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At least 559 records · Page 31

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NASA NTRS1982

Pole placement and order reduction in two-time-scale control systems through Riccati iteration

A transformation of variables taken from singular perturbations may be applied to two-time-scale linear systems in state space form to reduce the system to block-diagonal form with slow and fast modes decoupled. The transformation is easily computed by applying the new Riccati iteration. The iteration yields a solution to the nonsymmetric algebraic Riccati equation obtained by partitioning the original system matrix A. The numerical procedure is initiated with the trivial iterate L(0) = 0, and is globally convergent to the desired unique time scale decoupling solution. After transformation, the decoupled system may be used in controller design to achieve exact closed loop pole placement in the slow subsystem without altering the poles of the fast subsystem. The decoupled form may also be used to reduce system order by wetting a small parameter to zero. Provided the fast subsystem is stable, the order reduction can be expected to yield a good approximation to the original system. These methods are demonstrated using the 16th order linear model of a turbofan engine.

Anderson, L. R.↗

NASA NTRS1983

A revised version of the transfer matrix method to analyze one-dimensional structures

A new and general method to analyze both free and forced vibration characteristics of one-dimensional structures is discussed in this paper. This scheme links for the first time the classical transfer matrix method with the recently developed integrating matrix technique to integrate systems of differential equations. Two alternative approaches to the problem are presented. The first is based upon the lumped parameter model to account for the inertia properties of the structure. The second releases that constraint allowing a more precise description of the physical system. The free vibration of a straight uniform beam under different support conditions is analyzed to test the accuracy of the two models. Finally some results for the free vibration of a 12th order system representing a curved, rotating beam prove that the present method is conveniently extended to more complicated structural dynamics problems.

Nitzsche, F.↗

NASA NTRS1983

Flutter and forced response of mistuned rotors using standing wave analysis

A standing wave approach is applied to the analysis of the flutter and forced response of tuned and mistuned rotors. The traditional traveling wave cascade airforces are recast into standing wave arbitrary motion form using Pade approximants, and the resulting equations of motion are written in the matrix form. Applications for vibration modes, flutter, and forced response are discussed. It is noted that the standing wave methods may prove to be more versatile for dealing with certain applications, such as coupling flutter with forced response and dynamic shaft problems, transient impulses on the rotor, low-order engine excitation, bearing motions, and mistuning effects in rotors.

Dugundji, J.↗

NASA NTRS1983

Flutter and forced response of mistuned rotors using standing wave analysis

Bundas, D. J.↗

NASA NTRS1983

Closed-form solutions for a class of optimal quadratic tracking problems

Closed-form solutions are derived for a class of tracking problems including a linear optimal regulator and a prefilter for a time-invariant plant. The solutions for the prefilter equation and state trajectory coupled by the Riccati equation are exponentially related to the stability matrix of the plant. A computational procedure is presented in recursive form when the desired output state dynamics is assumed linear and time-invariant. Several examples are given for illustration.

Turner, J. D.↗

NASA NTRS1987

Identification of large space structures: A state-of-practice report

An outline of this work is presented. It begins with a schematic flow diagram and a logical flow diagram of the identification process for large space structures (LSS). Next, the task is defined by a structure model definition. A matrix polynomial formulation with a node displacement equation and a state variable formulation with node displacement and velocities are outlined. Further outlined is the identification of LSS on orbit; modeling errors and uncertainties; verification and validation of model; and noise, computations, and data collection.

Source record↗

NASA NTRS1989

Sequential design of discrete linear quadratic regulators via optimal root-locus techniques

A sequential method employing classical root-locus techniques has been developed in order to determine the quadratic weighting matrices and discrete linear quadratic regulators of multivariable control systems. At each recursive step, an intermediate unity rank state-weighting matrix that contains some invariant eigenvectors of that open-loop matrix is assigned, and an intermediate characteristic equation of the closed-loop system containing the invariant eigenvalues is created.

Shieh, Leang S.↗

NASA NTRS1991

An initial investigation into methods of computing transonic aerodynamic sensitivity coefficients

The three dimensional quasi-analytical sensitivity analysis and the ancillary driver programs are developed needed to carry out the studies and perform comparisons. The code is essentially contained in one unified package which includes the following: (1) a three dimensional transonic wing analysis program (ZEBRA); (2) a quasi-analytical portion which determines the matrix elements in the quasi-analytical equations; (3) a method for computing the sensitivity coefficients from the resulting quasi-analytical equations; (4) a package to determine for comparison purposes sensitivity coefficients via the finite difference approach; and (5) a graphics package.

Carlson, Leland A.↗

NASA NTRS1991

Time-domain finite elements in optimal control with application to launch-vehicle guidance

A time-domain finite element method is developed for optimal control problems. The theory derived is general enough to handle a large class of problems including optimal control problems that are continuous in the states and controls, problems with discontinuities in the states and/or system equations, problems with control inequality constraints, problems with state inequality constraints, or problems involving any combination of the above. The theory is developed in such a way that no numerical quadrature is necessary regardless of the degree of nonlinearity in the equations. Also, the same shape functions may be employed for every problem because all strong boundary conditions are transformed into natural or weak boundary conditions. In addition, the resulting nonlinear algebraic equations are very sparse. Use of sparse matrix solvers allows for the rapid and accurate solution of very difficult optimization problems. The formulation is applied to launch-vehicle trajectory optimization problems, and results show that real-time optimal guidance is realizable with this method. Finally, a general problem solving environment is created for solving a large class of optimal control problems. The algorithm uses both FORTRAN and a symbolic computation program to solve problems with a minimum of user interaction. The use of symbolic computation eliminates the need for user-written subroutines which greatly reduces the setup time for solving problems.

