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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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2008

Integrating the Gradient of the Thin Wire Kernel

A formulation for integrating the gradient of the thin wire kernel is presented. This approach employs a new expression for the gradient of the thin wire kernel derived from a recent technique for numerically evaluating the exact thin wire kernel. This approach should provide essentially arbitrary accuracy and may be used with higher-order elements and basis functions using the procedure described in [4].When the source and observation points are close, the potential integrals over wire segments involving the wire kernel are split into parts to handle the singular behavior of the integrand [1]. The singularity characteristics of the gradient of the wire kernel are different than those of the wire kernel, and the axial and radial components have different singularities. The characteristics of the gradient of the wire kernel are discussed in [2]. To evaluate the near electric and magnetic fields of a wire, the integration of the gradient of the wire kernel needs to be calculated over the source wire. Since the vector bases for current have constant direction on linear wire segments, these integrals reduce to integrals of the form

Champagne, Nathan J.↗
NASA NTRS1992

Failure of the method of slowly varying amplitude and phase for non-linear, singular oscillators

It is shown that the method of slowly varying amplitude and phase yields erroneous results in the study of the mathematical properties of nonlinear singular oscillator systems. The analytical solution is described in which the phase function is constant and for which a special limiting behavior exists when the wavelength is zero. The previous method based on the condition of boundedness cannot be satisfied for nonlinear singular characteristics, and the erroneous designation of the expansion parameter is identified.

Mickens, R. E.↗
NASA NTRS1996

On the Stochastic Quantization Method: Characteristics and Applications to Singular Systems

Introducing the generalized Langevin equation, we extend the stochastic quantization method so as to deal with singular dynamical systems beyond the ordinary territory of quantum mechanics. We also show how the uncertainty relation is built up to the quantum mechanical limit with respect to fictitious time, irrespective of its initial value, within the framework of the usual stochastic quantization method.

Kanenaga, Masahiko↗
NASA NTRS1976

A lifting surface theory for the analysis of nonplanar lifting systems

A new nonlinear, nonplanar lifting surface theory is presented. The method is regarded as a lifting surface theory in that the effects of wing thickness are neglected, but none of the usual small perturbation assumptions inherent in most other lifting surface theories are made. The method represents nonplanar lifting systems by distributed vorticity, including the leading edge singular behavior characteristic of thin wings. The method is well suited to the computation of induced drag of nonplanar systems because leading edge suction is calculated from the leading edge singularity. The method has been used to compute the induced drag benefit of winglets (vortex diffusers), and the agreement with NASA experimental data is excellent.

Goldhammer, M. I.↗
NASA NTRS1985

Hand controllers for teleoperation. A state-of-the-art technology survey and evaluation

Hand controller technology for teleoperation is surveyed in three major catagories: (1) hand grip design, (2) control input devices, and (3) control strategies. In the first category, 14 hand grip designs are reviewed and evaluated in light of human factor considerations. In the second, 12 hand controller input devices are evaluated in terms of task performance, configuration and force feedback, controller/slave correspondence, operating volume, operator workload, human limitations, cross coupling, singularities, anthropomorphic characteristics, physical complexity, control/display interference, accuracy, technological base, cost, and reliability. In the third catagory, control strategies, commonly called control modes, are surveyed and evaluated. The report contains a bibliography with 189 select references on hand controller technology.

Brooks, T. L.↗
NASA NTRS1985

Regions of stability with unequal saturation limits and non-zero set point

Constraints on the magnitudes of control variables limit the region where open-loop unstable systems can be stabilized using feedback control. Variations in regions of stability with unequal control saturation limits and non-zero set points are illustrated for single-input unstable linear systems which have one or two unstable eigenvalues. The regions of stability for saddle-point- and unstable-node-type singularities increase with the increase in one of the saturation limits, but they become invariant when the larger control limit exceeds a certain value; the stability regions vanish for non-zero set-points that saturate the controls. The unstable-focus-type singularity exhibits strikingly different characteristics. These results suggest guidelines for obtaining desired stability regions for different types of singularities.

Stengel, R. F.↗
NASA NTRS1985

A study of methods to predict and measure the transmission of sound through the walls of light aircraft. Integration of certain singular boundary element integrals for applications in linear acoustics

An alternative method for performing singular boundary element integrals for applications in linear acoustics is discussed. The method separates the integral of the characteristic solution into a singular and nonsingular part. The singular portion is integrated with a combination of analytic and numerical techniques while the nonsingular portion is integrated with standard Gaussian quadrature. The method may be generalized to many types of subparametric elements. The integrals over elements containing the root node are considered, and the characteristic solution for linear acoustic problems are examined. The method may be generalized to most characteristic solutions.

Zimmerle, D.↗
NASA NTRS1992

Singularity perturbed zero dynamics of nonlinear systems

Stability properties of zero dynamics are among the crucial input-output properties of both linear and nonlinear systems. Unstable, or 'nonminimum phase', zero dynamics are a major obstacle to input-output linearization and high-gain designs. An analysis of the effects of regular perturbations in system equations on zero dynamics shows that whenever a perturbation decreases the system's relative degree, it manifests itself as a singular perturbation of zero dynamics. Conditions are given under which the zero dynamics evolve in two timescales characteristic of a standard singular perturbation form that allows a separate analysis of slow and fast parts of the zero dynamics.

