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At least 1,639 records · Page 91
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NASA NTRS1992

Analytical shape sensitivities and approximations of modal response of generally laminated tapered skew plates

In the present determination of the derivatives of natural frequencies and mode shapes of a generally laminated tapered skew plate, with respect to various shape parameters, springs are used to simulate the essential boundary conditions. The independent shape parameters are plate surface area, aspect ratio, taper ratio, and sweep angle. Eigenvalues and eigenvectors are approximated over the range of the variable using linear, exponential, and pseudoexponential approximation schemes, and are compared with reanalysis-obtained values. Numerical results are presented for symmetrically and unsymmetrically laminated plates.

Singhvi, Sarvesh↗
NASA NTRS1992

ROM/RMF control of the flexible, articulated-truss space crane

The large size and extreme flexibility of an articulated space crane entail great difficulties in precision positioning. Control strategies for the flexible multibody system are here developed using a Timoshenko-beam finite-element model (FEM) which captures the system's low frequency characteristics. From the FEM, a reduced-order model (ROM) controller is designed which rotates the fixed shape crane about the base alpha joint to actuate positioning control. Eigenvalue analysis of the closed-loop system shows the destabilizing effect of controller-structure interaction (CSI). Making use of a parallel bank of residual mode filters (RMFs) compensated for CSI, restoring system stability and performance. The linear control law is simulated in closed-loop with the beam model. The ROM-based control law with RMF compensation is an effective, low-order controller.

Reisenauer, Brian T.↗
NASA NTRS1992

Structural damage detection using a subspace rotation algorithm

A computationally inexpensive algorithm is developed to provide an insight to the location of structural damage, using the original finite element model and a subset of measured eigenvalues and eigenvectors. The computational requirements of the algorithm may make the technique suitable for real-time implementation. With damage location determined, a second algorithm is developed to determine the extent of damage. The algorithms are demonstrated using two classes of structural models. The effects of eigenvector measurement error is demonstrated and techniques to overcome the effects of noise are discussed.

Zimmerman, David C.↗
NASA NTRS1991

A variable multi-step method for transient heat conduction

A variable explicit time integration algorithm is developed for unsteady diffusion problems. The algorithm uses nodal partitioning and allows the nodal groups to be updated with different time steps. The stability of the algorithm is analyzed using energy methods and critical time steps are found in terms of element eigenvalues with no restrictions on element types. Several numerical examples are given to illustrate the accuracy of the method.

Smolinski, Patrick↗
NASA NTRS1992

On the placement of active members in adaptive truss structures for vibration control

The problem of optimal placement of active members which are used for vibration control in adaptive truss structures is investigated. The control scheme is based on the method of eigenvalue assignment as a means of shaping the transient response of the controlled adaptive structures, and the minimization of required control action is considered as the optimization criterion. To this end, a performance index which measures the control strokes of active members is formulated in an efficient way. In order to reduce the computation burden, particularly for the case where the locations of active members have to be selected from a large set of available sites, several heuristic searching schemes are proposed for obtaining the near-optimal locations. The proposed schemes significantly reduce the computational complexity of placing multiple active members to the order of that when a single active member is placed.

Lu, L.-Y.↗
NASA NTRS1992

Calculation of two-dimensional shear-driven cavity flows at high Reynolds numbers

The time-dependent Navier-Stokes equations are numerically integrated for two-dimensional incompressible viscous flow in a shear-driven square cavity. Using a time-splitting method and finite differences on a staggered mesh, the momentum and pressure equations are directly solved by a tensor product method where one finite difference direction is diagonalized by eigenvalue decomposition. The effects of increasing Reynolds number are studied and the developing boundary layer is captured by using a finely clustered mesh. At Re = 30,000 the flow is in a continuously developing unsteady regime. Power spectrum plots indicate that the unsteady flow oscillates with one fundamental frequency and exhibits some characteristics of transition between laminar and turbulent states.

Huser, A.↗
NASA NTRS1992

On development of a finite dynamic element and solution of associated eigenproblem by a block Lanczos procedure

The paper first presents the details of the development of a new six-noded plane triangular finite dynamic element. A block Lanczos algorithm is developed next for the accurate and efficient solution of the quadratic matrix eigenvalue problem associated with the finite dynamic element formulation. The resulting computer program fully exploits matrix sparsity inherent in such a discretization and proves to be most efficient for the extraction of the usually required first few roots and vectors, including repeated ones. Most importantly, the present eigenproblem solution is shown to be comparable to that of the corresponding finite element analysis, thereby rendering the associated dynamic element method rather attractive owing to superior convergence characteristics of such elements, presented herein.

