SEARCH · Engineering Papers

Results for “Displacement”

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 1,243 records · Page 69

All sources NASA NTRS DOE OSTI

NASA NTRS1998

An Assessment of the Axial and Radial Dilation of a DPIMS Tantalum Cartridge for Space Shuttle Flight Experiments

Ground-based heat treatment tests are planned on an argon gas-filled tantalum cartridge developed as pan of a Diffusion Processes in Molten Semiconductors (DPIMS) experiment conducted on NASA's Space Shuttle. The possibility that the cartridge may creep during testing and touch the furnace walls is of real concern in this program. The present paper discusses the results of calculations performed to evaluate this possibility. Deformation mechanism maps were constructed using literature data in order to identify the creep mechanism dominant under the appropriate stresses and temperatures corresponding to the test conditions. These results showed that power-law creep was dominant when the grain size of the material exceeded 55 gm but Coble creep was the important mechanism below this value of grain size. Finite element analysis was used to analyze the heat treatment tWs assuming a furnace run away condition (which is a worst case scenario) using the appropriate creep parameters corresponding to grain sizes of 1 and 100 gm. Calculations were also conducted to simulate the effect of an initial 3 tilt of the cartridge assembly, the maximum possible tilt angle. The von Mises stress and su-ain distributions were calculated assuming that the cartridge was fixed at one end as it was heated from ambient temperature to 1823 K in 1.42 h, maintained at 1823 K for 9.5 h and then further heated to an over temperature condition of 2028 K in 0.3 h. The inelastic axial and radial displacements of the cartridge walls were evaluated by resolving the von Mises strain along the corresponding directions. These calculations reveal that the maximum axial and radial displacements are expected to be about 2.9 and 0.25 mm, respectively, for both fine and coarse-grained materials at 2028 K. It was determined that these displacements occur during heat-up to temperature and creep of the cartridge is likely to be relatively insignificant irrespective of grain size. Furthermore, with a 3' tilt of the cartridge, the deflection is increased by only 0.39 gm which is negligible. Since the gap between the furnace heating elements and the cartridge is about 7.5 mm and less than the maximum radial dilation of 0.25 mm at 2028 K, it is concluded that the cartridge is unlikely to touch the furnace walls during the experiments.

Raj, S.V.↗

NASA NTRS1961

An Automatic Terminal Guidance System for Rendezvous with a Satellite

This study includes a consideration of the design philosophy for an automatic terminal guidance system, a derivation of guidance equations required, and an outline of the general type of instrumentation necessary to provide the essential information. A control system for a sample vehicle is analyzed. A representative case, rendezvous with a satellite in circular orbit at 400 nautical miles, was examined. Terminal-stage nominal burning times of 200 and 400 seconds were used. For the 200-second case, initial errors in circumferential displacement of +/- 25,000 feet, in radial displacement of 7,000 to -9,000 feet, and in lateral displacement of +/- 20,000 feet were within the capabilities of the system. Velocity errors of 300 to -400 ft/sec in the circumferential direction, 180 to -200 ft/sec in the radial direction, and velocity offsets of at least 20 (+/- 800 ft/sec) in the lateral direction could also be handled. The 400-second case was capable of correcting larger errors, but limits were not determined. The dependence of required characteristic velocity on initial errors was determined and it was found that increases over the nominal terminal-stage characteristic velocity of the order of 15 percent covered most of the previously mentioned in-plane errors. The requirements were more severe for cases with lateral velocity offsets. A simplified set of guidance equations was tested and produced only slight variations in performance. Overall velocity requirements and mass ratios were determined for terminal-stage burning times of 100, 200, 300, and 400 seconds and for a range of transfer angles by using exact calculations for the terminal stage and an impulsive launching velocity. These results indicated that the shortest burning time consistent with the launch guidance errors expected gave the best mass ratio.

