SEARCH · Engineering Papers

Results for “parameter compensation”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 361 records · Page 20

All sources NASA NTRS DOE OSTI

NASA NTRS1989

Low-order design and high-order simulation of active closed-loop control for aerospace structures under construction

Partially constructed/assembled structures in space are complicated enough but their dynamics will also be operating in closed-loop with feedback controllers. The dynamics of such structures are modeled by large-scale finite element models. The model dimension L is extremely large (approximately 10,000) while the numbers of actuators (M) and sensors (P) are small. The model parameters M(sub m) mass matrix, D(sub o) damping matrix, and K(sub o) stiffness matrix, are all symmetric and sparse (banded). Thus simulation of open-loop structure models of very large dimension can be accomplished by special integration techniques for sparse matrices. The problem of simulation of closed-loop control of such structures is complicated by the addition of controllers. Simulation of closed-loop controlled structures is an essential part of the controller design and evaluation process. Current research in the following areas is presented: high-order simulation of actively controlled aerospace structures; low-order controller design and SCI compensation for unmodeled dynamics; prediction of closed-loop stability using asymptotic eigenvalue series; and flexible robot manipulator control experiment.

Balas, Mark J.↗

NASA NTRS2004

Evaluation of Droplet Splashing Algorithm in LEWICE 3.0

The Icing Branch at NASA Glenn Research has developed a computer program to simulate ice formation on the leading edge of an aircraft wing during flight through cold, moist air. As part of the branch's current research, members have developed software known as LEWICE. This program is capable of predicting the formation of ice under designated weather conditions. The success of LEWICE is an asset to airplane manufacturers, ice protection system manufacturers, and the airline industry. Simulations of ice formation conducted in the tunnel and in flight is costly and time consuming. However, the danger of in-flight icing continues to be a concern for both commercial and military pilots. The LEWICE software is a step towards inexpensive and time efficient prediction of ice collection. In the most recent version of the program, LEWICE contains an algorithm for droplet splashing. Droplet splashing is a natural occurrence that causes accumulation of ice on aircraft surfaces. At impingement water droplets lose a portion of their mass to splashing. With part of each droplet joining the airflow and failing to freeze, early versions of LEWICE without the splashing algorithm over-predicted the collection of ice on the leading edge. The objective of my project was to determine whether the revised version of LEWICE accurately reflected the ice collection data obtained from the Icing Research Tunnel (IRT). The experimental data from the IRT was collected by Mark Potapczuk in January, March and July of 2001 and April and December of 2002. Experimental data points were the result of ice tracings conducted shortly after testing in the tunnel. Run sheets, which included a record of velocity, temperature, liquid water content and droplet diameter, served as the input of the LEWICE computer program. Parameters identical to the tunnel conditions were used to run LEWICE 2.0 and LEWICE 3.0. The results from IRT and versions of LEWICE were compared graphically. After entering the raw experimental data and computer output into a spread sheet, I mapped each ice formation onto a clean airfoil. The LEWICE output provided the data points to graphically depict ice formations developed by the program. weather conditions of runs conducted in January 2001, it was evident that the splashing algorithm of LEWICE 3.0 predicts ice formations more accurately than LEWICE 2.0. Especially at conditions with droplet size between 80 and 160 microns, the splashing algorithm of the new LEWICE version compensated for the loss of droplet mass as a result of splashing. In contrast, LEWICE 2.0 consistently over-predicted the mass of the ice in conditions with droplet size exceeding 80 microns. This evidence confirms that changes made to algorithms of LEWICE 3.0 have increased the accuracy of predicting ice collection.

Homenko, Hilary N.↗

NASA NTRS1992

Dynamic rain fade compensation techniques for the advanced communications technology satellite

The dynamic and composite nature of propagation impairments that are incurred on earth-space communications links at frequencies in and above the 30/20 GHz Ka band necessitate the use of dynamic statistical identification and prediction processing of the fading signal in order to optimally estimate and predict the levels of each of the deleterious attenuation components. Such requirements are being met in NASA's Advanced Communications Technology Satellite (ACTS) project by the implementation of optimal processing schemes derived through the use of the ACTS Rain Attenuation Prediction Model and nonlinear Markov filtering theory. The ACTS Rain Attenuation Prediction Model discerns climatological variations on the order of 0.5 deg in latitude and longitude in the continental U.S. The time-dependent portion of the model gives precise availability predictions for the 'spot beam' links of ACTS. However, the structure of the dynamic portion of the model, which yields performance parameters such as fade duration probabilities, is isomorphic to the state-variable approach of stochastic control theory and is amenable to the design of such statistical fade processing schemes which can be made specific to the particular climatological location at which they are employed.

