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At least 451 records · Page 25

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NASA NTRS2016

IN11B-1621: Quantifying How Climate Affects Vegetation in the Amazon Rainforest

Amazon droughts in 2005 and 2010 have raised serious concern about the future of the rainforest. Amazon forests are crucial because of their role as the largest carbon sink in the world which would effect the global warming phenomena with decreased photosynthesis activity. Especially, after a decline in plant growth in 1.68 million km2 forest area during the once-in-a-century severe drought in 2010, it is of primary importance to understand the relationship between different climatic variables and vegetation. In an earlier study, we have shown that non-linear models are better at capturing the relation dynamics of vegetation and climate variables such as temperature and precipitation, compared to linear models. In this research, we learn precise models between vegetation and climatic variables (temperature, precipitation) for normal conditions in the Amazon region using genetic programming based symbolic regression. This is done by removing high elevation and drought affected areas and also considering the slope of the region as one of the important factors while building the model. The model learned reveals new and interesting ways historical and current climate variables affect the vegetation at any location. MAIAC data has been used as a vegetation surrogate in our study. For temperature and precipitation, we have used TRMM and MODIS Land Surface Temperature data sets while learning the non-linear regression model. However, to generalize the model to make it independent of the data source, we perform transfer learning where we regress a regularized least squares to learn the parameters of the non-linear model using other data sources such as the precipitation and temperature from the Climatic Research Center (CRU). This new model is very similar in structure and performance compared to the original learned model and verifies the same claims about the nature of dependency between these climate variables and the vegetation in the Amazon region. As a result of this study, we are able to learn, for the very first time how exactly different climate factors influence vegetation at any location in the Amazon rainforests, independent of the specific sources from which the data has been obtained.

global warming↗

NASA NTRS2000

Probabilistic Multi-Scale, Multi-Level, Multi-Disciplinary Analysis and Optimization of Engine Structures

Aircraft engines are assemblies of dynamically interacting components. Engine updates to keep present aircraft flying safely and engines for new aircraft are progressively required to operate in more demanding technological and environmental requirements. Designs to effectively meet those requirements are necessarily collections of multi-scale, multi-level, multi-disciplinary analysis and optimization methods and probabilistic methods are necessary to quantify respective uncertainties. These types of methods are the only ones that can formally evaluate advanced composite designs which satisfy those progressively demanding requirements while assuring minimum cost, maximum reliability and maximum durability. Recent research activities at NASA Glenn Research Center have focused on developing multi-scale, multi-level, multidisciplinary analysis and optimization methods. Multi-scale refers to formal methods which describe complex material behavior metal or composite; multi-level refers to integration of participating disciplines to describe a structural response at the scale of interest; multidisciplinary refers to open-ended for various existing and yet to be developed discipline constructs required to formally predict/describe a structural response in engine operating environments. For example, these include but are not limited to: multi-factor models for material behavior, multi-scale composite mechanics, general purpose structural analysis, progressive structural fracture for evaluating durability and integrity, noise and acoustic fatigue, emission requirements, hot fluid mechanics, heat-transfer and probabilistic simulations. Many of these, as well as others, are encompassed in an integrated computer code identified as Engine Structures Technology Benefits Estimator (EST/BEST) or Multi-faceted/Engine Structures Optimization (MP/ESTOP). The discipline modules integrated in MP/ESTOP include: engine cycle (thermodynamics), engine weights, internal fluid mechanics, cost, mission and coupled structural/thermal, various composite property simulators and probabilistic methods to evaluate uncertainty effects (scatter ranges) in all the design parameters. The objective of the proposed paper is to briefly describe a multi-faceted design analysis and optimization capability for coupled multi-discipline engine structures optimization. Results are presented for engine and aircraft type metrics to illustrate the versatility of that capability. Results are also presented for reliability, noise and fatigue to illustrate its inclusiveness. For example, replacing metal rotors with composites reduces the engine weight by 20 percent, 15 percent noise reduction, and an order of magnitude improvement in reliability. Composite designs exist to increase fatigue life by at least two orders of magnitude compared to state-of-the-art metals.