Carney, Terrance M.↗

NASA NTRS1998

Permanent GPS Geodetic Array in Southern California

The southern California Permanent GPS Geodetic Array (PGGA) was established in the spring of 1990 to evaluate continuous Global Positioning System (GPS) measurements as a new too] for monitoring crustal deformation. Southern California is an ideal location because of the relatively high rate of tectonic deformation, the high probability of intense seismicity, the long history of conventional and space geodetic measurements, and the availability of a well developed infrastructure to support continuous operations. Within several months of the start of regular operations, the PGGA recorded far-field coseismic displacements induced by the June 28, 1992 (M(sub w)=7.3), Landers earthquake, the largest magnitude earthquake in California in the past 40 years and the first one to be recorded by a continuous GPS array. Only nineteen months later, on 17 January 1994, the PGGA recorded coseismic displacements for the strongest earthquake to strike the Los Angeles basin in two decades, the (M(sub e)=6.7) Northridge earthquake. At the time of the Landers earthquake, only seven continuous GPS sites were operating in southern California; by the beginning of 1994, three more sites had been added to the array. However, only a pair of sites were situated in the Los Angeles basin. The destruction caused by the Northridge earthquake spurred a fourfold increase in the number of continuous GPS sites in southern California within 2 years of this event. The PGGA is now the regional component of the Southern California Integrated GPS Network (SCIGN), a major ongoing densification of continuous GPS sites, with a concentration in the Los Angeles metropolitan region. Continuous GPS provides temporally dense measurements of surface displacements induced by crustal deformation processes including interseismic, coseismic, postseismic, and aseismic deformation and the potential for detecting anomalous events such as preseismic deformation and interseismic strain variations. Although strain meters yield much higher short-term resolution to a period of about 1 year, a single continuous GPS site is significantly less expensive than a single strain meter and probably has better long-term stability beyond a 1-year period. Compared to less frequent field measurements, continuous GPS provides the means to better characterize the errors in GPS position measurements and thereby obtain more realistic estimates of derived parameters such as site velocities.

Green, Cecil H.↗

NASA NTRS1999

Ferroelectric Stirling-Cycle Refrigerator

A Stirling-cycle refrigerator has a three-pump configuration and pumping sequence, in which one pump serves as a compressor. one pump serves as an expander, and one pump serves as a displacer. The pumps are ferroelectrically actuated diaphragm pumps which are coordinated by synchronizing the ferroelectric-actuator voltages in such a way that the net effect of the displacer is to reduce the deleterious effect of dead space; that is, to circulate a greater fraction of the working fluid through the heat exchangers than would be possible by use of the compressor and expander alone. In addition. the displacer can be controlled separately to make the flow of working fluid in the heat exchangers turbulent (to increase the rate of transfer of heat at the cost of greater resistance to flow) or laminar (to decrease the resistance to flow at the cost of a lower heat-transfer rate).

Jalink, Antony, Jr.↗

NASA NTRS1998

Ionic Polymer-Metal Composites (IPMCs) as Biomimetic Sensors, Actuators and Artificial Muscles: A Review

This paper presents an introduction to ionic polymer-metal composites and some mathematical modeling pertaining to them. It further discusses a number of recent findings in connection with ion-exchange polymer-metal composites (IPMCS) as biomimetic sensors and actuators. Strips of these composites can undergo large bending and flapping displacement if an electric field is imposed across their thickness. Thus, in this sense they are large motion actuators. Conversely by bending the composite strip, either quasi-statically or dynamically, a voltage is produced across the thickness of the strip. Thus, they are also large motion sensors. The output voltage can be calibrated for a standard size sensor and correlated to the applied loads or stresses. They can be manufactured and cut in any size and shape. In this paper first the sensing capability of these materials is reported. The preliminary results show the existence of a linear relationship between the output voltage and the imposed displacement for almost all cases. Furthermore, the ability of these IPMCs as large motion actuators and robotic manipulators is presented. Several muscle configurations are constructed to demonstrate the capabilities of these IPMC actuators. This paper further identifies key parameters involving the vibrational and resonance characteristics of sensors and actuators made with IPMCS. When the applied signal frequency varies, so does the displacement up to a critical frequency called the resonant frequency where maximum deformation is observed, beyond which the actuator response is diminished. A data acquisition system was used to measure the parameters involved and record the results in real time basis. Also the load characterizations of the IPMCs were measured and it was shown that these actuators exhibit good force to weight characteristics in the presence of low applied voltages. Finally reported are the cryogenic properties of these muscles for potential utilization in an outer space environment of a few Torrs and temperatures of the order of - 140 degrees Celsius. These muscles are shown to work quite well in such harsh cryogenic environments and thus present a great potential as sensors and actuators that can operate at cryogenic temperatures.