Gupta, K. K.↗
NASA NTRS1992

The inviscid stability of supersonic flow past heated or cooled axisymmetric bodies

The inviscid, linear, nonaxisymmetric, temporal stability of the boundary layer associated with the supersonic flow past axisymmetric bodies (with particular emphasis on long thin, straight circular cylinders), subject to heated or cooled wall conditions is investigated. The eigenvalue problem is computed in some detail for a particular Mach number or 3.8, revealing that the effect of curvature and the choice of wall conditions both have a significant effect on the stability of the flow. Both the asymptotic, large azimuthal wavenumber solution and the asymptotic, far downstream solution are obtained for the stability analysis and compared with numerical results. Additionally, asymptotic analyses valid for large radii of curvature with cooled/heated wall conditions are presented. In general, important differences were found to exist between the wall temperature conditions imposed and the adiabatic wall conditions considered previously.

Shaw, Stephen J.↗
NASA NTRS1992

A numerical method for systems of conservation laws of mixed type admitting hyperbolic flux splitting

The present treatment of elliptic regions via hyperbolic flux-splitting and high order methods proposes a flux splitting in which the corresponding Jacobians have real and positive/negative eigenvalues. While resembling the flux splitting used in hyperbolic systems, the present generalization of such splitting to elliptic regions allows the handling of mixed-type systems in a unified and heuristically stable fashion. The van der Waals fluid-dynamics equation is used. Convergence with good resolution to weak solutions for various Riemann problems are observed.

Shu, Chi-Wang↗
NASA NTRS1992

Solution strategies and heat transfer calculations for three-dimensional configurations at hypersonic speeds

A procedure which reduces the memory requirements for computing the viscous flow over a modified Orbiter geometry at a hypersonic flight condition is presented. The Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) code which incorporates a thermochemical nonequilibrium chemistry model, a finite rate catalytic wall boundary condition and wall temperature distribution based on radiation equilibrium is used in this study. In addition, the effect of choice of 'min mod' function, eigenvalue limiter and grid density on surface heating is investigated. The surface heating from a flowfield calculation at Mach number 22, altitude of 230,000 ft and 40 deg angle of attack is compared with flight data from three Orbiter flights.

Weilmuenster, K. J.↗
NASA NTRS1992

Flight-determined stability analysis of multiple-input-multiple-output control systems

Singular value analysis can give conservative stability margin results. Applying structure to the uncertainty can reduce this conservatism. This paper presents flight-determined stability margins for the X-29A lateral-directional, multiloop control system. These margins are compared with the predicted unscaled singular values and scaled structured singular values. The algorithm was further evaluated with flight data by changing the roll-rate-to-aileron-command-feedback gain by +/- 20 percent. Also presented are the minimum eigenvalues of the return difference matrix which bound the singular values. Extracting multiloop singular values from flight data and analyzing the feedback gain variations validates this technique as a measure of robustness. This analysis can be used for near-real-time flight monitoring and safety testing.

Burken, John J.↗
NASA NTRS1993

Ideal State Reconstructor For Control System

Ideal state reconstructor is conceptual subsystem of deterministic digital control system estimating state of controlled plant periodically at discrete sampling intervals of duration T. Does not add new states, eigenvalues, or dynamics. Based on concepts described in "State-Variable Representations For Moving-Average Sampling" (MFS-28405).

Polites, Michael E.↗
NASA NTRS1993

Two-Stage Reduction Of Dynamical Models

No longer necessary to solve eigenvalue problems of high order. Component-mode projection-and-assembly model-reduction (COMPARE) method provides approximation of dynamics of vibrations of complicated, multiple flexible bodies by use of mathematical models of reduced order. Incorporates component-mode synthesis (CMS) method and enhanced projection-and-assembly (EP&A) method, described in "Enhanced Method of Reduction of Dynamical Models" (NPO-18402), providing for somewhat simplified two-stage process in which order of applicable mathematical models reduced. Reduced-order models used to design algorithms of control systems to suppress vibrations or otherwise control structure.

Lee, Allan Y.↗
NASA NTRS1992

Flight-determined stability analysis of multiple-input-multiple-output control systems

Singular value analysis can give conservative stability margin results. Applying structure to the uncertainty can reduce this conservatism. This paper presents flight-determined stability margins for the X-29A lateral-directional, multiloop control system. These margins are compared with the predicted unscaled singular values and scaled structured singular values. The algorithm was further evaluated with flight data by changing the roll-rate-to-aileron command-feedback gain by +/- 20 percent. Minimum eigenvalues of the return difference matrix which bound the singular values are also presented. Extracting multiloop singular values from flight data and analyzing the feedback gain variations validates this technique as a measure of robustness. This analysis can be used for near-real-time flight monitoring and safety testing.

