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NASA NTRS1993

Hybrid equations of motion for flexible multibody systems using quasi-coordinates

A variety of engineering systems, such as automobiles, aircraft, rotorcraft, robots, spacecraft, etc., can be modeled as flexible multibody systems. The individual flexible bodies are in general characterized by distributed parameters. In most earlier investigations they were approximated by some spatial discretization procedure, such as the classical Rayleigh-Ritz method or the finite element method. This paper presents a mathematical formulation for distributed-parameter multibody systems consisting of a set of hybrid (ordinary and partial) differential equations of motion in terms of quasi-coordinates. Moreover, the equations for the elastic motions include rotatory inertia and shear deformation effects. The hybrid set is cast in state form, thus making it suitable for control design.

Meirovitch, L.↗

NASA NTRS1992

A piecewise continuous Timoshenko beam model for the dynamic analysis of tapered beam-like structures

Distributed parameter modeling offers a viable alternative to the finite element approach for modeling large flexible space structures. The introduction of the transfer matrix method into the continuum modeling process provides a very useful tool to facilitate the distributed parameter model applied to some more complex configurations. A uniform Timoshenko beam model for the estimation of the dynamic properties of beam-like structures has given comparable results. But many aeronautical and aerospace structures are comprised of non-uniform sections or sectional properties, such as aircraft wings and satellite antennas. This paper proposes a piecewise continuous Timoshenko beam model which is used for the dynamic analysis of tapered beam-like structures. A tapered beam is divided into several segments of uniform beam elements. Instead of arbitrarily assumed shape functions used in finite element analysis, the closed-form solution of the Timoshenko beam equation is used. Application of the transfer matrix method relates all the elements as a whole. By corresponding boundary conditions and compatible conditions a characteristic equation for the global tapered beam has been developed, from which natural frequencies can be derived. A computer simulation is shown in this paper, and compared with the results obtained from the finite element analysis. While piecewise continuous Timoshenko beam model decreases the number of elements significantly; comparable results to the finite element method are obtained.

Shen, Ji Yao↗

NASA NTRS1980

Closed-loop stability of large space structures via singular and regular perturbation techniques - New results

Large Space Structures are treated as a special class of highly oscillatory distributed parameter systems. Practical controllers will need to be finite dimensional; however, this calls the closed-loop stability into question due to spillover interactions. Recent results, obtained using regular and singular perturbations theory, give stability bounds for closed-loop control of this type of distributed parameter system; this paper surveys these results and their implications for large space structures.

Balas, M. J.↗

NASA NTRS1985

A Residuals Approach to Filtering, Smoothing and Identification for Static Distributed Systems

An approach for state estimation and identification of spatially distributed parameters embedded in static distributed (elliptic) system models is advanced. The method of maximum likelihood is used to find parameter values that maximize a likelihood functional for the system model, or equivalently, that minimize the negative logarithm of this functional. To find the minimum, a Newton-Raphson search is conducted that from an initial estimate generates a convergent sequence of parameter estimates. For simplicity, a Gauss-Markov approach is used to approximate the Hessian in terms of products of first derivatives. The gradient and approximate Hessian are computed by first arranging the negative log likelihood functional into a form based on the square root factorization of the predicted covariance of the measurement process. The resulting data processing approach, referred to here by the new term of predicted data covariance square root filtering, makes the gradient and approximate Hessian calculations very simple. A closely related set of state estimates is also produced by the maximum likelihood method: smoothed estimates that are optimal in a conditional mean sense and filtered estimates that emerge from the predicted data covariance square root filter.

Rodriguez, G.↗

NASA NTRS1994

Computational Control of Flexible Aerospace Systems

Sharpe, Lonnie, Jr.↗

NASA NTRS1994

Computational control of flexible aerospace systems

The main objective of this project is to establish a distributed parameter modeling technique for structural analysis, parameter estimation, vibration suppression and control synthesis of large flexible aerospace structures. This report concentrates on the research outputs produced in the last two years. The main accomplishments can be summarized as follows. A new version of the PDEMOD Code had been completed based on several incomplete versions. The verification of the code had been conducted by comparing the results with those examples for which the exact theoretical solutions can be obtained. The theoretical background of the package and the verification examples has been reported in a technical paper submitted to the Joint Applied Mechanics & Material Conference, ASME. A brief USER'S MANUAL had been compiled, which includes three parts: (1) Input data preparation; (2) Explanation of the Subroutines; and (3) Specification of control variables. Meanwhile, a theoretical investigation of the NASA MSFC two-dimensional ground-based manipulator facility by using distributed parameter modeling technique has been conducted. A new mathematical treatment for dynamic analysis and control of large flexible manipulator systems has been conceived, which may provide an embryonic form of a more sophisticated mathematical model for future modified versions of the PDEMOD Codes.

