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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

The Oscillations and Stability of Differentially Rotating Neutron Stars

Studies of the oscillations and stability of neutron stars are motivated by the fact that vibrating neutron stars are a promising source of gravitational waves. One important factor is the influence of differential rotation, which is likely to arise in a neutron star at times, such as the immediate aftermath of the supernova, when we expect strong vibrations. I will discuss two phenomena unique to differentially rotating systems: dynamical shear instabilities, and the existence of a co-rotation band (a frequency band in which mode pattern speed matches the local angular velocity). Using a simple model, we have found dynamical shear instabilities that arise where modes cross into the co-rotation band, if the degree of differential rotation exceeds a certain threshold. We are currently investigating whether this mechanism operates in more realistic stellar models, and whether it is responsible for the dynamical instabilities occurring at low ratios of kinetic to potential energy that have been observed by several authors. I will present the latest results of these studies. Another topic of investigation is the nature of oscillations within the co-rotation band. The band gives rise to a continuous spectrum whose collective physical perturbation exhibits complicated temporal behaviour. I will also discuss the existence of modes within the continuous spectrum that appear physically indistinguishable from the discrete modes outside the band, despite the apparently singular nature of their eigenfunctions.

Watts, A.↗
NASA NTRS1998

A Search for r-Modes from 1825 to the Present

Global oscillations (r-modes) of the Sun's outer convective envelope with periods approximately 1 month and longer have been detected in several short data strings of several years duration. To test whether r-modes might persist beyond one 11 year cycle, the daily sunspot numbers from 1825 to the present were analyzed. Good evidence, but confidence level less than 3sigma, was found for most of the 14 r-modes with spherical harmonic index lambda less than or equal to 5 that can exist in the presence of solar differential rotation. The characteristic rotation rate of almost every such r-mode was detected, displaced systematically from its expected value by only 0.15%. If this probable detection is real, then most low harmonic r-modes have lifetimes exceeding one century and the rotation of the Sun's outer layers varies by less than 0.05%, except possibly at solar minimum.

Wolff, Charles L.↗
NASA NTRS1975

Nonlinear behavior of acoustic waves in combustion chambers

The nonlinear growth and limiting amplitude of acoustic waves in a combustion chamber are considered. A formal framework is provided within which practical problems can be treated with a minimum of effort and expense. The general conservation equations were expanded in two small parameters, one characterizing the mean flow field and one measuring the amplitude of oscillations, and then combined to yield a nonlinear inhomogeneous wave equation. The unsteady pressure and velocity fields were expressed as syntheses of the normal modes of the chamber, but with unknown time-varying amplitudes. This procedure yielded a representation of a general unsteady field as a system of coupled nonlinear oscillators. The system of nonlinear equations was treated by the method of averaging to produce a set of coupled nonlinear first order differential equations for the amplitudes and phases of the modes. The analysis is applicable to any combustion chamber. The most interesting applications are probably to solid rockets, liquid rockets, or thrust augmentors on jet engines.

Culick, F. E. C.↗
NASA NTRS2016

Influence of Stationary Crossflow Modulation on Secondary Instability

A likely scenario for swept wing transition on subsonic aircraft with natural laminar flow involves the breakdown of stationary crossflow vortices via high frequency secondary instability. A majority of the prior research on this secondary instability has focused on crossflow vortices with a single dominant spanwise wavelength. This paper investigates the effects of the spanwise modulation of stationary crossflow vortices at a specified wavelength by a subharmonic stationary mode. Secondary instability of the modulated crossflow pattern is studied using planar, partial-differential-equation based eigenvalue analysis. Computations reveal that weak modulation by the first subharmonic of the input stationary mode leads to mode splitting that is particularly obvious for Y-type secondary modes that are driven by the wall-normal shear of the basic state. Thus, for each Y mode corresponding to the fundamental wavelength of results in unmodulated train of crossflow vortices, the modulated flow supports a pair of secondary modes with somewhat different amplification rates. The mode splitting phenomenon suggests that a more complex stationary modulation such as that induced by natural surface roughness would yield a considerably richer spectrum of secondary instability modes. Even modest levels of subharmonic modulation are shown to have a strong effect on the overall amplification of secondary disturbances, particularly the Z-modes driven by the spanwise shear of the basic state. Preliminary computations related to the nonlinear breakdown of these secondary disturbances provide interesting insights into the process of crossflow transition in the presence of the first subharmonic of the dominant stationary vortex.