Shahinpoor, M.↗

NASA NTRS1999

Instrumentation and Methods to Measure Dynamic Forces During Exercise Using the Horizontal Exercise Machine

It is hypothesized that bone loss experienced by astronauts in zero gravity conditions may be curtailed by appropriate exercise. According to Wolf's law, bone regenerates when muscles produce stresses by pulling on the bone during daily activity and/or exercise on Earth. To use this theory to prevent or decrease bone loss, one needs to quantify musculoskeletal loads and relate them to bone density changes. In the context of the space program, it is desirable to determine musculoskeletal loads during exercise so that one may make similar measurements on Earth and in space. In this manner, load measurements on Earth may be used as reference to generate similar loads during exercise in space. A research project to investigate the effects of high-resistive exercise to decrease bone density loss underzero-gravity conditions is being carried out in Life Sciences Research Laboratories at NASA JSC. The project consists of a bed-rest study whereby subjects remain in horizontal position for seventeen weeks. During the study, a subset of those subjects executes a regime of resistive exercises in the horizontal exercise machine (HEM). The HEM was designed so that subjects remain horizontal while exercising to minimize gravity loading even during exercise. Bone density of each subject is measured throughout the duration of their participation. The objective of the study is to determine if the resistive exercises are effective in diminishing or eliminating bone loss. My participation in this project relates to instrumentation, measurement, and processing of signals from displacement sensors (optical encoders) and load-cells. Measurement of displacements will be used to determine the motion of the body during exercise, and load measurements will be used (along with displacement data) to determine forces and torques exerted on each section of the body during exercise. Further, I have assisted in specifying new sensors to be added to the HEM and to a new prototype resistive exercise machine called the Interim Resistive Exercise Device (IRED). New load cells and encoders should be mounted in these devices to obtain more complete kineto-dynamic information. This report includes a description of the instrumentation that was built to perform measurements in the HEM and the IRED, along with the software that was developed to collect the measurements. It also includes examples of measurements taken in the HEM. Finally, a plan is laid out that describes how these measurements may be used to determine forces exerted by muscles for each exercise.

Figueroa, Fernando↗

NASA NTRS1999

Waves: Internal Tides

Oceanic internal tides are internal waves with tidal periodicities. They are ubiquitous throughout the ocean, although generally more pronounced near large bathymetric features such as mid-ocean ridges and continental slopes. The internal vertical displacements associated with these waves can be extraordinarily large. Near some shelf breaks where the surface tides are strong, internal displacements (e.g., of an isothermal surface) can exceed 200 meters. Displacements of 10 meters in the open ocean are not uncommon. The associated current velocities are usually comparable to or larger than the currents of the surface tide. On continental shelves internal tides can occasionally generate packets of internal solitons, which are detectable in remote sensing imagery. Other common nonlinear features are generation of higher harmonics (e.g., 6-hr waves) and wave breaking. Internal tides are known to be an important energy source for mixing of shelf waters. Recent research suggests that they may also be a significant energy source for deep-ocean mixing.

Ray, Richard D.↗

NASA NTRS2000

Crustal Deformation Associated with Glacial Fluctuations in the Eastern Chugach Mountains, Alaska

The changes of the solid Earth in south central Alaska in response to two major glacial fluctuations on different temporal and spatial scales have been estimated and we evaluated their influence on the stress state and ongoing tectonic deformation of the region. During the recent (1993-1995) Bering Glacier surge, a large transfer of ice from the Bagley Ice Field to the Bering Glacier terminus region occurred. We estimated the elastic displacement of the solid Earth due to ice mass redistribution from Global Positioning System (GPS) measurements at sites near the surging glacier. We can account for these displacements by transfer of an ice volume of about 14 cubic km from the surge reservoir area to the terminus region. We examined the background seismicity (M(sub L) > 2.5) before, during, and after the surge. We found that the occurrence of small earthquakes (M(sub L) < 4.0) in the surge reservoir region increased during the surge time interval possibly in response to a decrease in ice mass. This suggests that a small decrease in the vertical stress, o,3, could be enough to modulate the occurrence of small, shallow earthquakes in this dominantly thrust fault setting. During this century the southern Alaska coastal glaciers have been undergoing an overall decrease in volume. Based on our compilation of changes in the extent and thickness of the coastal glaciers between the Malaspina and Bering, we calculated surface displacements due to the Earth's viscoelastic response to annual thinning and to the cumulative retreat over the last 100 years. The uplift of the region due to an average annual thinning rate of 1-6 m/yr in the ablation region is 1-12 mm/yr. For our reference model with a viscosity of 5 x 10(exp 19) Pa s for depths between approximately equal 40 and 200 km the total viscoelastic response due to the retreat over the last century may be as much as a couple of meters within the coastal ablation zone near Icy Bay. The maximum decrease in sigma(sub V) between 0 and 10 km was approximately equal 1.0 MPa, which is significant in relation to the stress drops in recent earthquakes (approximately 2 to 10 MPa) but small in relation to the estimated tectonic stress magnitude. Therefore the occurrence of an earthquake such as the St. Elias (1979, M(sub S) = 7.2) may have been advanced in time; however, most of the ongoing stress accumulation would be primarily due to tectonic forces.