Bless, Robert R.↗

NASA NTRS1992

Radiative transfer theory for polarimetric remote sensing of pine forest

The radiative transfer theory is applied to interpret polarimetric radar backscatter from pine forest with clustered vegetation structures. To take into account the clustered structures with the radiative transfer theory, the scattering function of each cluster is calculated by incorporating the phase interference of scattered fields from each component. Subsequently, the resulting phase matrix is used in the radiative transfer equations to evaluate the polarimetric backscattering coefficients from random medium layers embedded with vegetation clusters. Upon including the multi-scale structures, namely, trunks, primary and secondary branches, as well as needles, we interpret and simulate the polarimetric radar responses from pine forest for different frequencies and looking angles. The preliminary results are shown to be in good agreement with the measured backscattering coefficients at the Landes maritime pine forest during the MAESTRO-1 experiment.

Hsu, C. C.↗

NASA NTRS1992

Radiative transfer theory for polarimetric remote sensing of pine forest

The radiative transfer theory is applied to interpret polarimetric radar backscatter from pine forest with clustered vegetation structures. The scattering function of each cluster is calculated by incorporating the phase interference of scattered fields from each component. The resulting phase matrix is used in the radiative transfer equations to evaluate the polarimetric backscattering coefficients from random medium layers embedded with vegetation clusters. Upon including multiscale structures (trunks, primary and secondary branches, and needles), polarimetric radar responses from pine forest for different frequencies and looking angles are interpreted and simulated. Preliminary results are shown to be in good agreement with the measured backscattering coefficients at the Landes maritime pine forest during the MAESTRO-1 experiment.

Hsu, C. C.↗

NASA NTRS1998

High Strain Rate Deformation Modeling of a Polymer Matrix Composite: Composite Micromechanical Model - Part 2

Recently applications have exposed polymer matrix composite materials to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under these extreme conditions. In this second paper of a two part report, a three-dimensional composite micromechanical model is described which allows for the analysis of the rate dependent, nonlinear deformation response of a polymer matrix composite. Strain rate dependent inelastic constitutive equations utilized to model the deformation response of a polymer are implemented within the micromechanics method. The deformation response of two representative laminated carbon fiber reinforced composite materials with varying fiber orientation has been predicted using the described technique. The predicted results compare favorably to both experimental values and the response predicted by the Generalized Method of Cells, a well-established micromechanics analysis method.

Goldberg, Robert K.↗

NASA NTRS2010

Nonlinear Dynamics of Cantilever-Sample Interactions in Atomic Force Microscopy

The interaction of the cantilever tip of an atomic force microscope (AFM) with the sample surface is obtained by treating the cantilever and sample as independent systems coupled by a nonlinear force acting between the cantilever tip and a volume element of the sample surface. The volume element is subjected to a restoring force from the remainder of the sample that provides dynamical equilibrium for the combined systems. The model accounts for the positions on the cantilever of the cantilever tip, laser probe, and excitation force (if any) via a basis set of set of orthogonal functions that may be generalized to account for arbitrary cantilever shapes. The basis set is extended to include nonlinear cantilever modes. The model leads to a pair of coupled nonlinear differential equations that are solved analytically using a matrix iteration procedure. The effects of oscillatory excitation forces applied either to the cantilever or to the sample surface (or to both) are obtained from the solution set and applied to the to the assessment of phase and amplitude signals generated by various acoustic-atomic force microscope (A-AFM) modalities. The influence of bistable cantilever modes of on AFM signal generation is discussed. The effects on the cantilever-sample surface dynamics of subsurface features embedded in the sample that are perturbed by surface-generated oscillatory excitation forces and carried to the cantilever via wave propagation are accounted by the Bolef-Miller propagating wave model. Expressions pertaining to signal generation and image contrast in A-AFM are obtained and applied to amplitude modulation (intermittent contact) atomic force microscopy and resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM). The influence of phase accumulation in A-AFM on image contrast is discussed, as is the effect of hard contact and maximum nonlinearity regimes of A-AFM operation.