Chamis, Christos C.↗

NASA NTRS2001

Temperature Dependent Modal Test/Analysis Correlation of X-34 Fastrac Composite Rocket Nozzle

A unique high temperature modal test and model correlation/update program has been performed on the composite nozzle of the FASTRAC engine for the NASA X-34 Reusable Launch Vehicle. The program was required to provide an accurate high temperature model of the nozzle for incorporation into the engine system structural dynamics model for loads calculation; this model is significantly different from the ambient case due to the large decrease in composite stiffness properties due to heating. The high-temperature modal test was performed during a hot-fire test of the nozzle. Previously, a series of high fidelity modal tests and finite element model correlation of the nozzle in a free-free configuration had been performed. This model was then attached to a modal-test verified model of the engine hot-fire test stand and the ambient system mode shapes were identified. A reduced set of accelerometers was then attached to the nozzle, the engine fired full-duration, and the frequency peaks corresponding to the ambient nozzle modes individually isolated and tracked as they decreased during the test. To update the finite-element model of the nozzle to these frequency curves, the percentage differences of the anisotropic composite moduli due to temperature variation from ambient, which had been used in the initial modeling and which were obtained by small sample coupon testing, were multiplied by an iteratively determined constant factor. These new properties were used to create high-temperature nozzle models corresponding to 10 second engine operation increments and tied into the engine system model for loads determination.

Brown, Andrew M.↗

NASA NTRS2002

The Distribution of Ozone in the Early Stages of Polar Vortex Development

Previous analysis has shown that the distribution of O3 at high northern latitudes in the lower-to-middle stratosphere at the beginning of the winter season, 1999-2000 has a characteristic distribution, which is consistent between in situ and satellite measurements [Kawa et al., The Interaction Between Dynamics and Chemistry of Ozone in the Set-up Phase of the Northern Hemisphere Polar Vortex, submitted manuscript, 2001 ]. Initial O3 profiles in the vortex are similar to each other and are quite different from outside the vortex at the same latitude and also from a zonal mean climatology. In the vortex, O3 is nearly constant from 500 to above 800 K with a value at 3 ppmv +/- approx.10%. Values outside the vortex are up to a factor of 2 higher and increase significantly with potential temperature. The seasonal time series of POAM data shows that relatively low O3 mixing ratios, which characterize the vortex in late fall, are already present at high latitudes at the end of summer in September before the vortex circulation sets up. This suggests a possible feedback role between O3 chemistry and the formation of the vortex, which is dominated by the seasonal radiation balance. Here we show that these characteristic O3 distributions are consistent from year to year and between the hemispheres. We will attempt to determine whether variations in fall vortex O3 are related in any way to O3 abundances and vortex structure later during winter and into spring.

Kawa, S. R.↗

NASA NTRS1995

Large HAWT wake measurement and analysis

From the theoretical fluid dynamics point of view, the wake region of a large horizontal-axis wind turbine has been defined and described, and numerical models of wake behavior have been developed. Wind tunnel studies of single turbine wakes and turbine array wakes have been used to verify the theory and further refine the numerical models. However, the effects of scaling, rotor solidity, and topography on wake behavior are questions that remain unanswered. In the wind tunnel studies, turbines were represented by anything from scaled models to tea strainers or wire mesh disks whose solidity was equivalent to that of a typical wind turbine. The scale factor compensation for the difference in Reynolds number between the scale model and an actual turbine is complex, and not typically accounted for. Though it is wise to study the simpler case of wakes in flat topography, which can be easily duplicated in the wind tunnel, current indications are that wind turbine farm development is actually occurring in somewhat more complex terrain. Empirical wake studies using large horizontal-axis wind turbines have not been thoroughly composited, and, therefore, the results have not been applied to the well-developed theory of wake structure. The measurement programs have made use of both in situ sensor systems, such as instrumented towers, and remote sensors, such as kites and tethered, balloonborne anemometers. We present a concise overview of the work that has been performed, including our own, which is based on the philosophy that the MOD-2 turbines are probably their own best detector of both the momentum deficit and the induced turbulence effect downwind. Only the momentum deficit aspects of the wake/machine interactions have been addressed. Both turbine power output deficits and wind energy deficits as measured by the onsite meteorological towers have been analyzed from a composite data set. The analysis has also evidenced certain topographic influences on the operation of spatially diverse wind turbines.