Sauber, Jeanne↗

NASA NTRS1997

ENSO Mechanisms

This current leading theory of the El Nino-Southern Oscillation (ENSO) phenomenon involves reflection of equatorial waves on the western ocean boundary to shift the ENSO phase from El Nino to La Nina and vice versa. However, recent satellite altimetry and In situ observations indicate that this theory has several flaws. These include imperfect equatorial wave reflection on the western ocean boundary, a maxima of the simulated coupled wind-sea surface temperature (SST) interaction located too far into the eastern equatorial Pacific, and an excessive role of thermocline displacement on SST in this region. We show that the central equatorial Pacific SST is fundamental in driving the EIVSO ocean-atmosphere coupled system, through the east-west displacement of the eastern edge of the warm pool, perfectly related with ENSO. Within the equatorial wave-guide, the dominance of surface zonal advection in these displacements is demonstrated with four different satellite and in situ data sets and three ocean models. This demonstration is supported by the evidence of a convergence of water masses into the eastern edge of the warm pool, resulting in a well-defined salinity front. All these results lead us to propose a notable modification of the leading delayed-action oscillator theory for the oscillatory nature of ENSO. Simulations with a linearized coupled ocean-atmosphere model result in 3-6 year ENSO-like oscillations, with many Of the variable model parameters found very close to their observed values. This simple model suggests that ocean processes ignored or underestimated in the delayed action oscillator theory, such as zonal current convergence, zonal advection of sea surface temperature and equatorial wave reflection from the eastern-ocean boundary, are fundamental to the development of ENSO, in particular to its manifestations in the central equatorial Pacific.

Picaut, Joel↗

NASA NTRS2000

Polar Plate Theory for Orthogonal Anisotropy

Laminated fiber-reinforced (or filamentary) composites are used today for their high strength-to-weight and stiffness-to-weight ratios. However, because of the anisotropic behavior of composites, determining the response on a macroscopic scale is challenging. This is particularly evident in the evaluation of the governing differential equations of a circular disk with the fibers of the lamina oriented with rectilinear orthogonality. This includes any situation involving a composite plate of circular geometry in which out-of-plane displacements due to load are desired, such as fastener pull through loading of a composite plate. Current analysis techniques use numerical methods with rectilinear coordinate systems to solve problems with circular geometry. These analyses over predict plate stiffness by 20% and underpredict failure by 70%. Consequently, there is a need to transform classical composite plate theory to a polar coordinate system. In order to better analyze structures with circular geometries the classical composite plate equations are transformed into the plate equations for a rectilinearly anisotropic composite in polar coordinates. A composite plate is typically a laminate of fibers in rectilinear directions. Subsequent to the lay-tip the necessary geometry is cut out of a rectangular plate. In a similar manner, the derivation of the plate equation starts with the fundamental definitions of strain, displacement and curvature and incorporates the material property angular dependence into the equilibrium equations for a differential polar element. In the transformed state, the stiffness coefficients are no longer constant, adding to the complexity of the governing differential equations. This paper discusses the new derivation and evaluation of the plate equations for a circular composite disk with orthogonal rectilinear anisotropy. The resultant new three partial differential equations, which describe the circular anisotropic plate, can be used to evaluate out-of-plane displacements for given load conditions in design of composite Structures. Without the formation of these unique plate equations, design of such structures is not a precise engineering accomplishment due to the lack of precise design tools. Such structures are over designed to compensate and costly tests need to be performed after production to validate safety. Though impossible to present the mathematical solution within the limits of this paper, the application of the newly derived plate equation in its orthotropic form for a balanced symmetric laminate compared favorably with test results and surpassed the results of standard numerical methods. Within the limitations of the problem foundation the predictive model provides a mechanism for establishing out-of-plane deflection levels for a circular composite plate. Future work in this area should include incorporating the circular composite plate equations in Finite Element Models. The new anisotropic polar plate equations call be utilized as a design tool so that the design more accurately meets the requirements, thus taking full advantage of the weight savings of composites. These accomplishments have not previously been presented to the engineering community nor ever proposed to the IAF. Should the proposed paper be accepted for presentation, attendance is assured.