Sharpe, Lonnie, Jr.↗

NASA NTRS1991

Combined structures-controls optimization of lattice trusses

The role that distributed parameter model can play in CSI is demonstrated, in particular in combined structures controls optimization problems of importance in preliminary design. Closed form solutions can be obtained for performance criteria such as rms attitude error, making possible analytical solutions of the optimization problem. This is in contrast to the need for numerical computer solution involving the inversion of large matrices in traditional finite element model (FEM) use. Another advantage of the analytic solution is that it can provide much needed insight into phenomena that can otherwise be obscured or difficult to discern from numerical computer results. As a compromise in level of complexity between a toy lab model and a real space structure, the lattice truss used in the EPS (Earth Pointing Satellite) was chosen. The optimization problem chosen is a generic one: of minimizing the structure mass subject to a specified stability margin and to a specified upper bond on the rms attitude error, using a co-located controller and sensors. Standard FEM treating each bar as a truss element is used, while the continuum model is anisotropic Timoshenko beam model. Performance criteria are derived for each model, except that for the distributed parameter model, explicit closed form solutions was obtained. Numerical results obtained by the two model show complete agreement.

Balakrishnan, A. V.↗

NASA NTRS1969

A comparison of numerical techniques for determining the parameters of distributed RC networks

Numerical techniques for modeling distributed RC networks

Huelsman, L. P.↗

NASA NTRS2001

Driving Parameters for Distributed and Centralized Air Transportation Architectures

This report considers the problem of intersecting aircraft flows under decentralized conflict avoidance rules. Using an Eulerian standpoint (aircraft flow through a fixed control volume), new air traffic control models and scenarios are defined that enable the study of long-term airspace stability problems. Considering a class of two intersecting aircraft flows, it is shown that airspace stability, defined both in terms of safety and performance, is preserved under decentralized conflict resolution algorithms. Performance bounds are derived for the aircraft flow problem under different maneuver models. Besides analytical approaches, numerical examples are presented to test the theoretical results, as well as to generate some insight about the structure of the traffic flow after resolution. Considering more than two intersecting aircraft flows, simulations indicate that flow stability may not be guaranteed under simple conflict avoidance rules. Finally, a comparison is made with centralized strategies to conflict resolution.

Feron, Eric↗

NASA NTRS2001

Properties of Air Traffic Conflicts for Free and Structured Routing

This paper analyzes the properties of air traffic conflicts in a future free routing system against those in the current structured routing system. Simulation of en route air traffic operations (above 18,000 ft) over the contiguous United States for a 24-hour period, constructed with initial conditions from actual air traffic data, were conducted using the Future ATM Concepts Evaluation Tool (FACET). Free routes were modeled as great circle (direct) routes from origin to destination, and structured routes were derived from actual flight plans along the current system of air routes. The conflict properties analyzed in this study include: (1) Total number of conflicts; (2) Distributions of key conflict parameters; and, (3) Categorization of conflicts into independent conflicts and two types of interacting conflicts. Preliminary results (for Denver Center traffic) indicate that conflict properties in a free routing system are different from those in the current structured routing system. In particular, a free routing system has significantly fewer conflicts, involving a correspondingly smaller number of aircraft, compared to the current structured routing system. Additionally, the conflict parameter distributions indicate that free routing conflicts are less intrusive than structured routing conflicts, and would therefore require small trajectory deviations for resolution.