Miller, A. H.↗

NASA NTRS2002

The Winds of B Supergiants

We present the most suitable data sets available in the International Ultraviolet Explorer (IUE) archive for the study of time-dependent stellar winds in early B supergiants. The UV line profile variability in 11 B0 to B3 stars is analyzed, compared and discussed, based on 16 separate data sets comprising over 600 homogeneously reduced high-resolution spectrograms. The targets include 'normal' stars with moderate rotation rates and examples of rapid rotators. A gallery of grey-scale images (dynamic spectra) is presented, which demonstrates the richness and range of wind variability and highlights different structures in the winds of these stars. This work emphasizes the suitability of B supergiants for wind studies, under-pinned by the fact that they exhibit unsaturated wind lines for a wide range of ionization. The wind activity of B supergiants is substantial and has highly varied characteristics. The variability evident in individual stars is classified and described in terms of discrete absorption components, spontaneous absorption, bowed structures, recurrence, and ionization variability and stratification. Similar structures can occur in stars of different fundamental parameters but also different structures may occur in the same star at a given epoch. We discuss the physical phenomena that may be associated with the spectral signatures, and highlight the challenges that these phenomena present to theoretical studies of time-dependent outflows in massive stars. In addition, SEI line-synthesis modelling of the UV wind lines is used to provide further information about the state of the winds in our program stars. Typically the range, implied by the line profile variability, in the product of mass-loss rate and ion fraction (M qi) is a factor of approximately 1.5, when integrated between 0.2 and 0.9 v infinity; it it can however be several times larger over localized velocity regions. At a given effective temperature the mean relative ion ratios can differ by a factor of 5. The general excess in predicted (forward-scattered) emission in the low velocity regime is discussed in turns of structured outflows. Mean ion fractions are estimated over the B0 to B1 spectral classes, and trends in the ionic ratios as a function of wind velocity are described. The low values obtained for the ion fractions of UV resonance lines may reflect the role of clumping in the wind.

Massa, Derck↗

NASA NTRS2020

Reduction of structural impacts and distinction of photosynthetic pathways in a global estimation of GPP from space-borne solar-induced chlorophyll fluorescence

Quantifying global photosynthesis remains a challenge due to a lack of accurate remote sensing proxies. Solar-induced chlorophyll fluorescence (SIF) has been shown to be a good indicator of photosynthetic activity across various spatial scales. However, a global and spatially challenging estimate of terrestrial gross primary production (GPP) based on satellite SIF remains unresolved due to the confounding effects of species-specific physical and physiological traits and external factors, such as canopy structure or photosynthetic pathway (C3orC4). Here we analyze an ensemble of far-red SIF data from OCO-2 satellite and ground observations at multiple sites, using the spectral invariant theory to reduce the effects of canopy structure and to retrieve a structure-corrected total canopy SIF emission (SIF total). We find that the relationships between observed canopy-leavingSIF and ecosystem GPP vary significantly among biomes. In contrast, the relationships between SIF total and GPP converge around two unique models, one for C3and one for C4plants. We show that the two single empirical models can be used to globally scale satellite SIF observations to terrestrial GPP. We obtain an independent estimate of global terrestrial GPP of 129.56 ± 6.54 PgC/year for the 2015–2017 period, which is consistent with the state-of-the-art data- and process-oriented models. The new GPP product shows improved sensitivity to previously undetected ‘hotspots’ of productivity, being able to resolve the double-peak in GPP due to rotational cropping systems. We suggest that the direct scheme to estimate GPP presented here, which is based on satelliteSIF, may open up new possibilities to resolve the dynamics of global terrestrial GPP across space and time.

scale satellite SIF observations to terrestrial GP↗

NASA NTRS2002

The Winds of B Supergiants

We present the most suitable data sets available in the International Ultraviolet Explorer (IUE) archive for the study of time-dependent stellar winds in early B supergiants. The UV line profile variability in 11 B0 to B3 stars is analyzed, compared and discussed, based on 16 separate data sets comprising over 600 homogeneously reduced high-resolution spectrograms. The targets include 'normal' stars with moderate rotation rates and examples of rapid rotators. A gallery of grey-scale images (dynamic spectra) is presented, which demonstrates the richness and range of wind variability and highlights different structures in the winds of these stars. This work emphasises the suitability of B supergiants for wind studies, under-pinned by the fact that they exhibit unsaturated wind lines for a wide range of ionization. The wind activity of B supergiants is substantial and has highly varied characteristics. The variability evident in individual stars is classified and described in terms of discrete absorption components, spontaneous absorption, bowed structures, recurrence, and ionization variability and stratification. Similar structures can occur in stars of different fundamental parameters, but also different structures may occur in the same star at a given epoch. We discuss the physical phenomena that may be associated with the spectral signatures, and highlight the challenges that these phenomena present to theoretical studies of time-dependent outflows in massive stars. In addition, SEI line-synthesis modelling of the UV wind lines is used to provide further information about the state of the winds in our program stars. Typically the range, implied by the line profile variability, in the product of mass-loss rate and ion fraction (M (dot) q(sub i)) is a factor of approximately 1.5, when integrated between 0.2 and 0.9 v infinity; it can however be several times larger over localized velocity regions. At a given effective temperature the mean relative ion ratios can differ by a factor of 5. The general excess in predicted (forward-scattered) emission in the low velocity regime is discussed in terms of structured outflows. Mean ion fractions are estimated over the B0 to B1 spectral classes, and trends in the ionic ratios as a function of wind velocity are described. The low values obtained for the ion fractions of UV resonance lines may reflect the role of clumping in the wind.

