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At least 37 records · Page 2

Differential Correction Schemes in Nonlinear Regression

Classical iterative methods in nonlinear regression are reviewed and improved upon. This is accomplished by discussion of the geometrical and theoretical motivation for introducing modifications using generalized matrix inversion. Examples having inherent pitfalls are presented and compared in terms of results obtained using classical and modified techniques. The modification is shown to be useful alone or in conjunction with other modifications appearing in the literature.

Decell, H. P., Jr.↗

Seasonality of the Migrating Semidiurnal Tide in the Tropical Upper Mesosphere and Lower Thermosphere and its Thermodynamic and Momentum Budget

This work uses the Specified Dynamics-Whole Atmosphere Community Climate Model with Ionosphere/Thermosphere eXtension (SD-WACCM-X) to determine and explain the seasonality of the migrating semidiurnal tide (SW2) components of tropical upper mesosphere and lower thermosphere (UMLT) temperature, zonal wind, and meridional wind. This work also quantifies aliasing due to SW2 in satellite-based tidal estimates. Results show that during equinox seasons, the vertical profiles of tropical UMLT temperature SW2 and zonal-wind SW2’s amplitudes have a double-peak structure while they, along with meridional-wind SW2, have a single-peak structure in their amplitudes in June solstice. Hough mode reconstruction reveals that a linear combination of five SW2 Hough modes cannot fully reproduce these features. Tendency analysis reveals that for temperature, the adiabatic term, nonlinear advection term, and linear advection term are important. For the winds, the classical terms, nonlinear advection term, linear advection term, and gravity wave drag are important. Results of our alias analysis then indicate that SW2 can induce an ∼60% alias in zonal-mean and DW1 components calculated from sampling like that of the Thermosphere–Ionosphere–Mesosphere Energetics and Dynamics satellite and the Aura satellite. This work concludes that in situ generation by wave–wave interaction and/or by gravity waves plays significant roles in the seasonality of tropical UMLT temperature SW2, zonal-wind SW2, and meridional-wind SW2. The alias analysis further adds that one cannot simply assume that SW2 in the tropical UMLT is negligible.

Tides↗

Effect of joint damping and joint nonlinearity on the dynamics of space structures

Analyses of the effect of linear joint characteristics on the vibrations of a free-free, three-joint beam model show that increasing joint damping increases resonant frequencies and increases modal damping but only to the point where the joint gets 'locked up' by damping. This behavior is different from that predicted by modeling joint damping as proportional damping. Nonlinear analyses of the three-joint model with cubic springs at the joints show all the classical single DOF nonlinear response behavior at each resonance of the multiple DOF system: nondoubling of response for a doubling of forcing amplitude, multiple solutions, jump behavior, and resonant frequency shifts. These properties can be concisely quantified by characteristic backbone curves, which show the locus of resonant peaks for increasing forcing amplitude.

Bowden, Mary↗

Unsymmetrically laminated composites

Classical lamination theory predicts that the room-temperature shapes of all elevated-temperature cure, unsymmetrically laminated composites are saddles. However, experimental observation indicates that the shapes are often cylindrical. In addition, a second cylindrical can sometimes be obtained from the first by a simple snap-through action. A geometrically nonlinear extension to classical lamination theory is used to explain this behavior. Approximate solutions to the nonlinear extension are obtained by using a Rayleigh-Ritz minimization of the laminate's total potential energy. A stability analysis explains the dual cylindrical shapes.

Hyer, M. W.↗

Wave equations and computational models for sonic boom propagation through a turbulent atmosphere

The improved simulation of sonic boom propagation through the real atmosphere requires greater understanding of how the transient acoustic pulses popularly termed sonic booms are affected by atmospheric turbulence. A nonlinear partial differential equation that can be used to simulate the effects of smaller-scale atmospheric turbulence on sonic boom waveforms is described. The equation is first order in the time derivative and involves an extension of geometrical acoustics to include diffraction phenomena. Various terms in the equation are explained in physical terms. Such terms include those representing convection at the wave speed, diffraction, molecular relaxation, classical dissipation, and nonlinear steepening. The atmospheric turbulence enters through an effective sound speed, which varies with all three spatial coordinates, and which is the sum of the local sound speed and the component of the turbulent flow velocity projected along a central ray that connects the aircraft trajectory with the listener.

