis of a computer routine is presented starting from a thermodynamical formulation given by Schapery. This method gives in an accurate way the different material parameters in that nonlinear constitutive equation for different stresses and temperatures.

Hiel, C. C.↗

NASA NTRS1985

Exact finite difference schemes for the non-linear unidirectional wave equation

Attention is given to the construction of exact finite difference schemes for the nonlinear unidirectional wave equation that describes the nonlinear propagation of a wave motion in the positive x-direction. The schemes constructed for these equations are compared with those obtained by using the usual procedures of numerical analysis. It is noted that the order of the exact finite difference models is equal to the order of the differential equation.

Mickens, R. E.↗

NASA NTRS1985

Simulation of non-linear bearing forces for post-stability investigation

Different types of bearing designs were developed to improve dynamic properties of rotor-bearing systems. Elliptical bearings, multisleeve bearings, tilting pad and other designs such as herringbone groove were utilized to increase resistance to the onset of self excited vibrations. Experimental trials are costly, two alternative methods are used to gain a qualitative insight. The first one creates mathematical model and applies both a digital or an analog computer simulation. The second one investigates phenomena occurring on the laboratory rig with the bearing replaced by an electronic simulating device, working in a feedback loop, which produces forces,which are functions of journal displacement and velocity. The simulated hydrodynamic forces are produced according to assumed characteristics matched to the bearing type. The principal benefit of the analog simulation is that nonlinear characteristics of a subsystem are precisely identified and mathematical methods applied for a wide class of problems are checked on the experimental installation.

Parszewski, Z. A.↗

NASA NTRS1985

Non-linear guidance laws for automatic orbital rendezvous

In the automatic assembly of space stations or the automatic rendezvous and docking of a space-shuttle vehicle with a space station, it is of interest to determine suitable guidance laws for orbital rendezvous which are amenable to on-board implementation. In this paper, various forms of nonlinear guidance laws for automatic orbital rendezvous of two bodies represented by point masses in a central Newtonian gravitational field are derived. A basic requirement is that the approach be smooth and nonoscillatory. The global dynamic behavior of each of the resulting feedback systems is determined analytically and/or by computer simulation.

Wang, P. K. C.↗

NASA NTRS1985

Two types of chaos in non-linear mechanics

The two types of chaos, weak and strong, associated with the Liapunov and Hadamard instabilities respectively, are analyzed. The geometrical representation of weak chaos is considered, and criteria of this chaos are formulated using the geometrical interpretation of dynamics. Weak chaos in inertial motion of two-bar linkage is discussed. The analysis of strong chaos is restricted to a review of results published elsewhere.

Zak, M.↗

NASA NTRS1985

Construction of approximate analytical solutions to a new class of non-linear oscillator equation

The principle of harmonic balance is invoked in the development of an approximate analytic model for a class of nonlinear oscillators typified by a mass attached to a stretched wire. By assuming that harmonic balance will hold, solutions are devised for a steady state limit cycle and/or limit point motion. A method of slowly varying amplitudes then allows derivation of approximate solutions by determining the form of the exact solutions and substituting into them the lowest order terms of their respective Fourier expansions. The latter technique is actually a generalization of the method proposed by Kryloff and Bogoliuboff (1943).

Mickens, R. E.↗

NASA NTRS1986

Stability of dithered non-linear systems with backlash or hysteresis

A study is conducted of the effect of dither on the nonlinear element of a single-input single-outout feedback system. Nonlinearities are considered with memory (backlash, hysteresis), in the feedforward loop; a dither of a given amplitude is injected at the input of the nonlinearity. The nonlinearity is followed by a linear element with low-pass characteristic. The stability of the dithered system and an approximate equivalent system (in which the nonlinearity is a smooth function) are compared. Conditions on the input and on the dither frequency are obtained so that the approximate-system stability guarantees that of the given hysteretic system.

Desoer, C. A.↗

NASA NTRS1986

On the interaction of a sound pulse with the shear layer on an axisymmetric jet. III - Non-linear effects

The fluctuating field of a jet excited by transient mass injection is simulated numerically. The model is developed by expanding the state vector as a mean state plus a fluctuating state. Nonlinear terms are not neglected, and the effect of nonlinearity is studied. A high order numerical method is used to compute the solution. The results show a significant spectral broadening in the flow field due to the nonlinearity. In addition, large scale structures are broken down into smaller scales.

Bayliss, A.↗

NASA NTRS1987

Position Control for Non-linear, Multiple-Link Robots

Several approaches to complicated control problem examined. Report surveys methods for controlling motion of robot manipulators. Applies to coupled, highly nonlinear multiple-link robots. Presents adaptive control technique based on discrete linear model of robot arm, obtained by linearizing nonlinear dynamical equations about nominal trajectory. Parameters of model calculated with adaptive parameter-identification algorithm. Based on system model, optimal control input computed using position and velocity feedback.

Seraji, H.↗

NASA NTRS1985

Development of non-linear finite element computer code

Recent work has shown that the use of separable symmetric functions of the principal stretches can adequately describe the response of certain propellant materials and, further, that a data reduction scheme gives a convenient way of obtaining the values of the functions from experimental data. Based on representation of the energy, a computational scheme was developed that allows finite element analysis of boundary value problems of arbitrary shape and loading. The computational procedure was implemental in a three-dimensional finite element code, TEXLESP-S, which is documented herein.

Becker, E. B.↗

NASA NTRS1987

Non-linear unsteady wing theory, part 1. Quasi two-dimensional behavior: Airfoils and slender wings

The initial phases of a study of the large-amplitude unsteady aerodynamics of wings in severe maneuver are reported. The research centers on vortex flows, their initiation at wing surfaces, their subsequent convection, and interaction dynamically with wings and control surfaces. The focus is on 2D and quasi-2D aspects of the problem and features the development of an exact nonlinear unsteady airfoil theory as well as an approach to the crossflow problem for slender wing applications including leading-edge separation. The effective use of interactive on-line computing in quantifying and visualizing the nonsteady effects of severe maneuver is demonstrated. Interactive computational work is now possible, in which a maneuver can be initiated and its effects observed and analyzed immediately.

Mccune, J. E.↗