Manning, Robert M.↗

NASA NTRS1994

HST observations of globular clusters in M 31. 1: Surface photometry of 13 objects

We present the initial results of a study of globular clusters in M 31, using the Faint Object Camera (FOC) on the Hubble Space Telescope (HST). The sample of objects consists of 13 clusters spanning a range of properties. Three independent image deconvolution techniques were used in order to compensate for the optical problems of the HST, leading to mutually fully consistent results. We present detailed tests and comparisons to determine the reliability and limits of these deconvolution methods, and conclude that high-quality surface photometry of M 31 globulars is possible with the HST data. Surface brightness profiles have been extracted, and core radii, half-light radii, and central surface brightness values have been measured for all of the clusters in the sample. Their comparison with the values from ground-based observations indicates the later to be systematically and strongly biased by the seeing effects, as it may be expected. A comparison of the structural parameters with those of the Galactic globulars shows that the structural properties of the M 31 globulars are very similar to those of their Galactic counterparts. A candidate for a post-core-collapse cluster, Bo 343 = G 105, has been already identified from these data; this is the first such detection in the M 31 globular cluster system.

Pecci, F. Fusi↗

NASA NTRS2014

Performance Simulations for a Spaceborne Methane Lidar Mission

Future spaceborne lidar measurements of key anthropogenic greenhouse gases are expected to close current observational gaps particularly over remote, polar, and aerosol-contaminated regions, where actual in situ and passive remote sensing observation techniques have difficulties. For methane, a "Methane Remote Lidar Mission" was proposed by Deutsches Zentrum fuer Luft- und Raumfahrt and Centre National d'Etudes Spatiales in the frame of a German-French climate monitoring initiative. Simulations assess the performance of this mission with the help of Moderate Resolution Imaging Spectroradiometer and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations of the earth's surface albedo and atmospheric optical depth. These are key environmental parameters for integrated path differential absorption lidar which uses the surface backscatter to measure the total atmospheric methane column. Results showthat a lidar with an average optical power of 0.45W at 1.6 μm wavelength and a telescope diameter of 0.55 m, installed on a low Earth orbit platform(506 km), will measure methane columns at precisions of 1.2%, 1.7%, and 2.1% over land, water, and snow or ice surfaces, respectively, for monthly aggregated measurement samples within areas of 50 × 50 km2. Globally, the mean precision for the simulated year 2007 is 1.6%, with a standard deviation of 0.7%. At high latitudes, a lower reflectance due to snow and ice is compensated by denser measurements, owing to the orbital pattern. Over key methane source regions such as densely populated areas, boreal and tropical wetlands, or permafrost, our simulations show that the measurement precision will be between 1 and 2%.

methane↗

NASA NTRS1991

Using a focal-plane array to estimate antenna pointing errors

The use of extra collecting horns in the focal plane of an antenna as a means of determining the Direction of Arrival (DOA) of the signal impinging on it, provided it is within the antenna beam, is considered. Our analysis yields a relatively simple algorithm to extract the DOA from the horns' outputs. An algorithm which, in effect, measures the thermal noise of the horns' signals and determines its effect on the uncertainty of the extracted DOA parameters is developed. Both algorithms were implemented in software and tested in simulated data. Based on these tests, it is concluded that this is a viable approach to the DOA determination. Though the results obtained are of general applicability, the particular motivation for the present work is their application to the pointing of a mechanically deformed antenna. It is anticipated that the pointing algorithm developed for a deformed antenna could be obtained as a small perturbation of the algorithm developed for an undeformed antenna. In this context, it should be pointed out that, with a deformed antenna, the array of horns and its associated circuitry constitute the main part of the deformation-compensation system. In this case, the pointing system proposed may be viewed as an additional task carried out by the deformation-compensation hardware.