Vortex structure↗
NASA NTRS2010

Solar Array Disturbances to Spacecraft Pointing During the Lunar Reconnaissance Orbiter (LRO) Mission

The Lunar Reconnaissance Orbiter (LRO), the first spacecraft to support NASA s return to the Moon, launched on June 18, 2009 from the Cape Canaveral Air Force Station aboard an Atlas V launch vehicle. It was initially inserted into a direct trans-lunar trajectory to the Moon. After a five day transit to the Moon, LRO was inserted into the Lunar orbit and successfully lowered to a low altitude elliptical polar orbit for spacecraft commissioning. Successful commissioning was completed in October 2009 when LRO was placed in its near circular mission orbit with an approximate altitude of 50km. LRO will spend at least one year orbiting the Moon, collecting lunar environment science and mapping data, utilizing a suite of seven instruments to enable future human exploration. The objective is to provide key science data necessary to facilitate human return to the Moon as well as identification of opportunities for future science missions. LRO's instrument suite will provide the high resolution imaging data with sub-meter accuracy, highly accurate lunar cartographic maps, mineralogy mapping, amongst other science data of interest. LRO employs a 3-axis stabilized attitude control system (ACS) whose primary control mode, the "Observing Mode", provides Lunar nadir, off-nadir, and inertial fine pointing for the science data collection and instrument calibration. This controller combines the capability of fine pointing with on-demand large angle full-sky attitude reorientation. It provides simplicity of spacecraft operation as well as additional flexibility for science data collection. A conventional suite of ACS components is employed in the Observing Mode to meet the pointing and control objectives. Actuation is provided by a set of four reaction wheels developed in-house at NASA Goddard Space Flight Center (GSFC). Attitude feedback is provided by a six state Kalman filter which utilizes two SELEX Galileo Star Trackers for attitude updates, and a single Honeywell Miniature Inertial Measurement Unit (MIMU) to provide body rates for attitude propagation. Rate is computed by differentiating accumulated angle provided by the MIMU. The Observing Mode controller is required to maintain fine pointing while a large fully-articulated solar array (SA) maintains its panel normal to the solar incidence. This paper describes the disturbances to the attitude control resulting from the SA articulation. Observing Mode performance in the presence of this disturbance was assessed while the spacecraft was in an initial elliptical low altitude orbit during the commissioning phase, which started about two weeks after launch and lasted for 90 days. LRO demonstrated excellent pointing performance during Observing Mode nadir and inertial attitude target operations during this phase. Transient LRO attitude errors observed during commissioning resulted primarily from three sources, Diviner instrument calibrations, RW zero crossings, and SA articulation. Even during times of considerable disturbance from SA articulation, the attitude errors were maintained below the statistical attitude error requirement level of 15 arc-sec (3 sigma).

Calhoun, Philip↗
NASA NTRS1991

Active control of panel vibrations induced by boundary-layer flow

Some problems in active control of panel vibration excited by a boundary layer flow over a flat plate are studied. In the first phase of the study, the optimal control problem of vibrating elastic panel induced by a fluid dynamical loading was studied. For a simply supported rectangular plate, the vibration control problem can be analyzed by a modal analysis. The control objective is to minimize the total cost functional, which is the sum of a vibrational energy and the control cost. By means of the modal expansion, the dynamical equation for the plate and the cost functional are reduced to a system of ordinary differential equations and the cost functions for the modes. For the linear elastic plate, the modes become uncoupled. The control of each modal amplitude reduces to the so-called linear regulator problem in control theory. Such problems can then be solved by the method of adjoint state. The optimality system of equations was solved numerically by a shooting method. The results are summarized.