Bailey, Michelle D.↗

NASA NTRS2000

Proton Damage in Linear and Digital Optocouplers

Optocoupler failures occurred on the Topex-Poseidon spacecraft after about two years of operation. Later work in the laboratory showed that the failures were due to extreme sensitivity of LEDs within the optocouplers to displacement damage from protons. Although earlier work had been done on displacement damage in light-emitting diodes, none of the devices studied previously had been heavily damaged at the low radiation levels where the optocouplers failed in space. Subsequent work has shown that LED damage varies over an extremely wide range, depending on the particular manufacturing technology. This paper discusses proton degradation of linear and digital optocouplers. One obvious way to harden optocoupler technologies is to select LEDs that are more resistant to displacement damage. A direct comparison is made of degradation of a commercial linear optocoupler from one manufacturer with a modified version of the same device with a different LED technology. Other factors, including degradation of optical photoresponse and transistor -ain are also discussed, along with basic comparisons of digital and analog optocouplers. Linear optocouplers are designed with somewhat different requirements than digital optocouplers, which not only affects their radiation response but also the interpretation of radiation test data.

Johnston, A. H.↗

NASA NTRS2000

Dependence of the Element Patterns of HYDROSTAR on Mutual Coupling

HYDROSTAR is a hybrid synthesis radiometer, intended for spaceborne applications, which employs a real aperture (waveguide stick antenna) for resolution along track and employs aperture synthesis to obtain resolution across track. This L-band system is an extension of the successful aircraft prototype, the Electronically Steered Thinned Array Radiometer (ESTAR). A proof-of-concept, full size system was constructed (45 wavelength in the synthesis direction) and subjected to extensive antenna pattern and associated microwave component measurements in an outdoor antenna test facility. HYDROSTAR employs a thinned array of 16 elements each 5.8 inches long in the along track dimension and spanning 9.5 inches across track. Each element is a narrow-wall shunt slot array with 36 slots. The polarization is linear (along-track). In the across track dimension, the antennas are deployed in a minimum redundancy array which has 90 independent baselines spaced in integer multiples of half a wavelength. The closest spacings used are for the first three elements at each end, which are spaced by only one-half wavelength. This study was intended to assess how closely each of 16 stick element patterns compare with their nominal values (as an individual, isolated radiator), when installed in their intended composite thinned array configuration. Extensive pattern measurements of the 16 elements that constitute the HYDROSTAR antenna subsystem were conducted to observe their relative features along the synthesis plane. Data was also collected for the mutual coupling between pairs of selected antennas. All antenna patterns had features different from that of an isolated element indicating some level of interaction among neighboring radiators. Those elements which had nearest neighbors at least five wavelengths away were located near the middle of the array. Their radiation patterns displayed sonic small, symmetric ripple across their full azimuth range. The patterns of elements that lie within 2.5 wavelengths of their neighbors showed stronger and asymmetric features. These are believed to be caused by mutual coupling among these structures. Evidence for this was seen when an antenna position was displaced by 0.05 wavelengths, Its pattern and those of its near neighbors were seen to change. Displacement within the plane of the array were observed to have different effects than displacements out-of-plane. A program of data analysis and theoretical development is in progress to provide a physical interpretation of the properties of these antenna patterns and to develop methods which can optimize the performance of this synthetic aperture imaging system. This includes compensation for pattern asymmetries and element position perturbation.