Zohar, S.↗

NASA NTRS1981

Venus gravity fields

Results of Pioneer Venus Orbiter observations concerning the gravity field of Venus are presented. The gravitational data was obtained from reductions of Doppler radio tracking data for the Orbiter, which is in a highly eccentric orbit with periapsis altitude varying from 145 to 180 km and nearly fixed periapsis latitude of 15 deg N. The global gravity field was obtained through the simultaneous estimation of the orbit state parameters and gravity coefficients from long-period variations in orbital element rates. The global field has been described with sixth degree and order spherical harmonic coefficients, which are capable of resolving the three major topographical features on Venus. Local anomalies have been mapped using line-of-sight accelerations derived from the Doppler residuals between 40 deg N and 10 deg S latitude at approximately 300 km spatial resolution. Gravitational data is observed to correspond to topographical data obtained by radar altimeter, with most of the gravitational anomalies about 20-30 milligals. Simulations evaluating the isostatic states of two topographic features indicate that at least partial isostasy prevails, with the possibility of complete compensation.

Sjogren, W. L.↗

NASA NTRS2011

Conical Probe Calibration and Wind Tunnel Data Analysis of the Channeled Centerbody Inlet Experiment

For a multi-hole test probe undergoing wind tunnel tests, the resulting data needs to be analyzed for any significant trends. These trends include relating the pressure distributions, the geometric orientation, and the local velocity vector to one another. However, experimental runs always involve some sort of error. As a result, a calibration procedure is required to compensate for this error. For this case, it is the misalignment bias angles resulting from the distortion associated with the angularity of the test probe or the local velocity vector. Through a series of calibration steps presented here, the angular biases are determined and removed from the data sets. By removing the misalignment, smoother pressure distributions contribute to more accurate experimental results, which in turn could be then compared to theoretical and actual in-flight results to derive any similarities. Error analyses will also be performed to verify the accuracy of the calibration error reduction. The resulting calibrated data will be implemented into an in-flight RTF script that will output critical flight parameters during future CCIE experimental test runs. All of these tasks are associated with and in contribution to NASA Dryden Flight Research Center s F-15B Research Testbed s Small Business Innovation Research of the Channeled Centerbody Inlet Experiment.

Truong, Samson Siu↗

NASA NTRS1999

Temporary arterial shunts to maintain limb perfusion after arterial injury: an animal study

BACKGROUND: Temporary shunt placement can quickly restore perfusion after extremity arterial injury. This study examined the adequacy of limb blood flow with shunt use, non-heparin-bonded shunt patency over prolonged periods, and the safety of this technique. METHODS: Common iliac arteries were divided and 4.0-mm Silastic Sundt shunts placed in 16 anesthetized pigs. Eight (group I) had shunts placed immediately; eight others (group II) were shunted after an hour of limb ischemia and hemorrhagic shock. Physiologic parameters and femoral artery blood flow in both hindlimbs were continuously monitored. Limb lactic acid generation, oxygen utilization, and hematologic and metabolic effects were serially evaluated for 24 hours. RESULTS: Shunts remained patent in 13 of 16 pigs. Shunts thrombosed in two group I animals because of technical errors, but functioned well after thrombectomy and repositioning. Patency could not be maintained in one animal that died from shock. Flow in group I shunted limbs was 57 (+/-11 SD) % of control. For group II animals in shock, shunted limb flow initially averaged 46 +/- 15% of control, but 4 hours after shunt placement, the mean limb blood flow was the same as in group I. Increased oxygen extraction compensated for the lower flow. Lactic acid production was not increased in comparison to control limbs. CONCLUSION: Shunts provided adequate flow in this model of extremity trauma. Correctly placed shunts stayed patent for 24 hours, without anticoagulation, if shunt placement followed resuscitation.