Pierce, Allan D.↗

Transient cooling of solid bodies of classical form by radiation

An approximate analytic method is presented for analysis of the unsteady process of radiative cooling of solid bodies of classical form. The nonlinear heat transfer problem is solved by the cascade linearization technique with use of the iteration method. Comparison of the results obtained even in the first approximation with the available numerical solutions indicates adequate engineering accuracy of the proposed technique.

Novikov, V. S.↗

Nonlinear structural and life analyses of a combustor liner

Three dimensional, nonlinear finite element structural analyses were performed for a simulated combustor liner specimen to assess the capability of nonlinear analyses using classical inelastic material models to represent the thermoplastic creep response of the one half scale component. Results indicate continued cyclic hardening and ratcheting while experimental data suggested a stable stress strain response after only a few loading cycles. The computed stress strain history at the critical location was put into two life prediction methods, strainrange partitioning and a Pratt and Whitney combustor life prediction method to evaluate their ability to predict cyclic crack initiation. It is found that the life prediction analyses over predicted the observed cyclic crack initiation life.

Moreno, V.↗

The room-temperature shapes of four-layer unsymmetric cross-ply laminates

A geometrically nonlinear extension of classical lamination theory developed by Hyer (1981) for predicting the room-temperature shapes of unsymmetric laminates is reformulated using relaxed restrictions regarding the inplane strains. The inplane residual strains of unsymmetric laminates which have cooled from curing into a cylindrical room-temperature shape are examined numerically. Results show that the residual strains are compressive and practically independent of spatial location on the laminate. In addition, the room temperature shapes of the four-layer unsymmetric cross-ply laminates are predicted, and it is shown that the temperature shapes are a strong function of their size and their stacking arrangement. It is demonstrated that, depending on the parameters selected, the room-temperature shape of a four-layer cross-ply unsymmetric laminate can be a unique saddle shape, a unique cylindrical shape, or a cylindrical shape that can be snapped through to another cylindrical shape.

Hyer, M. W.↗

Nonlinear structural and life analyses of a combustor liner

Three-dimensional, nonlinear, finite element structural analyses were performed for a simulated aircraft combustor liner specimen in order to assess the capability of nonlinear analyses using classical inelastic material models to represent the thermoplastic-creep response of the component. In addition, the computed stress-strain history at the critical location was input into life prediction methods in order to evaluate the ability of these procedures to predict crack initiation life. It is concluded that: (1) elastic analysis is adequate for obtaining strain range and critical location; (2) inelastic analyses did not accurately represent cyclic behavior of materials; and (3) none of the crack initiation life prediction methods were satisfactory.

Kaufman, A.↗

Linearization of digital derived rate algorithm for use in linear stability analysis

The digital derived rate (DDR) algorithm is used to calculate the rate of rotation of the Centaur upper-stage rocket. The DDR is highly nonlinear algorithm, and classical linear stability analysis of the spacecraft cannot be performed without linearization. The performance of this rate algorithm is characterized by a gain and phase curve that drop off at the same frequency. This characteristic is desirable for many applications. A linearization technique for the DDR algorithm is investigated. The linearization method is described. Examples of the results of the linearization technique are illustrated, and the effects of linearization are described. A linear digital filter may be used as a substitute for performing classical linear stability analyses, while the DDR itself may be used in time response analysis.

Graham, R. E.↗

Linearization of digital derived rate algorithm for use in linear stability analysis

The digital derived rate (DDR) algorithm is used to calculate the rate of rotation of the Centaur upper-stage rocket. The DDR is highly nonlinear algorithm, and classical linear stability analysis of the spacecraft cannot be performed without linearization. The performance of this rate algorithm is characterized by a gain and phase curve that drop off at the same frequency. This characteristic is desirable for many applications. A linearization technique for the DDR algorithm is investigated. The linearization method is described. Examples of the results of the linearization technique are illustrated, and the effects of linearization are described. A linear digital filter may be used as a substitute for performing classical linear stability analyses, while the DDR itself may be used in time response analysis.