Chow, Pao-Liu↗
NASA NTRS1999

Reusable Launch Vehicle Control in Multiple Time Scale Sliding Modes

A reusable launch vehicle control problem during ascent is addressed via multiple-time scaled continuous sliding mode control. The proposed sliding mode controller utilizes a two-loop structure and provides robust, de-coupled tracking of both orientation angle command profiles and angular rate command profiles in the presence of bounded external disturbances and plant uncertainties. Sliding mode control causes the angular rate and orientation angle tracking error dynamics to be constrained to linear, de-coupled, homogeneous, and vector valued differential equations with desired eigenvalues placement. The dual-time scale sliding mode controller was designed for the X-33 technology demonstration sub-orbital launch vehicle in the launch mode. 6DOF simulation results show that the designed controller provides robust, accurate, de-coupled tracking of the orientation angle command profiles in presence of external disturbances and vehicle inertia uncertainties. It creates possibility to operate the X-33 vehicle in an aircraft-like mode with reduced pre-launch adjustment of the control system.

Shtessel, Yuri↗
NASA NTRS2021

Seasonal Glacier and Snow Loading in Svalbard Recovered from Geodetic Observations

We processed time series from seven Global Navigation Satellite System (GNSS) stations and one Very Long Baseline Interferometry (VLBI) station in Svalbard. The goal was to capture the seasonal vertical displacements caused by elastic response of variable mass load due to ice and snow accumulation. We found that estimates of the annual signal in different GNSS solutions disagree by more than 3 mm which makes geophysical interpretation of raw GNSS time series problematic. To overcome this problem, we have used an enhanced Common Mode (CM) filtering technique. The time series are differentiated by the time series from remote station BJOS with known mass loading signals removed a priori. Using this technique, we have achieved a substantial reduction of the differences between the GNSS solutions. We have computed mass loading time series from a regional Climatic Mass Balance (CMB) and snow model that provides the amount of water equivalent at a 1 km resolution with a time step of 7 days. We found that the entire vertical loading signal is present in data of two totally independent techniques at a statistically significant level of 95%. This allowed us to conclude that the remaining errors in vertical signal derived from the CMB model are less than 0.2 mm at that significance level. Refining the land water storage loading model with a CMB model resulted in a reduction of the annual amplitude from 2:1 mm to 1:1 mm in the CM filtered time series, while it had only a marginal impact on raw time series. This provides a strong evidence that CM filtering is essential for revealing local periodic signals when a millimetre level of accuracy is required.

H P Kierulf↗
NASA NTRS2003

Computation of Large-Scale Structure Jet Noise Sources With Weak Nonlinear Effects Using Linear Euler

An approximate technique is presented for the prediction of the large-scale turbulent structure sound source in a supersonic jet. A linearized Euler equations code is used to solve for the flow disturbances within and near a jet with a given mean flow. Assuming a normal mode composition for the wave-like disturbances, the linear radial profiles are used in an integration of the Navier-Stokes equations. This results in a set of ordinary differential equations representing the weakly nonlinear self-interactions of the modes along with their interaction with the mean flow. Solutions are then used to correct the amplitude of the disturbances that represent the source of large-scale turbulent structure sound in the jet.

Dahl, Milo D.↗
NASA NTRS2010

Algorithm for Stabilizing a POD-Based Dynamical System

This algorithm provides a new way to improve the accuracy and asymptotic behavior of a low-dimensional system based on the proper orthogonal decomposition (POD). Given a data set representing the evolution of a system of partial differential equations (PDEs), such as the Navier-Stokes equations for incompressible flow, one may obtain a low-dimensional model in the form of ordinary differential equations (ODEs) that should model the dynamics of the flow. Temporal sampling of the direct numerical simulation of the PDEs produces a spatial time series. The POD extracts the temporal and spatial eigenfunctions of this data set. Truncated to retain only the most energetic modes followed by Galerkin projection of these modes onto the PDEs obtains a dynamical system of ordinary differential equations for the time-dependent behavior of the flow. In practice, the steps leading to this system of ODEs entail numerically computing first-order derivatives of the mean data field and the eigenfunctions, and the computation of many inner products. This is far from a perfect process, and often results in the lack of long-term stability of the system and incorrect asymptotic behavior of the model. This algorithm describes a new stabilization method that utilizes the temporal eigenfunctions to derive correction terms for the coefficients of the dynamical system to significantly reduce these errors.

