SEARCH · Engineering Papers
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Large space structures (LSSs) and other dynamical systems of current interest are often extremely complex assemblies of rigid and flexible bodies subjected to kinematical constraints. A formulation is presented for the governing equations of constrained multibody systems via the application of singular value decomposition (SVD). The resulting equations of motion are shown to be of minimum dimension.
The Active Flexible Wing Project is a collaborative effort between the NASA Langley Research Center and Rockwell International. The objectives are the validation of methodologies associated with mathematical modeling, flutter suppression control law development and digital implementation of the control system for application to flexible aircraft. A flutter suppression control law synthesis for this project is described. The state-space mathematical model used for the synthesis included ten flexible modes, four control surface modes and rational function approximation of the doublet-lattice unsteady aerodynamics. The design steps involved developing the full-order optimal control laws, reducing the order of the control law, and optimizing the reduced-order control law in both the continuous and the discrete domains to minimize stochastic response. System robustness was improved using singular value constraints. An 8th order robust control law was designed to increase the symmetric flutter dynamic pressure by 100 percent. Preliminary results are provided and experiences gained are discussed.
Research on control, design and programming of kinematically redundant robot manipulators (KRRM) is discussed. These are devices in which there are more joint space degrees of freedom than are required to achieve every position and orientation of the end-effector necessary for a given task in a given workspace. The technological developments described here deal with: kinematic programming techniques for automatically generating joint-space trajectories to execute prescribed tasks; control of redundant manipulators to optimize dynamic criteria (e.g., applications of forces and moments at the end-effector that optimally distribute the loading of actuators); and design of KRRMs to optimize functionality in congested work environments or to achieve other goals unattainable with non-redundant manipulators. Kinematic programming techniques are discussed, which show that some pseudo-inverse techniques that have been proposed for redundant manipulator control fail to achieve the goals of avoiding kinematic singularities and also generating closed joint-space paths corresponding to close paths of the end effector in the workspace. The extended Jacobian is proposed as an alternative to pseudo-inverse techniques.
An elastic stress analysis was conducted for a double cantilever beam (DCB) specimen using finite-element methods. The purpose of this study was to identify the important parameters that influence stresses ahead of the delamination front. The study focused on an aluminum DCB specimen, typical of adhesively-bonded joints, and on a graphite/epoxy specimen representing a cocured composite. Opening mode sigma sub y stresses ahead of the crack tip were calculated and compared with those for a monolithic reference specimen. Beyond the singularity-dominated region very near the crack tip, the sigma sub y distribution was elevated compared to the monolithic case. Both the adhesive thickness and the adherend transverse (thickness-direction) stiffness were found to influence the elevation of sigma sub y. In contrast, adherend thickness and longitudinal stiffness has very little effect on this stress distribution. Estimates for adhesive yielding beyond the aluminum DCB crack tip showed that both the area and height of the plastic zone increased to a peak value for increasing adhesive thicknesses. Results from this study would provide insight for comparing data from different DCB specimens and for designing new DCB specimens.
In order to obtain the physically relevant discontinuous numerical solution, the steady-state inviscid Burgers' equation is singularly perturbed through the addition of a small amount of viscosity. A 'cell-centered' finite-difference scheme is proposed which employs two points for the inviscid part and four points for the viscous one. While difficulties are experienced in the capture of interior layers centered at node points, computational results for interior layers centered between node points, and for boundary layers, exhibit accurate nonoscillatory solutions whose discontinuities are captured in one cell on both coarse and fine grids.
The polar exponential arrays whose geometric parameters are presently analyzed have proven superior to X-Y raster imaging sensors when wide FOV, high central resolution, and rotation- and zoom-invariance are required; attractive applications for such arrays are in spacecraft docking/tracking/stationkeeping and mobile robot navigation. Attention is given to optimal designs minimizing sensor configuration and computation requirements, and the relation of geometric parameters to the three-dimensional sensing precision requirements driving sensor design. A method for smooth patching of the 'blind-spot' singularity in the sensor with a uniformly high-resolution 'fovea' is also presented.
It is shown how the genus per unit volume of isodensity surfaces in general nonlinear universes is related to the entire hierarchy of correlation functions. The general relation between the correlation function, the probability distribution of densities at several points, and the probability distributions of density and its derivatives at a point are given. Formulas for the area and genus per unit volume of isodensity surfaces are presented. As an application, after first reviewing the case of Gaussian fields, analytic results are reported for one particular example of a thoroughly nonlinear universe, Mandelbrot's Rayleigh-Levy random-walk fractal. While this fractal bears little resemblance to the real universe of galaxies, it possesses the singular and theoretically interesting property that in it cluster-cluster correlations are identically equal to galaxy-galaxy correlations to all orders.