Isidori, A.↗
NASA NTRS1982

Boundary-layer effects in composite laminates. I - Free-edge stress singularities. II - Free-edge stress solutions and basic characteristics

The fundamental nature of the boundary-layer effect in fiber-reinforced composite laminates is formulated in terms of the theory of anisotropic elasticity. The basic structure of the boundary-layer field solution is obtained by using Lekhnitskii's stress potentials (1963). The boundary-layer stress field is found to be singular at composite laminate edges, and the exact order or strength of the boundary layer stress singularity is determined using an eigenfunction expansion method. A complete solution to the boundary-layer problem is then derived, and the convergence and accuracy of the solution are analyzed, comparing results with existing approximate numerical solutions. The solution method is demonstrated for a symmetric graphite-epoxy composite.

Wang, S. S.↗
NASA NTRS1983

Predicting aerodynamic characteristics of vortical flows on three-dimensional configurations using a surface-singularity panel method

A general low-order surface-singularity panel method is used to predict the aerodynamic characteristics of a problem where a wing-tip vortex from one wing closely interacts with an aft mounted wing in a low Reynolds Number flow; i.e., 125,000. Nonlinear effects due to wake roll-up and the influence of the wings on the vortex path are included in the calculation by using a coupled iterative wake relaxation scheme. The interaction also affects the wing pressures and boundary layer characteristics: these effects are also considered using coupled integral boundary layer codes and preliminary calculations using free vortex sheet separation modelling are included. Calculated results are compared with water tunnel experimental data with generally remarkably good agreement.

Maskew, B.↗
NASA NTRS1980

Stress singularities at the vertex of a cylindrically anisotropic wedge

The plane elasticity problem for a cylindrically anisotropic solid is formulated. The form of the solution for an infinite wedge shaped domain with various homogeneous boundary conditions is derived and the nature of the stress singularity at the vertex of the wedge is studied. The characteristic equations giving the stress singularity and the angular distribution of the stresses around the vertex of the wedge are obtained for three standard homogeneous boundary conditions. The numerical examples show that the singular behavior of the stresses around the vertex of an anisotropic wedge may be significantly different from that of the isotropic material. Some of the results which may be of practical importance are that for a half plane the stress state at r = 0 may be singular and for a crack the power of stress singularity may be greater or less than 1/2.

Delale, F.↗
NASA NTRS1989

A complete analytical solution for the inverse instantaneous kinematics of a spherical-revolute-spherical (7R) redundant manipulator

Using a method based upon resolving joint velocities using reciprocal screw quantities, compact analytical expressions are generated for the inverse solution of the joint rates of a seven revolute (spherical-revolute-spherical) manipulator. The method uses a sequential decomposition of screw coordinates to identify reciprocal screw quantities used in the resolution of a particular joint rate solution, and also to identify a Jacobian null-space basis used for the direct solution of optimal joint rates. The results of the screw decomposition are used to study special configurations of the manipulator, generating expressions for the inverse velocity solution for all non-singular configurations of the manipulator, and identifying singular configurations and their characteristics. Two functions are therefore served: a new general method for the solution of the inverse velocity problem is presented; and complete analytical expressions are derived for the resolution of the joint rates of a seven degree of freedom manipulator useful for telerobotic and industrial robotic application.

Podhorodeski, R. P.↗
NASA NTRS2001

Dynamic modeling of gene expression data

We describe the time evolution of gene expression levels by using a time translational matrix to predict future expression levels of genes based on their expression levels at some initial time. We deduce the time translational matrix for previously published DNA microarray gene expression data sets by modeling them within a linear framework by using the characteristic modes obtained by singular value decomposition. The resulting time translation matrix provides a measure of the relationships among the modes and governs their time evolution. We show that a truncated matrix linking just a few modes is a good approximation of the full time translation matrix. This finding suggests that the number of essential connections among the genes is small.

NASA Discipline Plant Biology↗
NASA NTRS1974

A note on a broken layer in an orthotropic laminate composite

An orthotropic laminate composite containing a completely broken layer is considered. The problem is formulated in terms of integral transforms and then reduced to a singular integral equation which is solved numerically. The strength of stress singularity at the crack tip is determined from a characteristic equation which is obtained by studying the dominant part of the singular integral equation near the end points. The stress intensity factors are given for various material properties.

Arin, K.↗
NASA NTRS1977

A note on a broken layer in an orthotropic laminate composite

An orthotropic laminate composite containing a completely broken layer is considered. The problem is formulated in terms of integral transforms and then reduced to a singular integral equation which is solved numerically. The strength of stress singularity at the crack tip is determined from a characteristic equation which is obtained by studying the dominant part of the singular integral equation near the end points. The stress intensity factors are given for various material properties.

Arin, K.↗
NASA NTRS1981

Boundary-layer effects in composite laminates: Free-edge stress singularities, part 6

A rigorous mathematical model was obtained for the boundary-layer free-edge stress singularity in angleplied and crossplied fiber composite laminates. The solution was obtained using a method consisting of complex-variable stress function potentials and eigenfunction expansions. The required order of the boundary-layer stress singularity is determined by solving the transcendental characteristic equation obtained from the homogeneous solution of the partial differential equations. Numerical results obtained show that the boundary-layer stress singularity depends only upon material elastic constants and fiber orientation of the adjacent plies. For angleplied and crossplied laminates the order of the singularity is weak in general.

Wanag, S. S.↗
NASA NTRS1989

On the Lagrangian description of unsteady boundary layer separation. Part 1: General theory

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.

Vandommelen, Leon L.↗
NASA NTRS1990

On the Lagrangian description of unsteady boundary-layer separation. I - General theory

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.

Van Dommelen, Leon L.↗