Kalb, Virginia L.↗
NASA NTRS1992

Diskoseismology: Probing accretion disks. II - G-modes, gravitational radiation reaction, and viscosity

A scalar potential is used to derive a single partial differential equation governing the oscillation of a disk. The eigenfunctions and eigenfrequencies of a variety of disk models are found to fall into two main classes which are analogous to the p-modes and g-modes in the sun. Specifically, the eigenfunctions and eigenfrequencies of isothermal disks are computed, and the way in which these results can be generalized to other disk models is indicated. The (assumed) relatively small rates of growth or damping of the modes due to various mechanisms, in particular gravitational radiation reaction and parameterized models of viscosity are also computed. It is found that for certain parameters the p-modes are unstable to gravitational radiation reaction (CFS instability), while both the p-modes and g-modes are unstable to viscosity unless highly anisotropic viscosity models are considered.

Nowak, Michael A.↗
NASA NTRS1981

Computation of the modes and polar moment of inertial of the blades of an HAWT

The coupled differential equations of motion of the blades of a horizontal axis wind turbine are solved numerically, permitting the optimization of the design at relatively low cost. The equation of motion is transformed into a set of first order equations and solved with fourth order Runge-Kutta integrators. This technique is applied to a twisted, tapered blade of variable cross section and stiffness including discontinuities. The first six natural frequencies and mode shapes are obtained. The polar moment of inertia of the blades is obtained as a function of frequency and rotational speed.

Beaulieu, G.↗
NASA NTRS2010

Nonlinear Dynamics of Cantilever-Sample Interactions in Atomic Force Microscopy

The interaction of the cantilever tip of an atomic force microscope (AFM) with the sample surface is obtained by treating the cantilever and sample as independent systems coupled by a nonlinear force acting between the cantilever tip and a volume element of the sample surface. The volume element is subjected to a restoring force from the remainder of the sample that provides dynamical equilibrium for the combined systems. The model accounts for the positions on the cantilever of the cantilever tip, laser probe, and excitation force (if any) via a basis set of set of orthogonal functions that may be generalized to account for arbitrary cantilever shapes. The basis set is extended to include nonlinear cantilever modes. The model leads to a pair of coupled nonlinear differential equations that are solved analytically using a matrix iteration procedure. The effects of oscillatory excitation forces applied either to the cantilever or to the sample surface (or to both) are obtained from the solution set and applied to the to the assessment of phase and amplitude signals generated by various acoustic-atomic force microscope (A-AFM) modalities. The influence of bistable cantilever modes of on AFM signal generation is discussed. The effects on the cantilever-sample surface dynamics of subsurface features embedded in the sample that are perturbed by surface-generated oscillatory excitation forces and carried to the cantilever via wave propagation are accounted by the Bolef-Miller propagating wave model. Expressions pertaining to signal generation and image contrast in A-AFM are obtained and applied to amplitude modulation (intermittent contact) atomic force microscopy and resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM). The influence of phase accumulation in A-AFM on image contrast is discussed, as is the effect of hard contact and maximum nonlinearity regimes of A-AFM operation.

Cantrell, John H.↗
NASA NTRS1994

Vibration suppression in flexible structures via the sliding-mode control approach

Sliding mode control became very popular recently because it makes the closed loop system highly insensitive to external disturbances and parameter variations. Sliding algorithms for flexible structures have been used previously, but these were based on finite-dimensional models. An extension of this approach for differential-difference systems is obtained. That makes if possible to apply sliding-mode control algorithms to the variety of nondispersive flexible structures which can be described as differential-difference systems. The main idea of using this technique for dispersive structures is to reduce the order of the controlled part of the system by applying an integral transformation. We can say that transformation 'absorbs' the dispersive properties of the flexible structure as the controlled part becomes dispersive.

Drakunov, S.↗
NASA NTRS1987

Pressure-Transducer Simulator

Simulation circuit operates under remote, automatic, or manual control to produce electrical outputs similar to pressure transducer. Specific circuit designed for simulations of Space Shuttle main engine. General circuit concept adaptable to other simulation and control systems involving several operating modes. Switches and amplifiers respond to external control signals and panel control settings to vary differential excitation of resistive bridge. Output voltage or passive terminal resistance made to equal pressure transducer in any of four operating modes.