Massa, D.↗

NASA NTRS1992

Long-term lunar stations: Some ecological considerations

A major factor for long-term success of a lunar station is the ability to keep an agroecosystem functioning at a desirable, stable steady-state with ecological stability and reliability. Design for a long-lived extraterrestrial manned station must take into account interactions among its subsystems to insure that overall functionality is enhanced (or at least not compromised). Physical isolation of feed production, human living areas, recycling, and other systems may be straightforward, however, microbiological isolation will be very difficult. While it is possible to eliminate plant-associated microbiological communities by growing the plants asepticallly, it is not practical to keep plants germ-free on a large scale if humans are working with them. Ecological theory strongly suggests that some kinds of communities or organisms effectively increase the stability of ecosystems and will protect the plants from potential pathogens. A carefully designed and maintained (lunar-derived) soil can provide a variety of habitats for effective microbial buffers while adding structure to the agroecosystem. A soil can also increase ecosystem reliability through buffering otherwise large element and compound fluctuations (of nutrients, wastes, etc.) as well as buffering temperature level and atmosphere composition. We are doing experiments in ecological dynamics and attempting to extend the relevant theories.

Maguire, Bassett, Jr.↗

NASA NTRS1996

SEADYN Analysis of a Tow Line for a High Altitude Towed Glider

The concept of using a system, consisting of a tow aircraft, glider and tow line, which would enable subsonic flight at altitudes above 24 km (78 kft) has previously been investigated. The preliminary results from these studies seem encouraging. Under certain conditions these studies indicate the concept is feasible. However, the previous studies did not accurately take into account the forces acting on the tow line. Therefore in order to investigate the concept further a more detailed analysis was needed. The code that was selected was the SEADYN cable dynamics computer program which was developed at the Naval Facilities Engineering Service Center. The program is a finite element based structural analysis code that was developed over a period of 10 years. The results have been validated by the Navy in both laboratory and at actual sea conditions. This code was used to simulate arbitrarily-configured cable structures subjected to excitations encountered in real-world operations. The Navy's interest was mainly for modeling underwater tow lines, however the code is also usable for tow lines in air when the change in fluid properties is taken into account. For underwater applications the fluid properties are basically constant over the length of the tow line. For the tow aircraft/glider application the change in fluid properties is considerable along the length of the tow line. Therefore the code had to be modified in order to take into account the variation in atmospheric properties that would be encountered in this application. This modification consisted of adding a variable density to the fluid based on the altitude of the node being calculated. This change in the way the code handled the fluid density had no effect on the method of calculation or any other factor related to the codes validation.

Colozza, Anthony J.↗

NASA NTRS2011

Full-Scaled Advanced Systems Testbed: Ensuring Success of Adaptive Control Research Through Project Lifecycle Risk Mitigation

The National Aeronautics and Space Administration's Dryden Flight Research Center completed flight testing of adaptive controls research on the Full-Scale Advance Systems Testbed (FAST) in January of 2011. The research addressed technical challenges involved with reducing risk in an increasingly complex and dynamic national airspace. Specific challenges lie with the development of validated, multidisciplinary, integrated aircraft control design tools and techniques to enable safe flight in the presence of adverse conditions such as structural damage, control surface failures, or aerodynamic upsets. The testbed is an F-18 aircraft serving as a full-scale vehicle to test and validate adaptive flight control research and lends a significant confidence to the development, maturation, and acceptance process of incorporating adaptive control laws into follow-on research and the operational environment. The experimental systems integrated into FAST were designed to allow for flexible yet safe flight test evaluation and validation of modern adaptive control technologies and revolve around two major hardware upgrades: the modification of Production Support Flight Control Computers (PSFCC) and integration of two, fourth-generation Airborne Research Test Systems (ARTS). Post-hardware integration verification and validation provided the foundation for safe flight test of Nonlinear Dynamic Inversion and Model Reference Aircraft Control adaptive control law experiments. To ensure success of flight in terms of cost, schedule, and test results, emphasis on risk management was incorporated into early stages of design and flight test planning and continued through the execution of each flight test mission. Specific consideration was made to incorporate safety features within the hardware and software to alleviate user demands as well as into test processes and training to reduce human factor impacts to safe and successful flight test. This paper describes the research configuration, experiment functionality, overall risk mitigation, flight test approach and results, and lessons learned of adaptive controls research of the Full-Scale Advanced Systems Testbed.

