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NASA NTRS1973

Part 2: Oscillations of elastic systems

Problems of oscillations of linear systems are discussed, including systems with a fractional number of degrees of freedom as well as free oscillations of a cantilever in the field of centrifugal forces. Four methods of solving the problem of the action of periodic instantaneous impulses are presented. The Tacoma catastrophe is analyzed and used as an example of aeroelastic oscillations. Problems of nonlinear system oscillations include the vibration maintenance of rotation, the Sommerfeld effect, and self-oscillations of a quasi-system with dry friction.

Source record↗
NASA NTRS1987

Solar oscillations - A method for deriving nonlinear effects

The frequencies of solar oscillations are so closely spaced that nonlinear interactions among modes are probable. The rate of interaction is proportional to an integral involving the eigenfunctions of the interacting modes, which usually are known only numerically. An approximation in which the eigenfunctions are strictly sinusoidal functions of a suitably defined radial variable, and the numerical details of stellar structure are banished to a coefficient in the integrand, are here explored. The physical assumptions are the same as in the asymptotic approximation of p- or g-modes. This method should allow a general investigation as to likely nonlinear interactions and which modes may participate in such interactions. The coupling of two p-modes by possible large-scale internal magnetic fields is introduced as an anisotropic pressure response to a displacement. Pairs of modes differing in frequency by less than the fraction magnetic/thermal pressure are strongly coupled, and energy appears to oscillate slowly between the two associated spherical harmonics. Potentially, upper limits may be derived for internal magnetic fields.

Wentzel, Donat G.↗
NASA NTRS1992

Pulsatile instability in rapid directional solidification: Strongly-nonlinear analysis

In models of rapid directional solidification, non-equilibrium interfacial conditions are employed. As a result, there is an oscillatory mode of instability, as well as the steady cellular mode, found in the equilibrium model of Mullins and Sekerka. When the temperature field is decoupled from the problem, the preferred wave number for the oscillatory mode is zero, and the interface pulsates in time while remaining spatially uniform. Results from multiple scale analyses in the two limiting cases of the parameters are reported. In these limits, it is found that the instability is a bifurcation to relaxation oscillations; these nonlinear oscillations may be related to the observed microstructure that results from rapid solidification processes such as laser surface remelting.

Braun, Richard J.↗
NASA NTRS1983

Transformations of the perturbed two-body problem to unperturbed harmonic oscillators

Singular, nonlinear, and Liapunov unstable equations are made regular and linear through transformations that change the perturbed planar problem of two bodies into unperturbed and undamped harmonic oscillators with constant coefficients, so that the stable solution may be immediately written in terms of the new variables. The use of arbitrary and special functions for the transformations allows the systematic discussion of previously introduced and novel anomalies. For the case of the unperturbed two-body problem, it is proved that if transformations are power functions of the radial variable, only the eccentric and the true anomalies (with the corresponding transformations of the radial variable) will result in harmonic oscillators. The present method significantly reduces computation requirements in autonomous space operations.

Szebehely, V.↗
NASA NTRS2007

Calligraphic Poling for WGM Resonators

By engineering the geometry of a nonlinear optical crystal, the effective efficiency of all nonlinear optical oscillations can be increased dramatically. Specifically, sphere and disk shaped crystal resonators have been used to demonstrate nonlinear optical oscillations at sub-milliwatt input power when cs light propagates in a Whispering Gallery Mode (WGM) of such a resonant cavity. in terms of both device production and experimentation in quantum optics, some nonlinear optical effects with naturally high efficiency can occult the desired nonlinear scattering process. the structure to the crystal resonator. In this paper, I will discuss a new method for generating poling structures in ferroelectric crystal resonators called calligraphic poling. The details of the poling apparatus, experimental results and speculation on future applications will be discussed.

microsphere↗
NASA NTRSDate not supplied

Computationally Efficient Frequency Domain Method for Dynamic Control Derivative Estimation with Application to Transonic Truss-Braced Wing

This paper presents a computationally efficient method for dynamic control derivative estimation technique via control surface oscillation numerical experiments. Unsteady RANS CFD simulations in FUN3D are performed to simulate the control surface oscillations with a prescribed truncated square wave containing sufficient frequencies of interest. The truncated square wave oscillation offers the computational efficiency which reduces the computational cost by almost an order of magnitude compared to a sine wave oscillation. The nonlinear effect of large control surface oscillation amplitudes creates a spillover effect whereby the frequency response at the same input frequencies contains not only the linear aerodynamic response but also nonlinear aerodynamic response. A correction procedure is developed to remove the spillover effect from the linear aerodynamic response. A frequency-domain regression is performed to estimate the dynamic control derivatives after the correction. The results generally agree with the previous results obtained from the sine wave oscillation.