Weissman, David E.↗

NASA NTRS2000

Limits on Line Bisector Variability for Stars with Extrasolar Planets

We present an analysis of high-resolution synoptic spectra of ten F- and G-type stars, seven of which exhibit periodic radial velocity variations due to the presence of one or more substellar companions. We searched for subtle periodic variations in photospheric line asymmetry, as characterized by line bisectors. In principle, periodic variations in line asymmetry observed at lower spectral resolution could mimic the radial velocity signature of a companion, but we find no significant evidence of such behavior in our data. Observations were obtained from 1998 March to 1999 February using the National Solar Observatory (NSO) 1.52-m McMath-Pierce Solar Telescope Facility on Kitt Peak in conjunction with the solar-stellar spectrograph, achieving a resolving power of 1.2x10(exp5). To characterize line asymmetry, we first measured line bisectors for the unblended Fe I photospheric line at 625.26 nm. To improve sensitivity to small fluctuations, we then combined points in each bisector to form a velocity displacement with respect to the line core. We searched for periodic variations in this displacement, finding no substantial difference between stars with substellar companions and those without reported companions. We find no correlation between bisector velocity displacement and the known orbital phase of substellar companions around our target stars. Simulations of a periodic signal with noise levels that mimic our measurement errors suggest that we can exclude bisector variations with amplitudes greater than about 20 m/s. These results support the conclusion that extrasolar planets best explain the observed periodic variations in radial velocity.

Povich, M. S.↗

NASA NTRS1999

Analysis of Composite Panels Subjected to Thermo-Mechanical Loads

The results of a detailed study of the effect of cutout on the nonlinear response of curved unstiffened panels are presented. The panels are subjected to combined temperature gradient through-the-thickness combined with pressure loading and edge shortening or edge shear. The analysis is based on a first-order, shear deformation, Sanders-Budiansky-type shell theory with the effects of large displacements, moderate rotations, transverse shear deformation, and laminated anisotropic material behavior included. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, principal strains, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the nonlinear response to variations in the panel parameters, as well as in the material properties of the individual layers. Numerical results are presented for cylindrical panels and show the effects of variations in the loading and the size of the cutout on the global and local response quantities as well as their sensitivity to changes in the various panel, layer, and micromechanical parameters.

Noor, Ahmed K.↗

NASA NTRS2000

Inertial Effects in Suspension Dynamics

The present work analyses the dynamics of a suspension of heavy particles in shear flow. The magnitude of the particle inertia is given by the Stokes number St = m(gamma/6(pi)a, which is the ratio of the viscous relaxation time of a particle tau(sub p) = m=6pi(eta)a to the flow time gamma(sup -1). Here, m is the mass of the particle, a is its size, eta is the viscosity of the suspending fluid and gamma is the shear rate. The ratio of the Stokes number to the Reynolds number, Re = (rho)f(gamma)a(exp 2)/eta, is the density ratio rho(sub p)/rho(sub f). Of interest is to understand the separate roles of particle (St) and fluid (Re) inertia in the dynamics of suspensions. In this study we focus on heavy particles, rho(sub p)/rho(sub f) much greater than 1, for which the Stokes number is finite, but the Reynolds number is sufficiently small for inertial forces in the fluid to be neglected; thus, the fluid motion is governed by the Stokes equations. On the other hand, the probability density governing the statistics of the suspended particles satisfies a Fokker-Planck equation that accounts for both configuration and momentum coordinates, the latter being essential for finite St. The solution of the Fokker-Planck equation is obtained to O(St) via a Chapman-Enskog type-procedure, and the conditional velocity distribution so obtained is used to derive a configuration-space Smoluchowski equation with inertial corrections. The inertial effects are responsible for asymmetry in the relative trajectories of two spheres in shear flow, in contrast to the well known symmetric structure in the absence of inertia. Finite St open trajectories in the plane of shear suffer a downward lateral displacement resulting from the inability of a particle of finite mass to follow the curvature of the zero-Stokes-number pathlines. In addition to the induced asymmetry, the O(St) inertial perturbation dramatically alters the nature of the near-field trajectories. The stable closed orbits (for St = 0) in the plane of shear now spiral in, approaching particle-particle contact in the limit. All trajectories starting from an initial offset of O(St(sup 1/2) or less (which remain open for St = 0) also spiral in. The asymmetry of the trajectories leads to a non-Newtonian rheology and diffusive behavior. The latter because a given particle (moving along a finite St open trajectory) suffers a net displacement in the transverse direction after a single interaction. A sequence of such uncorrelated displacements leads to the particle executing a random walk. The inertial diffusivity tensor is anisotropic on account of differing strengths of interaction in the gradient and vorticity directions. Since the entire region (constituting an in finite area) of closed orbits in the plane of shear spirals onto contact for #finite St, the latter represents a singular surface for the pair-distribution function. The exact form of the pair-distribution function at contact is still, however, indeterminate in the absence of non-hydrodynamic effects. It should also be noted that finite St non-rectilinear flows do not support a spatially uniform number density owing to the cross-streamline inertial migration of particles.