Bilimoria, Karl D.↗

NASA NTRS2017

Global Distribution and Parameter Dependences of Gravity Wave Activity in the Martian Upper Thermosphere Derived from MAVEN NGIMS Observations

Wavelike perturbations in the Martian upper thermosphere observed by the Neutral Gas Ion Mass Spectrometer (NGIMS) onboard the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft have been analyzed. The amplitudes of small-scale perturbations with apparent wavelengths between approx. 100 and approx. 500 km in the Ar density around the exobase show a clear dependence on temperature (T(sub 0)) of the upper thermosphere. The average amplitude of the perturbations is approx. 10% on the dayside and approx. 20% on the nightside, which is about 2 and 10 times larger than those observed in the Venusian upper thermosphere and in the low-latitude region of Earths upper thermosphere, respectively. The amplitudes are inversely proportional to T(sub 0), suggesting saturation due to convective instability in the Martian upper thermosphere. After removing the dependence on T(sub 0), dependences of the average amplitude on the geographic latitude and longitude and solar wind parameters are found to be not larger than a few percent. These results suggest that the amplitudes of small-scale perturbations are mainly determined by convective breaking saturation in the upper thermosphere on Mars, unlike those on Venus and Earth.

Thermosphere↗

NASA NTRS1967

Effect of Propellant Feed System Coupling and Hydraulic Parameters on Analysis of Chugging

A digital distributed parameter model was used to study the effects of propellant-feed- system coupling and various hydraulic parameters on the analytical prediction of chugging instabilities. Coupling between the combustion chamber and feed system was controlled by varying the compliance of the injector-dome region. The coupling with the feed system above the pump was varied by changing the amount of cavitation compliance at the pump inlet. The stability limits and chugging frequencies proved to be strongly dependent on the degree of feed-system coupling. The maximum stability condition occurred with intermediate coupling. Under conditions of a high degree of feed-system-combustor coupling, the stability limits and chugging frequencies were primarily dependent on the feed-system characteristics; the responses were characterized by beating patterns. For the system analyzed, the pump suction line had little effect on the stability limits or chugging frequencies. Beating, present under the condition of near zero injector -dome compliance, was eliminated when the suction line was decoupled by employing a sufficiently high value of pump-inlet compliance. Under conditions of maximum feed-system coupling, the magnitude and distribution of line losses in the discharge line had a significant effect on the stability limits but had negligible effect on the chugging frequency and beating characteristics. Also, the length of the discharge line greatly affected the stability limits, chugging frequency, and beating characteristics. The length of the suction line, however, had little effect on the stability limits and chugging frequency but did influence the beating pattern. A resistive-shunt device attached to the pump discharge line to suppress chugging was investigated. The analysis showed that the device was effective under conditions of high feed-system coupling.

CHUGGING↗

NASA NTRS1991

Bremsstrahlung x rays from Jovian auroral electrons

In a recent paper by D. D. Barbosa, it is argued that electron bremsstrahlung is the most likely source of the auroral x-ray emissions that have been observed at Jupiter. Barbosa bases his argument on observational and theoretical studies of the production of secondary electrons in the Earth's aurora. It is argued here that Barbosa's interpretation is flawed because it ignors the constraint that the primary electron distribution parameters place on the parameters for the secondary electron distribution. As a result, Barbosa's postulated secondary electron fluxes are over three orders of magnitude greater than the theory of auroral electrons permits.

Waite, J. Hunter, Jr.↗

NASA NTRS2012

Microwave Properties of Ice-Phase Hydrometeors for Radar and Radiometers: Sensitivity to Model Assumptions

A simplied framework is presented for assessing the qualitative sensitivities of computed microwave properties, satellite brightness temperatures, and radar reflectivities to assumptions concerning the physical properties of ice-phase hydrometeors. Properties considered included the shape parameter of a gamma size distribution andthe melted-equivalent mass median diameter D0, the particle density, dielectric mixing formula, and the choice of complex index of refraction for ice. We examine these properties at selected radiometer frequencies of 18.7, 36.5, 89.0, and 150.0 GHz; and radar frequencies at 2.8, 13.4, 35.6, and 94.0 GHz consistent with existing and planned remote sensing instruments. Passive and active microwave observables of ice particles arefound to be extremely sensitive to the melted-equivalent mass median diameter D0 ofthe size distribution. Similar large sensitivities are found for variations in the ice vol-ume fraction whenever the geometric mass median diameter exceeds approximately 1/8th of the wavelength. At 94 GHz the two-way path integrated attenuation is potentially large for dense compact particles. The distribution parameter mu has a relatively weak effect on any observable: less than 1-2 K in brightness temperature and up to 2.7 dB difference in the effective radar reflectivity. Reversal of the roles of ice and air in the MaxwellGarnett dielectric mixing formula leads to a signicant change in both microwave brightness temperature (10 K) and radar reflectivity (2 dB). The choice of Warren (1984) or Warren and Brandt (2008) for the complex index of refraction of ice can produce a 3%-4% change in the brightness temperature depression.