Simon, Richard A.↗
NASA NTRS1999

Acoustic Emission Signals in Thin Plates Produced by Impact Damage

Acoustic emission (AE) signals created by impact sources in thin aluminum and graphite/epoxy composite plates were analyzed. Two different impact velocity regimes were studied. Low-velocity (less than 0.21 km/s) impacts were created with an airgun firing spherical steel projectiles (4.5 mm diameter). High-velocity (1.8 to 7 km/s) impacts were generated with a two-stage light-gas gun firing small cylindrical nylon projectiles (1.5 mm diameter). Both the impact velocity and impact angle were varied. The impacts did not penetrate the aluminum plates at either low or high velocities. For high-velocity impacts in composites, there were both impacts that fully penetrated the plate as well as impacts that did not. All impacts generated very large amplitude AE signals (1-5 V at the sensor), which propagated as plate (extensional and/or flexural) modes. In the low-velocity impact studies, the signal was dominated by a large flexural mode with only a small extensional mode component detected. As the impact velocity was increased within the low velocity regime, the overall amplitudes of both the extensional and flexural modes increased. In addition, a relative increase in the amplitude of high-frequency components of the flexural mode was also observed. Signals caused by high-velocity impacts that did not penetrate the plate contained both a large extensional and flexural mode component of comparable amplitudes. The signals also contained components of much higher frequency and were easily differentiated from those caused by low-velocity impacts. An interesting phenomenon was observed in that the large flexural mode component, seen in every other case, was absent from the signal when the impact particle fully penetrated through the composite plates.

Prosser, William H.↗
NASA NTRS1978

Aeromechanical stability of helicopters with a bearingless main rotor. Part 1: Equations of motion

Equations of motion for a coupled rotor-body system were derived for the purpose of studying air and ground resonance characteristics of helicopters that have bearingless main rotors. For the fuselage, only four rigid body degrees of freedom are considered; longitudinal and lateral translations, pitch, and roll. The rotor is assumed to consist of three or more rigid blades. Each blade is joined to the hub by means of a flexible beam segment (flexbeam or strap). Pitch change is accomplished by twisting the flexbeam with the pitch-control system, the characteristics of which are variable. Thus, the analysis is capable of implicitly treating aeroelastic couplings generated by the flexbeam elastic deflections, the pitch-control system, and the angular offsets of the blade and flexbeam. The linearized equations are written in the nonrotating system retaining only the cyclic rotor modes; thus, they comprise a system of homogeneous ordinary differential equations with constant coefficients. All contributions to the linearized perturbation equations from inertia, gravity, quasi-steady aerodynamics, and the flexbeam equilibrium deflections are retained exactly.

Hodges, D. H.↗
NASA NTRS2003

Finite-Element Methods for Real-Time Simulation of Surgery

Two finite-element methods have been developed for mathematical modeling of the time-dependent behaviors of deformable objects and, more specifically, the mechanical responses of soft tissues and organs in contact with surgical tools. These methods may afford the computational efficiency needed to satisfy the requirement to obtain computational results in real time for simulating surgical procedures as described in Simulation System for Training in Laparoscopic Surgery (NPO-21192) on page 31 in this issue of NASA Tech Briefs. Simulation of the behavior of soft tissue in real time is a challenging problem because of the complexity of soft-tissue mechanics. The responses of soft tissues are characterized by nonlinearities and by spatial inhomogeneities and rate and time dependences of material properties. Finite-element methods seem promising for integrating these characteristics of tissues into computational models of organs, but they demand much central-processing-unit (CPU) time and memory, and the demand increases with the number of nodes and degrees of freedom in a given finite-element model. Hence, as finite-element models become more realistic, it becomes more difficult to compute solutions in real time. In both of the present methods, one uses approximate mathematical models trading some accuracy for computational efficiency and thereby increasing the feasibility of attaining real-time up36 NASA Tech Briefs, October 2003 date rates. The first of these methods is based on modal analysis. In this method, one reduces the number of differential equations by selecting only the most significant vibration modes of an object (typically, a suitable number of the lowest-frequency modes) for computing deformations of the object in response to applied forces.

Basdogan, Cagatay↗