J. F. Brady↗

NASA NTRS2001

A Unified Development of Basis Reduction Methods for Rotor Blade Analysis

The axial foreshortening effect plays a key role in rotor blade dynamics, but approximating it accurately in reduced basis models has long posed a difficult problem for analysts. Recently, though, several methods have been shown to be effective in obtaining accurate,reduced basis models for rotor blades. These methods are the axial elongation method,the mixed finite element method, and the nonlinear normal mode method. The main objective of this paper is to demonstrate the close relationships among these methods, which are seemingly disparate at first glance. First, the difficulties inherent in obtaining reduced basis models of rotor blades are illustrated by examining the modal reduction accuracy of several blade analysis formulations. It is shown that classical, displacement-based finite elements are ill-suited for rotor blade analysis because they can't accurately represent the axial strain in modal space, and that this problem may be solved by employing the axial force as a variable in the analysis. It is shown that the mixed finite element method is a convenient means for accomplishing this, and the derivation of a mixed finite element for rotor blade analysis is outlined. A shortcoming of the mixed finite element method is that is that it increases the number of variables in the analysis. It is demonstrated that this problem may be rectified by solving for the axial displacements in terms of the axial forces and the bending displacements. Effectively, this procedure constitutes a generalization of the widely used axial elongation method to blades of arbitrary topology. The procedure is developed first for a single element, and then extended to an arbitrary assemblage of elements of arbitrary type. Finally, it is shown that the generalized axial elongation method is essentially an approximate solution for an invariant manifold that can be used as the basis for a nonlinear normal mode.

Ruzicka, Gene C.↗

NASA NTRS2001

Low-Field and High-Field Characterization of THUNDER Actuators

THUNDER (THin UNimorph DrivER) actuators are pre-stressed piezoelectric devices developed at NASA Langley Research Center (LaRC) that exhibit enhanced strain capabilities. As a result, they are of interest in a variety of aerospace applications. Characterization of their performance as a function of electric field, temperature and frequency is needed in order to optimize their operation. Towards that end, a number of THUNDER devices were obtained from FACE International Co. with a stainless steel substrate varying in thickness from 1 mil to 20 mils. The various devices were evaluated to determine low-field and high-field displacement its well as the polarization hysteresis loops. The thermal stability of these drivers was evaluated by two different methods. First, the samples were thermally cycled under electric field by systematically increasing the maximum temperature from 25 C to 200 C while the displacement was being measured. Second, the samples were isothermally aged at 0 C, 50 C, 100 C. and 150 C in air, and the isothermal decay of the displacement was measured at room temperature as a function of time.

Ounaies, Z.↗

NASA NTRS2001

Stress Formulation in Three-Dimensional Elasticity

The theory of elasticity evolved over centuries through the contributions of eminent scientists like Cauchy, Navier, Hooke Saint Venant, and others. It was deemed complete when Saint Venant provided the strain formulation in 1860. However, unlike Cauchy, who addressed equilibrium in the field and on the boundary, the strain formulation was confined only to the field. Saint Venant overlooked the compatibility on the boundary. Because of this deficiency, a direct stress formulation could not be developed. Stress with traditional methods must be recovered by backcalculation: differentiating either the displacement or the stress function. We have addressed the compatibility on the boundary. Augmentation of these conditions has completed the stress formulation in elasticity, opening up a way for a direct determination of stress without the intermediate step of calculating the displacement or the stress function. This Completed Beltrami-Michell Formulation (CBMF) can be specialized to derive the traditional methods, but the reverse is not possible. Elasticity solutions must be verified for the compliance of the new equation because the boundary compatibility conditions expressed in terms of displacement are not trivially satisfied. This paper presents the variational derivation of the stress formulation, illustrates the method, examines attributes and benefits, and outlines the future course of research.

Patnaik, Surya N.↗