Microwave properties↗

NASA NTRS1983

Parallelism and pipelining in high-speed digital simulators

The attainment of high computing speed as measured by the computational throughput is seen as one of the most challenging requirements. It is noted that high speed is cardinal in several distinct classes of applications. These classes are then discussed; they comprise (1) the real-time simulation of dynamic systems , (2) distributed parameter systems, and (3) mixed lumped and distributed systems. From the 1950s on, the quest for high speed in digital simulators concentrated on overcoming the limitations imposed by the so-called von Neumann bottleneck. Two major architectural approaches have made ig possible to circumvent this bottleneck and attain high speeds. These are pipelining and parallelism. Supercomputers, peripheral array processors, and microcomputer networks are then discussed.

Karplus, W. J.↗

NASA NTRS2003

Retrieval of Precipitation Profiles from Multiresolution, Multifrequency, Active and Passive Microwave Observations

In this study, a technique for estimating vertical profiles of precipitation from multifrequency, multiresolution active and passive microwave observations is investigated. The technique is applicable to the Tropical Rainfall Measuring Mission (TRMM) observations and it is based on models that simulate high-resolution brightness temperatures as functions of observed reflectivity profiles and a parameter related to the rain drop-size-distribution. The modeled high-resolution brightness temperatures are used to determine normalized brightness temperature polarizations at the microwave radiometer resolution. An optimal estimation procedure is employed to minimize the differences between the simulated and observed normalized polarizations by adjusting the drop-size-distribution parameter. The impact of other unknowns that are not independent variables in the optimal estimation but affect the retrievals is minimized through statistical parameterizations derived from cloud model simulations. The retrieval technique is investigated using TRMM observations collected during the Kwajalein Experiment (KWAJEX). These observations cover an area extending from 5 deg to deg N latitude and 166 deg to 172 deg E longitude from July to September 1999, and are coincident with various ground-based observations, facilitating a detailed analysis of the retrieved precipitation. Using the method developed in this study, precipitation estimates consistent with both the passive and active TRMM observations are obtained. Various parameters characterizing these estimates, i.e. the rain rate, the precipitation water content, the drop-size-distribution intercept, and the mass weighted mean drop diameter, are in good qualitative agreement with independent experimental and theoretical estimates. Combined rain estimates are in general higher than the official TRMM Precipitation Radar (PR) only estimates for the area and the period considered in the study. Ground-based precipitation estimates, derived from an analysis of rain gauge and ground radar data, are in better agreement with the combined estimates than with the TRMM PR-only estimates, which suggests that information useful for improving the radar-only estimates is contained in the brightness temperature data.

Grecu, Mircea↗

NASA NTRS1993

Frequency distributions and correlations of solar X-ray flare parameters

Frequency distributions of flare parameters are determined from over 12,000 solar flares. The flare duration, the peak counting rate, the peak hard X-ray flux, the total energy in electrons, and the peak energy flux in electrons are among the parameters studied. Linear regression fits, as well as the slopes of the frequency distributions, are used to determine the correlations between these parameters. The relationship between the variations of the frequency distributions and the solar activity cycle is also investigated. Theoretical models for the frequency distribution of flare parameters are dependent on the probability of flaring and the temporal evolution of the flare energy build-up. The results of this study are consistent with stochastic flaring and exponential energy build-up. The average build-up time constant is found to be 0.5 times the mean time between flares.

Crosby, Norma B.↗

NASA NTRS1985

Parameter identification in distributed systems

This paper describes a method for the identification of the parameters entering into the equations of motion of distributed systems. Because the motion of distributed systems is described in terms of partial differential equations, these parameters are in general continuous functions of the spatial variables. For vibrating systems, these parameters ordinarily represent the mass, stiffness and damping distributions. In this paper, these distributions are expanded in terms of finite series of known functions of the spatial variables multiplied by undetermined coefficients. It is assumed that the nature of the equations of motion is known and that a limited number of eigenvalues and eigenfunctions is identified in advance. Use is then made of the least squares method, in conjunction with the eigenfunctions' orthogonality, to compute the undetermined coefficients, thus identifying the system distributed parameters. A method for the identification of the eigensolution is also presented. The procedure for the identification of the eigensolution and of the system parameters is demonstrated via a numerical example.

Baruh, H.↗