Graham, R. E.↗

The nonlinear evolution of inviscid Goertler vortices in three-dimensional boundary layers

The nonlinear development of inviscid Gortler vortices in a three-dimensional boundary layer is considered. We do not follow the classical approach of weakly nonlinear stability problems and consider a mode which has just become unstable. Instead we extend the method of Blackaby, Dando, and Hall (1992), which considered the closely related nonlinear development of disturbances in stratified shear flows. The Gortler modes we consider are initially fast growing and we assume, following others, that boundary-layer spreading results in them evolving in a linear fashion until they reach a stage where their amplitudes are large enough and their growth rates have diminished sufficiently so that amplitude equations can be derived using weakly nonlinear and non-equilibrium critical-layer theories. From the work of Blackaby, Dando and Hall (1993) is apparent, given the range of parameters for the Gortler problem, that there are three possible nonlinear integro-differential evolution equations for the disturbance amplitude. These are a cubic due to viscous effects, a cubic which corresponds to the novel mechanism investigated in this previous paper, and a quintic. In this paper we shall concentrate on the two cubic integro-differential equations and in particular, on the one due to the novel mechanism as this will be the first to affect a disturbance. It is found that the consideration of a spatial evolution problem as opposed to temporal (as was considered in Blackaby, Dando, and Hall, 1992) causes a number of significant changes to the evolution equations.

Blackaby, Nicholas↗

Mid-Field Sonic Boom Extrapolation Methodology

In the design cycle of low-boom airplanes, sonic boom prediction must be accurate and efficient. The classical linear method, Whitham's F-function theory, has been widely applied to predict sonic boom signatures. However, linear theory fails to capture the nonlinear effects created by large civil transport. Computational fluid dynamics (CFD) has been used successfully to predict sonic boom signals at the near and mid fields. Nevertheless, it is computationally expansive in airplane design runs. In the present study, the method of characteristics is used to predict sonic boom signals in an efficient fashion. The governing equations are the axisymmetric Euler's equations with constant enthalpy. Since the method solves Euler's equations, it captures more nonlinear effects than the classical Whitham's F-function technique. Furthermore, the method of characteristics is an efficient marching scheme for initial value problems. In this study, we will first review the current CFD extrapolation technique and the work previously done in sonic boom extrapolation. Then, we will introduce the governing equations and the method of characteristics. Finally, we will show that the present method yields the same accurate results as previous CFD techniques, but with higher efficiency.

Cheung, Samson↗

Control of nonlinear systems with applications to constrained robots and spacecraft attitude stabilization

This thesis is organized in two parts. In Part 1, control systems described by a class of nonlinear differential and algebraic equations are introduced. A procedure for local stabilization based on a local state realization is developed. An alternative approach to local stabilization is developed based on a classical linearization of the nonlinear differential-algebraic equations. A theoretical framework is established for solving a tracking problem associated with the differential-algebraic system. First, a simple procedure is developed for the design of a feedback control law which ensures, at least locally, that the tracking error in the closed loop system lies within any given bound if the reference inputs are sufficiently slowly varying. Next, by imposing additional assumptions, a procedure is developed for the design of a feedback control law which ensures that the tracking error in the closed loop system approaches zero exponentially for reference inputs which are not necessarily slowly varying. The control design methodologies are used for simultaneous force and position control in constrained robot systems. The differential-algebraic equations are shown to characterize the slow dynamics of a certain nonlinear control system in nonstandard singularly perturbed form. In Part 2, the attitude stabilization (reorientation) of a rigid spacecraft using only two control torques is considered. First, the case of momentum wheel actuators is considered. The complete spacecraft dynamics are not controllable. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but a discontinuous feedback control strategy is constructed. Next, the case of gas jet actuators is considered. If the uncontrolled principal axis is not an axis of symmetry, the complete spacecraft dynamics are small time locally controllable. However, the spacecraft attitude cannot be asymptotically stabilized using continuous feedback, but a discontinuous stabilizing feedback control strategy is constructed. If the uncontrolled principal axis is an axis of symmetry, the complete spacecraft dynamics cannot be stabilized. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but again a discontinuous feedback control strategy is constructed.