Hindlimb/blood supply/injuries↗

NASA NTRS2008

An Integrated Approach to Damage Accommodation in Flight Control

In this paper we present an integrated approach to in-flight damage accommodation in flight control. The approach is based on Multiple Models, Switching and Tuning (MMST), and consists of three steps: In the first step the main objective is to acquire a realistic aircraft damage model. Modeling of in-flight damage is a highly complex problem since there is a large number of issues that need to be addressed. One of the most important one is that there is strong coupling between structural dynamics, aerodynamics, and flight control. These effects cannot be studied separately due to this coupling. Once a realistic damage model is available, in the second step a large number of models corresponding to different damage cases are generated. One possibility is to generate many linear models and interpolate between them to cover a large portion of the flight envelope. Once these models have been generated, we will implement a recently developed-Model Set Reduction (MSR) technique. The technique is based on parameterizing damage in terms of uncertain parameters, and uses concepts from robust control theory to arrive at a small number of "centered" models such that the controllers corresponding to these models assure desired stability and robustness properties over a subset in the parametric space. By devising a suitable model placement strategy, the entire parametric set is covered with a relatively small number of models and controllers. The third step consists of designing a Multiple Models, Switching and Tuning (MMST) strategy for estimating the current operating regime (damage case) of the aircraft, and switching to the corresponding controller to achieve effective damage accommodation and the desired performance. In the paper present a comprehensive approach to damage accommodation using Model Set Design,MMST, and Variable Structure compensation for coupling nonlinearities. The approach was evaluated on a model of F/A-18 aircraft dynamics under control effector damage, augmented by nonlinear cross-coupling terms and a structural dynamics model. The proposed approach achieved excellent performance under severe damage effects.

Boskovic, Jovan D.↗

NASA NTRS2004

The Average Quality Factors by TEPC for Charged Particles

The quality factor used in radiation protection is defined as a function of LET, Q(sub ave)(LET). However, tissue equivalent proportional counters (TEPC) measure the average quality factors as a function of lineal energy (y), Q(sub ave)(Y). A model of the TEPC response for charged particles considers energy deposition as a function of impact parameter from the ion s path to the volume, and describes the escape of energy out of sensitive volume by delta-rays and the entry of delta rays from the high-density wall into the low-density gas-volume. A common goal for operational detectors is to measure the average radiation quality to within accuracy of 25%. Using our TEPC response model and the NASA space radiation transport model we show that this accuracy is obtained by a properly calibrated TEPC. However, when the individual contributions from trapped protons and galactic cosmic rays (GCR) are considered; the average quality factor obtained by TEPC is overestimated for trapped protons and underestimated for GCR by about 30%, i.e., a compensating error. Using TEPC's values for trapped protons for Q(sub ave)(y), we obtained average quality factors in the 2.07-2.32 range. However, Q(sub ave)(LET) ranges from 1.5-1.65 as spacecraft shielding depth increases. The average quality factors for trapped protons on STS-89 demonstrate that the model of the TEPC response is in good agreement with flight TEPC data for Q(sub ave)(y), and thus Q(sub ave)(LET) for trapped protons is overestimated by TEPC. Preliminary comparisons for the complete GCR spectra show that Q(sub ave)(LET) for GCR is approximately 3.2-4.1, while TEPC measures 2.9-3.4 for QQ(sub ave)(y), indicating that QQ(sub ave)(LET) for GCR is underestimated by TEPC.

Kim, Myung-Hee Y.↗

NASA NTRS2007

The Determination of Titan Gravity Field from Doppler Tracking of the Cassini Spacecraft

In its tour of the Saturnian system, the spacecraft Cassini is carrying out measurements of the gravity field of Titan, whose knowledge is crucial for constraining the internal structure of the satellite. In the five flybys devoted to gravity science, the spacecraft is tracked in X (8.4 GHz) and Ka band (32.5 GHz) from the antennas of NASA's Deep Space Network. The use of a dual frequency downlink is used to mitigate the effects of interplanetary plasma, the largest noise source affecting Doppler measurements. Variations in the wet path delay are effectively compensated by means of advanced water vapor radiometers placed close to the ground antennas. The first three flybys occurred on February 27, 2006, December 28, 2006, and June 29, 2007. Two additional flybys are planned in July 2008 and May 2010. This paper presents the estimation of the mass and quadrupole field of Titan from the first two flybys, carried out by the Cassini Radio Science Team using a short arc orbit determination. The data from the two flybys are first independently fit using a dynamical model of the spacecraft and the bodies of the Saturnian system, and then combined in a multi-arc solution. Under the assumption that the higher degree harmonics are negligible, the estimated values of the gravity parameters from the combined, multi-arc solution are GM = 8978.1337 +/- 0.0025 km(exp 3) / s(exp 2), J (sub 2) = (2.7221 +/- 0.0185) 10 (exp -5) and C (sub 22) = (1.1159 +/- 0.0040) 10 (exp -5) The excellent agreement (within 1.7 sigma) of the results from the two flybys further increases the confidence in the solution and provides an a posteriori validation of the dynamical model.