Pavlock, Kate M.↗

NASA NTRS2016

Integrated Turbine Tip Clearance and Gas Turbine Engine Simulation

Gas turbine compressor and turbine blade tip clearance (i.e., the radial distance between the blade tip of an axial compressor or turbine and the containment structure) is a major contributing factor to gas path sealing, and can significantly affect engine efficiency and operational temperature. This paper details the creation of a generic but realistic high pressure turbine tip clearance model that may be used to facilitate active tip clearance control system research. This model uses a first principles approach to approximate thermal and mechanical deformations of the turbine system, taking into account the rotor, shroud, and blade tip components. Validation of the tip clearance model shows that the results are realistic and reflect values found in literature. In addition, this model has been integrated with a gas turbine engine simulation, creating a platform to explore engine performance as tip clearance is adjusted. Results from the integrated model explore the effects of tip clearance on engine operation and highlight advantages of tip clearance management.

gas path dynamics↗

NASA NTRS2016

Integrated Turbine Tip Clearance and Gas Turbine Engine Simulation

aerothermodynamics↗

NASA NTRSDate not supplied

Experimental Methods Using Force Application of A Single Boom for A 500-M²-Class Solar Sail

Solar sailing missions rely on deployable systems for large area-to-mass ratios once in space, while still being small enough for launcher envelopes in the stowed configuration. Many of these deployable systems feature booms that are flattened and subsequently coiled onto a spool / hub. As part of a collaborative deployable space structures research effort between the National Aeronautics and Space Administration (NASA) and German Aerospace Center (DLR), a boom deployment system for a future 500 m² solar sail has been developed. To achieve the respective solar sail size goal, 16.5-m-long booms produced by NASA were integrated into a DLR-designed deployer mechanism. This considerable size, as well as the lightweight construction of the booms and respective deployable systems makes testing on the ground a significant challenge. Some systems for gravity compensation as well as vertical testing to minimize the influence of gravity have been used in the past. However, an uncertainty factor remains towards the behaviour in the space environment. The focus of this paper is the load application testing of the integrated boom-deployment mechanism system under microgravity condition, as well as a comparison to vertical testing under gravity. Testing in microgravity was performed during a parabolic flight test inside an aircraft and it included stowage and full deployment of a single boom along the longitudinal axis of the aircraft. The load application was split into two categories: static testing, which induced a linear force ramp to the static boom for either compression or compression-bending; and dynamic testing, which applied a constant force to a boom during extension provided by the deployer mechanism. Both types of tests were performed multiple times at two distinct lengths of the boom, fully deployed (12.76 m) and ~28.6 % deployed (3.65 m). More parameters that are vital to the test philosophy are the angles of attack in the force application and the highest force applied. The data acquisition used for the applied load and deflection measurements of the boom is also presented.

Martin Richter↗

NASA NTRSDate not supplied

Experimental Methods Using Force Application of A Single Boom for A 500-M²-Class Solar Sail

Martin Richter↗

NASA NTRS2011

Atomic Simulation of Complex DNA DSBs and the Interactions with the Ku70/80 Heterodimer