Stability and Control↗
NASA NTRS2008

2007 Research and Engineering Annual Report

Selected research and technology activities at NASA Dryden Flight Research Center are summarized. These following activities exemplify the Center's varied and productive research efforts: Developing a Requirements Development Guide for an Automatic Ground Collision Avoidance System; Digital Terrain Data Compression and Rendering for Automatic Ground Collision Avoidance Systems; Nonlinear Flutter/Limit Cycle Oscillations Prediction Tool; Nonlinear System Identification Using Orthonormal Bases: Application to Aeroelastic/Aeroservoelastic Systems; Critical Aerodynamic Flow Feature Indicators: Towards Application with the Aerostructures Test Wing; Multidisciplinary Design, Analysis, and Optimization Tool Development Using a Genetic Algorithm; Structural Model Tuning Capability in an Object-Oriented Multidisciplinary Design, Analysis, and Optimization Tool; Extension of Ko Straight-Beam Displacement Theory to the Deformed Shape Predictions of Curved Structures; F-15B with Phoenix Missile and Pylon Assembly--Drag Force Estimation; Mass Property Testing of Phoenix Missile Hypersonic Testbed Hardware; ARMD Hypersonics Project Materials and Structures: Testing of Scramjet Thermal Protection System Concepts; High-Temperature Modal Survey of the Ruddervator Subcomponent Test Article; ARMD Hypersonics Project Materials and Structures: C/SiC Ruddervator Subcomponent Test and Analysis Task; Ground Vibration Testing and Model Correlation of the Phoenix Missile Hypersonic Testbed; Phoenix Missile Hypersonic Testbed: Performance Design and Analysis; Crew Exploration Vehicle Launch Abort System-Pad Abort-1 (PA-1) Flight Test; Testing the Orion (Crew Exploration Vehicle) Launch Abort System-Ascent Abort-1 (AA-1) Flight Test; SOFIA Flight-Test Flutter Prediction Methodology; SOFIA Closed-Door Aerodynamic Analyses; SOFIA Handling Qualities Evaluation for Closed-Door Operations; C-17 Support of IRAC Engine Model Development; Current Capabilities and Future Upgrade Plans of the C-17 Data Rack; Intelligent Data Mining Capabilities as Applied to Integrated Vehicle Health Management; STARS Flight Demonstration No. 2 IP Data Formatter; Space-Based Telemetry and Range Safety (STARS) Flight Demonstration No. 2 Range User Flight Test Results; Aerodynamic Effects of the Quiet Spike(tm) on an F-15B Aircraft; F-15 Intelligent Flight Controls-Increased Destabilization Failure; F-15 Integrated Resilient Aircraft Control (IRAC) Improved Adaptive Controller; Aeroelastic Analysis of the Ikhana/Fire Pod System; Ikhana: Western States Fire Missions Utilizing the Ames Research Center Fire Sensor; Ikhana: Fiber-Optic Wing Shape Sensors; Ikhana: ARTS III; SOFIA Closed-Door Flutter Envelope Flight Testing; F-15B Quiet Spike(TM) Aeroservoelastic Flight Test Data Analysis; and UAVSAR Platform Precision Autopilot Flight Results.

Stoliker, Patrick↗
NASA NTRS1982

Solar atmospheric dynamics. II - Nonlinear models of the photospheric and chromospheric oscillations

The one-dimensional, nonlinear dynamics of the solar atmosphere is investigated, and models of the observed photospheric (300 s) and chromospheric (200 s) oscillations are described. These are resonances of acoustic wave cavities formed by the variation of the temperature and ionization between the subphotospheric, hydrogen convection zone and the chromosphere-corona transition region. The dependence of the oscillations upon the excitation and boundary conditions leads to the conclusion that for the observed amplitudes, the modes are independently excited and, as trapped modes, transport little if any mechanical flux. In the upper photosphere and lower chromosphere, where the two modes have comparable energy density, interference between them leads to apparent vertical phase delays which might be interpreted as evidence of an energy flux.

Leibacher, J.↗
NASA NTRS1974

Nonlinearities in analyses of unsteady flow around oscillating wings

An analysis of nonlinearities involved in unsteady subsonic viscous flow around wings at high Reynolds numbers is presented. The finite element method was applied for the numerical integration of the vorticity transport equations. Physical and numerical aspects of the nonlinearities are discussed. Magnification of nonlinearities in the convection terms near wing surfaces due to changing geometry at leading and trailing edges of the wing chord is determined. As a bubble is generated near the leading edge, the timewise variation of vorticity and pressure distributions over the surface is shown. The different procedures for the integration of the vorticity transport equations in three dimensions along spanwise, chordwise, and normal directions are discussed.

Bratanow, T.↗
NASA NTRS1972

Nonlinear interaction of resonant plasma oscillations.

Using the water-bag model of an electron plasma the nonlinear interaction of two plasma wave pulses (each of sufficiently narrow wave-number spectrum) is discussed. It is shown that for the special case of a resonant (zero group velocity) pulse interacting with a nonresonant pulse, the interaction produces an effective slowing down of the group velocity of the nonresonant pulse. An application of this theory to the explanation of the apparent resonances at fractions of the plasma frequency observed in the ionosphere is discussed.

Lewak, G. J.↗
NASA NTRS1983

Nonlinear aerodynamic modeling of flap oscillations in transonic flow - A numerical validation

The regime of validity of a nonlinear aerodynamic force and moment formulation, based on concepts from nonlinear functional analysis and applicable to a transonic airfoil with a deflecting flap, is investigated. A time-dependent finite difference technique is used to evaluate the aerodynamic data of the formulation in terms of specified, characteristic motions. Flap-motion histories are generated from the flap inertial equations of motion, with aerodynamic reactions specified by the moment formulation. The motion histories depicting the cases of decaying and growing flap oscillations are compared with histories generated through simultaneous, coupled solution of the fluid-dynamic equations and flap inertial equations of motion. The range of applicability of the formulation is discussed.

Chyu, W. J.↗
NASA NTRS1987

High energy efficient solid state laser sources

Diode-laser-pumped solid-state laser oscillators and nonlinear processes were investigated. A new generation on nonplanar oscillator was fabricated, and it is anticipated that passive linewidths will be pushed to the kilohertz regime. A number of diode-pumped laser transitions were demonstrated in the rod configuration. Second-harmonic conversion efficiencies as high as 15% are routinely obtained in a servo-locked external resonant doubling crystal at 15 mW cw input power levels at 1064 nm.

Byer, Robert L.↗