Krishnan, Hariharan↗

Effects of nonlinear damping in flexible space structures

The classical Krylov-Bogoliubov "averaging" technique is used to study a class of nonlinear damping models, for which the damping force is proportional to the product of positive integer or fractional power of absolute values of displacement and that of velocity. The results are compared with linear viscous damping models. The amplitude decrement of free vibration for a single mode system with nonlinear models depends not only on damping ratio, but also on the initial amplitude, the time to measure the response, frequency of the system, and the powers of displacement and velocity. For the distributed system, the action of nonlinear damping is found to reduce energy of the system as well as to pass energy to higher modes. Experimental evidence such as in Spacecraft Control Laboratory Experiment seems to support the need for nonlinear models.

Hu, Anren↗

Planetary Protection Bioburden Analysis Program

This program is a Microsoft Access program that performed statistical analysis of the colony counts from assays performed on the Mars Science Laboratory (MSL) spacecraft to determine the bioburden density, 3-sigma biodensity, and the total bioburdens required for the MSL prelaunch reports. It also contains numerous tools that report the data in various ways to simplify the reports required. The program performs all the calculations directly in the MS Access program. Prior to this development, the data was exported to large Excel files that had to be cut and pasted to provide the desired results. The program contains a main menu and a number of submenus. Analyses can be performed by using either all the assays, or only the accountable assays that will be used in the final analysis. There are three options on the first menu: either calculate using (1) the old MER (Mars Exploration Rover) statistics, (2) the MSL statistics for all the assays, or This software implements penetration limit equations for common micrometeoroid and orbital debris (MMOD) shield configurations, windows, and thermal protection systems. Allowable MMOD risk is formulated in terms of the probability of penetration (PNP) of the spacecraft pressure hull. For calculating the risk, spacecraft geometry models, mission profiles, debris environment models, and penetration limit equations for installed shielding configurations are required. Risk assessment software such as NASA's BUMPERII is used to calculate mission PNP; however, they are unsuitable for use in shield design and preliminary analysis studies. The software defines a single equation for the design and performance evaluation of common MMOD shielding configurations, windows, and thermal protection systems, along with a description of their validity range and guidelines for their application. Recommendations are based on preliminary reviews of fundamental assumptions, and accuracy in predicting experimental impact test results. The software is programmed in Visual Basic for Applications for installation as a simple add-in for Microsoft Excel. The user is directed to a graphical user interface (GUI) that requires user inputs and provides solutions directly in Microsoft Excel workbooks. This work was done by Shannon Ryan of the USRA Lunar and Planetary Institute for Johnson Space Center. Further information is contained in a TSP (see page 1). MSC- 24582-1 Micrometeoroid and Orbital Debris (MMOD) Shield Ballistic Limit Analysis Program Lyndon B. Johnson Space Center, Houston, Texas Commercially, because it is so generic, Enigma can be used for almost any project that requires engineering visualization, model building, or animation. Models in Enigma can be exported to many other formats for use in other applications as well. Educationally, Enigma is being used to allow university students to visualize robotic algorithms in a simulation mode before using them with actual hardware. This work was done by David Shores and Sharon P. Goza of Johnson Space Center; Cheyenne McKeegan, Rick Easley, Janet Way, and Shonn Everett of MEI Technologies; Mark Manning of PTI; and Mark Guerra, Ray Kraesig, and William Leu of Tietronix Software, Inc. For further information, contact the JSC Innovation Partnerships Office at (281) 483-3809. MSC-24211-1 Spitzer Telemetry Processing System NASA's Jet Propulsion Laboratory, Pasadena, California The Spitzer Telemetry Processing System (SirtfTlmProc) was designed to address objectives of JPL's Multi-mission Image Processing Lab (MIPL) in processing spacecraft telemetry and distributing the resulting data to the science community. To minimize costs and maximize operability, the software design focused on automated error recovery, performance, and information management. The system processes telemetry from the Spitzer spacecraft and delivers Level 0 products to the Spitzer Science Center. SirtfTlmProc is a unique system with automated error notification and recovery, with a real-time continuous service that can go quiescent after periods of inactivity. The software can process 2 GB of telemetry and deliver Level 0 science products to the end user in four hours. It provides analysis tools so the operator can manage the system and troubleshoot problems. It automates telemetry processing in order to reduce staffing costs. This work was done by Alice Stanboli, Elmain M. Martinez, and James M. McAuley of Caltech for NASA's Jet Propulsion Laboratory. For more information, contact iaoffice @jpl.nasa.gov. This software is available for commercial licensing. Please contact Dan Broderick at Daniel.F. Broderick@jpl.nasa.gov. Refer to NPO-47803. NASA Tech Briefs, September 2013 29 This rapid response computer program predicts Orbiter Wing Leading Edge (WLE) damage caused by ice or foam impact during a Space Shuttle launch (Program "IMPACT2"). The program was developed after the Columbia accident in order to assess quickly WLE damage due to ice, foam, or metal impact (if any) during a Shuttle launch. IMPACT2 simulates an impact event in a few minutes for foam impactors, and in seconds for ice and metal impactors. The damage criterion is derived from results obtained from one sophisticated commercial program, which requires hours to carry out simulations of the same impact events. The program was designed to run much faster than the commercial program with prediction of projectile threshold velocities within 10 to 15% of commercial-program values. The mathematical model involves coupling of Orbiter wing normal modes of vibration to nonlinear or linear springmass models. IMPACT2 solves nonlinear or linear impact problems using classical normal modes of vibration of a target, and nonlinear/ linear time-domain equations for the projectile. Impact loads and stresses developed in the target are computed as functions of time. This model is novel because of its speed of execution. A typical model of foam, or other projectile characterized by material nonlinearities, impacting an RCC panel is executed in minutes instead of hours needed by the commercial programs. Target damage due to impact can be assessed quickly, provided that target vibration modes and allowable stress are known. This work was done by Robert Clark, Jr., Paul Cotter, and Constantine Michalopoulos of The Boeing Company for Johnson Space Center. For further information, contact the JSC Innovation Partnerships Office at (281) 483-3809. MSC-24988-1 Wing Leading Edge RCC Rapid Response Damage Prediction Tool (IMPACT2) Lyndon B. Johnson Space Center, Houston, Texas (3) the MSL statistics for only the accountable assays. Other options on the main menu include a data editing form and utility programs that produce various reports requested by the microbiologists and the project, and tools to generate the groupings for the final analyses. The analyses can be carried out in three ways: Each assay can be treated separately, the assays can be collectively treated for the whole zone as a group, or the assays can be collected in groups designated by the JPL Planetary Protection Manager. The latter approach was used to generate the final report because assays on the same equipment or similar equipment can be assumed to have been exposed to the same environment and cleaning. Thus, the statistics are improved by having a larger population, thereby reducing the standard deviation by the square root of N. For each method mentioned above, three reports are available. The first is a detailed report including all the data. This version was very useful in verifying the calculations. The second is a brief report that is similar to the full detailed report, but does not print out the data. The third is a grand total and summary report in which each assay requires only one line. For the first and second reports, most of the calculations are performed in the report section itself. For the third, all the calculations are performed directly in the query bound to the report. All the numerical results were verified by comparing them with Excel templates, then exporting the data from the Planetary Protection Analysis program to Excel.