Cantrell, John H.↗

NASA NTRS1992

Validation of three-dimensional incompressible spatial direct numerical simulation code: A comparison with linear stability and parabolic stability equation theories for boundary-layer transition on a flat plate

Spatially evolving instabilities in a boundary layer on a flat plate are computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations. In a truncated physical domain, a nonstaggered mesh is used for the grid. A Chebyshev-collocation method is used normal to the wall; finite difference and compact difference methods are used in the streamwise direction; and a Fourier series is used in the spanwise direction. For time stepping, implicit Crank-Nicolson and explicit Runge-Kutta schemes are used to the time-splitting method. The influence-matrix technique is used to solve the pressure equation. At the outflow boundary, the buffer-domain technique is used to prevent convective wave reflection or upstream propagation of information from the boundary. Results of the DNS are compared with those from both linear stability theory (LST) and parabolized stability equation (PSE) theory. Computed disturbance amplitudes and phases are in very good agreement with those of LST (for small inflow disturbance amplitudes). A measure of the sensitivity of the inflow condition is demonstrated with both LST and PSE theory used to approximate inflows. Although the DNS numerics are very different than those of PSE theory, the results are in good agreement. A small discrepancy in the results that does occur is likely a result of the variation in PSE boundary condition treatment in the far field. Finally, a small-amplitude wave triad is forced at the inflow, and simulation results are compared with those of LST. Again, very good agreement is found between DNS and LST results for the 3-D simulations, the implication being that the disturbance amplitudes are sufficiently small that nonlinear interactions are negligible.

Joslin, Ronald D.↗

NASA NTRS1977

Euler angles, quaternions, and transformation matrices for space shuttle analysis

Relationships between the Euler angles and the transformation matrix, the quaternion and the transformation matrix, and the Euler angles and the quaternion are analyzed, and equations developed are applied directly to current space shuttle problems. The twelve three-axis Euler transformation matrices as functions of the Euler angles, the equations for the quaternion as a function of the Euler angles, and the Euler angles as a function of the transformation matrix elements are included along with a group of utility subroutines to accomplish the Euler matrix, quaternion matrix, and Euler quaternion relationships.

Henderson, D. M.↗

NASA NTRS1993

Solving Modal Equations of Motion with Initial Conditions Using MSC/NASTRAN DMAP: Coupled Versus Uncoupled Integration - Part 2

By utilizing MSC/NASTRAN DMAP (Direct Matrix Abstraction Program) in an existing NASA Lewis Research Center coupled loads methodology, solving modal equations of motion with initial conditions is possible using either coupled (Newmark-Beta) or uncoupled (exact mode superposition) integration available within module TRD1. Both the coupled and newly developed exact mode superposition methods have been used to perform transient analyses of various space systems. However, experience has shown that in most cases, significant time savings are realized when the equations of motion are integrated using the uncoupled solver instead of the coupled solver. Through the results of a real-world engineering analysis, advantages of using the exact mode superposition methodology are illustrated.

Barnett, Alan R.↗

NASA NTRS2004

Modeling the Nonlinear, Strain Rate Dependent Deformation of Woven Ceramic Matrix Composites With Hydrostatic Stress Effects Included

An analysis method based on a deformation (as opposed to damage) approach has been developed to model the strain rate dependent, nonlinear deformation of woven ceramic matrix composites with a plain weave fiber architecture. In the developed model, the differences in the tension and compression response have also been considered. State variable based viscoplastic equations originally developed for metals have been modified to analyze the ceramic matrix composites. To account for the tension/compression asymmetry in the material, the effective stress and effective inelastic strain definitions have been modified. The equations have also been modified to account for the fact that in an orthotropic composite the in-plane shear stiffness is independent of the stiffness in the normal directions. The developed equations have been implemented into a commercially available transient dynamic finite element code, LS-DYNA, through the use of user defined subroutines (UMATs). The tensile, compressive, and shear deformation of a representative plain weave woven ceramic matrix composite are computed and compared to experimental results. The computed values correlate well to the experimental data, demonstrating the ability of the model to accurately compute the deformation response of woven ceramic matrix composites.

Goldberg, Robert K.↗

NASA NTRS1992

Mapping unstructured grid computations to massively parallel computers

Investigated here is this mapping problem: assign the tasks of a parallel program to the processors of a parallel computer such that the execution time is minimized. First, a taxonomy of objective functions and heuristics used to solve the mapping problem is presented. Next, we develop a highly parallel heuristic mapping algorithm, called Cyclic Pairwise Exchange (CPE), and discuss its place in the taxonomy. CPE uses local pairwise exchanges of processor assignments to iteratively improve an initial mapping. A variety of initial mapping schemes are tested and recursive spectral bipartitioning (RSB) followed by CPE is shown to result in the best mappings. For the test cases studied here, problems arising in computational fluid dynamics and structural mechanics on unstructured triangular and tetrahedral meshes, RSB and CPE outperform methods based on simulated annealing. Much less time is required to do the mapping and the results obtained are better. Compared with random and naive mappings, RSB and CPE reduce the communication time two fold for the test problems used. Finally, we use CPE in two applications on a CM-2. The first application is a data parallel mesh-vertex upwind finite volume scheme for solving the Euler equations on 2-D triangular unstructured meshes. CPE is used to map grid points to processors. The performance of this code is compared with a similar code on a Cray-YMP and an Intel iPSC/860. The second application is parallel sparse matrix-vector multiplication used in the iterative solution of large sparse linear systems of equations. We map rows of the matrix to processors and use an inner-product based matrix-vector multiplication. We demonstrate that this method is an order of magnitude faster than methods based on scan operations for our test cases.

Hammond, Steven Warren↗