Iess, L.↗

NASA NTRS1992

Derivation of surface properties from Magellan altimetry data

The fit of the Hagfors model to the Magellan altimetry data provides a means to characterize the surface properties of Venus. However, the derived surface properties are only meaningful if the model provides a good representation of the data. The Hagfors model provides a good representation of the data. The Hagfors model is generally a realistic fit to surface scattering properties of a nadir-directed antenna such as the Magellan altimeter; however, some regions of the surface of Venus are poorly described by the existing model, according to the goodness of fit parameter provided on the ARCDR CD-ROMs. Poorly characterized regions need to be identified and fit to new models in order to derive more accurate surface properties for use in inferring the geological processes that affect the surface in those regions. We have compared the goodness of fit of the Hagfors model to the distribution of features across the planet, and preliminary results show a correlation between steep topographic slopes and poor fits to the standard model, as has been noticed by others. In this paper, we investigate possible relations between many classes of features and the ability of the Hagfors model to fit the observed echo profiles. In the regions that are not well characterized by existing models, we calculate new models that compensate for topographic relief in order to derive improved estimates of surface properties. Areas investigated to date span from longitude 315 through 45, at all latitudes covered by Magellan. A survey of those areas yields preliminary results that suggest that topographically high regions are well suited to the current implementation of the Hagfors model. Striking examples of such large-scale good fits are Alpha Regio, the northern edges of Lada Terra, and the southern edge of Ishtar Terra. Other features that are typically well fit are the rims of coronae such as Heng-O and the peaks of volcanos such as Gula Mons. Surprisingly, topographically low regions, such as the ubiquitous plains areas, are modeled poorly in comparison. However, this generalization has has exceptions: Lakshmi Planum is an elevated region that is not well fit compared to the rest of neighboring Ishtar, while the southern parts of topographically low Guinevere Planitia are characterized quite well by the Hagfors model. Features that are candidates for improved models are impact craters, coronae, ridges of significant scale, complex ridged terrains, moderate-sized mountains, and sharp terrain boundaries. These features are chosen because the goodness of fit is likely to be most affected either by departures from normal incidence angles or by sharp changes in terrain type within a single footprint. Most large features that are elevated with respect to their surroundings will suffer from steep slope effects, and smaller coronae and impact craters will probably suffer due to rapid changes in their appearance within a single footprint (10-20 km).

Lovell, Amy J.↗

NASA NTRS1990

Stationary orbits of satellites of disk galaxies

The satellite of an S-galaxy will experience opposing dynamical-friction forces from the stars of the disk and the halo. If these forces are in balance, the satellite may travel in a stable, near-circular orbit whose radius, for a wide range of physical parameters, should be limited to a zone 1.2 to 1.4 times the disk radius, much as is observed. The idea is very simple. The dynamical friction acting on a small satellite, moving through a stellar galactic halo, makes this satellite slow down. On the other hand, a stellar disk, rotating faster than a satellite, makes it speed up. But the density distributions in radius for disk's and halo's stars in real flat galaxies are quite different (respectively, exponential and power-law). Moreover, the observational data show that the exponential profile for disk's surface density drops abruptly at some radius (r sub d). So it is natural to expect that a stationary orbit could be near the edge of a disk (where two effects are mutually compensated).

Polyachenko, Valerij L.↗

NASA NTRS1982

Bridgman-type apparatus for the study of growth-property relationships - Arsenic vapor pressure-GaAs property relationship

A precision Bridgman-type apparatus is described which was designed and constructed for the investigation of relationships between crystal growth parameters and the properties of GaAs crystals. Several key features of the system are highlighted, such as the use of a heat pipe for precise arsenic vapor pressure control and seeding without the presence of a viewing window. Pertinent growth parameters, such as arsenic source temperature, thermal gradients in the growing crystal and in the melt, and the macroscopic growth velocity can be independently controlled. During operation, thermal stability better than + or - 0.02 C is realized; thermal gradients can be varied up to 30 C/cm in the crystal region, and up to 20 C/cm in the melt region; the macroscopic growth velocity can be varied from 50 microns/hr to 6.0 cm/hr. It was found that the density of dislocations depends critically on As partial pressure; and essentially dislocation-free, undoped, crystals were grown under As pressure precisely controlled by an As source maintained at 617 C. The free carrier concentration varied with As pressure variations. This variation in free carrier concentration was found to be associated with variations in the compensation ratio rather than with standard segregation phenomena.