DNA double strand breaks (DSBs) induced by ionizing radiation (IR) usually contain modified bases such as 8-oxo-7,8-dihydroguanine (8-oxoG) and thymine glycol, apurinic/apyrimidinic (AP) sites, 2-deoxyribonolactone, or single-strand breaks (SSBs). The presence of such lesions in close proximity to the DSB terminus makes the DNA nicks more difficult to repair and rejoin than endogenously induced simple DSBs, and as such a major determinant of the biological effects of high linear energy transfer (LET) radiation as encountered in space travel. In this study we conducted molecular dynamics simulations on a series of DNA duplexes with various complex lesions of 8-oxoG and AP sites, in an effort to investigate the effects of such lesions to the structural integrity and stability of DNA after insulted by IR. We also simulated the interaction of such complex DSBs with the Ku70/80 heterodimer, the first protein in mammalian cells to embark the non-homologous end joining (NHEJ) DNA repair pathway. The results indicate, compared to DNA with simple DSBs, the complex lesions can enhance the hydrogen bonds opening rate at the DNA terminus, and increase the mobility of the whole duplex, thus they present more deleterious effects to the genome integrity if not captured and repaired promptly in cells. Simulations also demonstrate the binding of Ku drastically reduces structural disruption and flexibility caused by the complex lesions, and the interactions of Ku with complex DSBs have a different potential energy landscape from the bound structure with simple DSB. In all complex DSBs systems, the binding of DSB terminus with Ku70 is softened while the binding of the middle duplex with Ku80 is tightened. This energy shift may help the Ku protein to secure at the DSB terminus for a longer time, so that other end processing factors or repair pathways can proceed at the lesions before NHEJ repair process starts. These atomic simulations may provide valuable new insight into the selective action of repair proteins on damaged DNA.

Hu, Shaowen↗

NASA NTRS2003

Proof Test Diagrams for a Lithia-Alumina-Silica Glass-Ceramic

The glass-ceramic (Zerodur, Schott Glaswerke, Mainz, Germany) contains 70% to 78% by weight crystalline phase of high-quartz structure with a mean crystal size of 50-55 nm. The vitreous phase has a positive thermal expansion coefficient which is practically balanced by the negative coefficient of the crystalline phase. This results in a material which can maintain longitudinal stability during thermal cycling. This was one of the reasons for its choice as the material for the grazing incidence mirrors for the Chandra X-Ray Facility. Brittle materials such as glass and glass-ceramics which exhibit slow crack growth and subsequent fast fracture to failure exhibit a time dependence in strength. The decrease in strength for a constant applied load is known as static fatigue. In many cases, environment plays a major role in the material lifetime. It has been shown for silicate glasses that crack velocity will increase as the amount of water vapor in the environment surface finish and rate of loading. A rough surface finish leads to a lower tensile strength than for an optically polished surface. The strength of glass is observed in general to increase with increasing load rate. This phenomena is known as dynamic fatigue. This was observed for Zerodur by Tucker and Gent and Tucker in previous dynamic fatigue studies, in which lifetimes were obtained. All of the above named factors need to be considered when glass is to be used in load bearing applications.

Tucker, Dennis S.↗

NASA NTRS1995

Expendable launch vehicle studies

Analytical support studies of expendable launch vehicles concentrate on the stability of the dynamics during launch especially during or near the region of maximum dynamic pressure. The in-plane dynamic equations of a generic launch vehicle with multiple flexible bending and fuel sloshing modes are developed and linearized. The information from LeRC about the grids, masses, and modes is incorporated into the model. The eigenvalues of the plant are analyzed for several modeling factors: utilizing diagonal mass matrix, uniform beam assumption, inclusion of aerodynamics, and the interaction between the aerodynamics and the flexible bending motion. Preliminary PID, LQR, and LQG control designs with sensor and actuator dynamics for this system and simulations are also conducted. The initial analysis for comparison of PD (proportional-derivative) and full state feedback LQR Linear quadratic regulator) shows that the split weighted LQR controller has better performance than that of the PD. In order to meet both the performance and robustness requirements, the H(sub infinity) robust controller for the expendable launch vehicle is developed. The simulation indicates that both the performance and robustness of the H(sub infinity) controller are better than that for the PID and LQG controllers. The modelling and analysis support studies team has continued development of methodology, using eigensensitivity analysis, to solve three classes of discrete eigenvalue equations. In the first class, the matrix elements are non-linear functions of the eigenvector. All non-linear periodic motion can be cast in this form. Here the eigenvector is comprised of the coefficients of complete basis functions spanning the response space and the eigenvalue is the frequency. The second class of eigenvalue problems studied is the quadratic eigenvalue problem. Solutions for linear viscously damped structures or viscoelastic structures can be reduced to this form. Particular attention is paid to Maxwell and Kelvin models. The third class of problems consists of linear eigenvalue problems in which the elements of the mass and stiffness matrices are stochastic. dynamic structural response for which the parameters are given by probabilistic distribution functions, rather than deterministic values, can be cast in this form. Solutions for several problems in each class will be presented.

Bainum, Peter M.↗