Fundamental solutions which automatically satisfy boundary conditions at the interfaces of an elastic plate perfectly bonded to two elastic halfspaces are implemented in a three-dimensional BEM for crack problems. The BEM features a new integration scheme for highly singular kernels. The capability is achieved through a part analytic and part numerical integration procedure, such that the analytic part of the integration is similar for all slip/opening variations. Part-through elliptic cracks in an elastic plate with traction-free surfaces are analyzed and the SIF values along the crack front are found to compare favorably with the numerical SIF results of Raju and Newman (1979).
The problem of robust stability and performance in feedback control systems with n real (possibly related) uncertain parameters and structured unmodeled dynamics (the latter taking the form of m complex blocks dynamic uncertainties) is considered. A robustness margin rm is defined with respect to such model uncertainty structure and an algorithm is developed to compute it. Robust stability and performance are characterized in terms of r sub m or the structured singular value mu. An iterative procedure using the above algorithm is given to compute tight bounds on k sub m and mu. These bounds are exact for the case m = 3 or less.
The JPL (Jet Propulsion Laboratory) Orbit Determination Software System is a set of computer programs developed for the primary purpose of determining the flight path of deep-space mission spacecraft in NASA's Planetary Program and highly elliptical orbiting spacecraft in Earth orbit. The filtering processes available within the JPL Orbit Determination Software are discussed, and several examples are presented. In particular, solutions obtained by the Square Root Information Filter (SRIF) using Bierman's Estimation Subroutine Library (ESL) are discussed and compared with the solutions obtained by the singular value decomposition (SVD) technique. It is concluded that the SRIF filtering and smoothing algorithms are efficient and numerically stable for well-conditioned systems. The use of Bierman's ESL simplifies the task of maintaining the orbit determination software by providing efficient, tested filtering tools. For solving a large well-conditioned system (rank higher than 120), SRIF is approximately four times faster than SVD; however, for solving an ill-conditioned system, SVD is recommended.
A direct adaptive scheme based on the use of linear time-varying periodic controllers is proposed which estimates online the periodic coefficients of the controller. It is shown that adaptive stabilization is attained for all possibly nonstably invertible plants of known order but unknown delay. Although no appeal is made to persistency of excitation arguments, a provision is needed to avoid the singularity of an estimated matrix, this property being required only for the analysis and not the control calculations.
A new methodology is developed for the synthesis of linear, time-invariant (LTI) controllers for multivariable LTI systems. The aim is to achieve stability and performance robustness of the feedback system in the presence of multiple unstructured uncertainty blocks; i.e., to satisfy a frequency-domain inequality in terms of the structured singular value. The design technique is referred to as the causality recovery methodology (CRM). Starting with an initial (nominally) stabilizing compensator, the CRM produces a closed-loop system whose performance-robustness is at least as good as, and hopefully superior to, that of the original design. The robustness improvement is obtained by solving an infinite-dimensional, convex optimization program. A finite-dimensional implementation of the CRM was developed, and it was applied to a multivariate design example.
A new type of attractors - terminal attractors - for an addressable memory in neural networks operating in continuous time is introduced. These attractors represent singular solutions of the dynamical system. They intersect (or envelope) the families of regular solutions while each regular solution approaches the terminal attractor in a finite time period. It is shown that terminal attractors can be incorporated into neural networks such that any desired set of these attractors with prescribed basins is provided by an appropriate selection of the weight matrix.
The statistical properties of gravitational lensing due to smooth but nonuniform distributions of matter are considered. It is found that a majority of triple images had a parity characteristic for 'shear-induced' lensing. Almost all cases of triple or multiple imaging were associated with large surface density enhancements, and lensing objects were present between the images. Thus, the observed gravitational lens candidates for which no lensing object has been detected between the images are unlikely to be a result of asymmetric distribution of mass external to the image circle. In a model with smoothly variable surface mass density, moderately and highly amplified images tended to be single rather than multiple. An opposite trend was found in models which had singularities in the surface mass distribution.
The present evaluation of the method of asymptotic expansions (MAE) indicates that the various terms of the common solution of MAE can be generated as polynomials in stretched variables, without actually solving them from the outer solution, as is currently the practice. It is also noted that the common solution of the MAE and the intermediate solution of the singular-perturbation method are the same; these methods therefore yield identical results for a certain class of problems. Two illustrative problems are treated.
Recent developments in the theory of pattern formation in dendritic crystal growth and viscous fingering in fluids are reviewed. Consideration is given to the discovery that weak capillary forces act as singular perturbations which lead to selection mechanisms in dendritic crystal growth and fingering patterns. Other topics include the conventional thermodynamic model of the solidification of a pure substance from its melt, fingering instability, pattern selection, the solvability theory, dendritic growth rates, the bubble effect discovered by Couder et al. (1986), the dynamics of pattern-forming systems, and snowflake formation.
A stable, semi-Lagrangian, semi-implicit, two-time-level, gridpoint integration scheme for the shallow water equations on the sphere is presented. A rotated spherical coordinate system is used to integrate the equations of motion at each gridpoint poleward of a certain latitude, thus overcoming problems associated with the polar singularity. The results of medium term integrations of large scale test patterns using a long time step are presented.
Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.