Beaudet, Robert A.↗

Wing Leading Edge RCC Rapid Response Damage Prediction Tool (IMPACT2)

This rapid response computer program predicts Orbiter Wing Leading Edge (WLE) damage caused by ice or foam impact during a Space Shuttle launch (Program "IMPACT2"). The program was developed after the Columbia accident in order to assess quickly WLE damage due to ice, foam, or metal impact (if any) during a Shuttle launch. IMPACT2 simulates an impact event in a few minutes for foam impactors, and in seconds for ice and metal impactors. The damage criterion is derived from results obtained from one sophisticated commercial program, which requires hours to carry out simulations of the same impact events. The program was designed to run much faster than the commercial program with prediction of projectile threshold velocities within 10 to 15% of commercial-program values. The mathematical model involves coupling of Orbiter wing normal modes of vibration to nonlinear or linear springmass models. IMPACT2 solves nonlinear or linear impact problems using classical normal modes of vibration of a target, and nonlinear/ linear time-domain equations for the projectile. Impact loads and stresses developed in the target are computed as functions of time. This model is novel because of its speed of execution. A typical model of foam, or other projectile characterized by material nonlinearities, impacting an RCC panel is executed in minutes instead of hours needed by the commercial programs. Target damage due to impact can be assessed quickly, provided that target vibration modes and allowable stress are known.

Clark, Robert↗