Parsey, J. M.↗

NASA NTRS2003

Effects of a Scanning Reflectarray Antenna on Modulated Data Modeled

The ferroelectric reflectarray is a new type of scanning antenna under development for space and ground communications and radar applications at the NASA Glenn Research Center. The reflectarray offers tremendous cost, gain, and efficiency advantages in comparison to the state-of-the-art phased arrays, but there is an inherent intersymbol interference (ISI) problem with digital communication data streams processed through the array because of the way the reflectarray is operated. This interference stems from the fact that the antenna beam is formed by the superposition of reflected waves from the array elements. The delays from the elements to the observation point of each wave differ. Ferroelectric phase shifters are designed to compensate for the modulo-2p phase differences so that the waves will constructively interfere at the sinusoidal carrier level; however, the delays of the integer-number multiple of the carrier period are not compensated for. This lack of compensation causes ISI in digital modulated signals. ISI has not been a problem with analog modulations and low-rate digital modulations since the distortion (or ISI) introduced is negligible. The problem becomes acute when the data rate gets higher, and the electrical size of the array gets bigger. Moreover, there are intrinsic transient effects associated with the phase shifters and the controller that executes the algorithm to direct the beam. That is, phase shifter updates to redirect the beam may be initiated simultaneously, but nonlinearity will cause different settling times. The ISI problem and other effects ultimately limit the size (gain) and data rate of the reflectarray. An ISI analysis was required to prove or disprove the suitability of the reflectarray antenna for high-rate digitally modulated signals and to give guidance for determining antenna parameters. In this research, the nature of the ISI of the reflectarray has been mathematically modeled.

Romanofsky, Robert R.↗

NASA NTRS2015

Improved Band-to-Band Registration Characterization for VIIRS Reflective Solar Bands Based on Lunar Observations

Spectral bands of the Visible Infrared Imaging Radiometer Suite (VIIRS) instrumentaboard the Suomi National Polar-orbiting Partnership (S-NPP) satellite are spatially co-registered.The accuracy of the band-to-band registration (BBR) is one of the key spatial parameters that must becharacterized. Unlike its predecessor, the Moderate Resolution Imaging Spectroradiometer (MODIS), VIIRS has no on-board calibrator specifically designed to perform on-orbit BBR characterization.To circumvent this problem, a BBR characterization method for VIIRS reflective solar bands (RSB) based on regularly-acquired lunar images has been developed. While its results can satisfactorily demonstrate that the long-term stability of the BBR is well within +/- 0.1 moderate resolution bandpixels, undesired seasonal oscillations have been observed in the trending. The oscillations are most obvious between the visiblenear-infrared bands and short-middle wave infrared bands. This paper investigates the oscillations and identifies their cause as the band spectral dependence of the centroid position and the seasonal rotation of the lunar images over calibration events. Accordingly, an improved algorithm is proposed to quantify the rotation and compensate for its impact. After the correction, the seasonal oscillation in the resulting BBR is reduced from up to 0.05 moderate resolution band pixels to around 0.01 moderate resolution band pixels. After removing this spurious seasonal oscillation, the BBR, as well as its long-term drift are well determined.

Wang, Zhipeng↗

NASA NTRS1984

Dynamic characteristics of a hydrostatic gas bearing driven by oscillating exhaust pressure

Vibration of a statically loaded, inherently compensated hydrostatic journal bearing due to oscillating exhaust pressure is investigated. Both angular and radial vibration modes are analyzed. The time-dependent Reynolds equation governing the pressure distribution between the oscillating journal and sleeve is solved together with the journal equation of motion to obtain the response characteristics of the bearing. The Reynolds equation and the equation of motion are simplified by applying regular perturbation theory for small displacements. The numerical solutions of the perturbation equations are obtained by discretizing the pressure field using finite-difference aproximations with a discrete, nonuniform line-source model which excludes effects due to feeding hole volume. An iterative scheme is used to simultaneously satisfy the equations of motion for the journal. The results presented include Bode plots of bearing-oscillation gain and phase for a particular bearing configuration for various combinations of parameters over a range of frequencies, including the resonant frequency.

Watkins, C. B.↗