Burken, John J.↗
NASA NTRS1990

Implicit application of polynomial filters in a k-step Arnoldi method

The Arnoldi process is a well known technique for approximating a few eigenvalues and corresponding eigenvectors of a general square matrix. Numerical difficulties such as loss of orthogonality and assessment of the numerical quality of the approximations as well as a potential for unbounded growth in storage have limited the applicability of the method. These issues are addressed by fixing the number of steps in the Arnoldi process at a prescribed value k and then treating the residual vector as a function of the initial Arnoldi vector. This starting vector is then updated through an iterative scheme that is designed to force convergence of the residual to zero. The iterative scheme is shown to be a truncation of the standard implicitly shifted QR-iteration for dense problems and it avoids the need to explicitly restart the Arnoldi sequence. The main emphasis of this paper is on the derivation and analysis of this scheme. However, there are obvious ways to exploit parallelism through the matrix-vector operations that comprise the majority of the work in the algorithm. Preliminary computational results are given for a few problems on some parallel and vector computers.

Sorensen, D. C.↗
NASA NTRS1992

On the convergence of the coupled-wave approach for lamellar diffraction gratings

Among the many existing rigorous methods for analyzing diffraction of electromagnetic waves by diffraction gratings, the coupled-wave approach stands out because of its versatility and simplicity. It can be applied to volume gratings and surface relief gratings, and its numerical implementation is much simpler than others. In addition, its predictions were experimentally validated in several cases. These facts explain the popularity of the coupled-wave approach among many optical engineers in the field of diffractive optics. However, a comprehensive analysis of the convergence of the model predictions has never been presented, although several authors have recently reported convergence difficulties with the model when it is used for metallic gratings in TM polarization. Herein, three points are made: (1) in the TM case, the coupled-wave approach converges much slower than the modal approach of Botten et al; (2) the slow convergence is caused by the use of Fourier expansions for the permittivity and the fields in the grating region; and (3) is manifested by the slow convergence of the eigenvalues and the associated modal fields. The reader is assumed to be familiar with the mathematical formulations of the coupled-wave approach and the modal approach.

Li, Lifeng↗
NASA NTRS1990

Robust control of systems with real parameter uncertainty and unmodelled dynamics

Two significant contributions have been made during this research period in the research 'Robust Control of Systems with Real Parameter Uncertainty and Unmodelled Dynamics' under NASA Research Grant NAG-1-1102. They are: (1) a fast algorithm for computing the optimal H(sub infinity) norm for the four-block, the two block, or the one-block optimal H(sub infinity) optimization problem; and (2) a construction of an optimal H infinity controller without numerical difficulty. In using GD (Glover and Doyle) or DGKF (Doyle, Glover, Khargonekar, and Francis) approach to solve the standard H infinity norm which required bisection search. In this research period, we developed a very fast iterative algorithm for this computation. Our algorithm was developed based on hyperbolic interpolations which is much faster than any existing algorithm. The lower bound of the parameter, gamma, in the H infinity Riccati equation for solution existence is shown to be the square root of the supremum over all frequencies of the maximum eigenvalue of a given transfer matrix which can be computed easily. The lower band of gamma such that the H infinity Riccati equation has positive semidefinite solution can be also obtained by hyperbolic interpolation search. Another significant result in this research period is the elimination of the numerical difficulties arising in the construction of an optimal H infinity controller by directly applying the Glover and Doyle's state-space formulas. With the fast iterative algorithm for the computation of the optimal H infinity norm and the reliable construction of an optimal H infinity controller, we are ready to apply these tools in the design of robust controllers for the systems with unmodelled uncertainties. These tools will be also very useful when we consider systems with structured uncertainties.

Chang, Bor-Chin↗
NASA NTRS1993

SCBUCKLE user's manual: Buckling analysis program for simple supported and clamped panels

The program SCBUCKLE calculates the buckling loads and mode shapes of cylindrically curved, rectangular panels. The panel is assumed to have no imperfections. SCBUCKLE is capable of analyzing specially orthotropic symmetric panels (i.e., A(sub 16) = A(sub 26) = 0.0, D(sub 16) = D(sub 26) = 0.0, B(sub ij) = 0.0). The analysis includes first-order transverse shear theory and is capable of modeling sandwich panels. The analysis supports two types of boundary conditions: either simply supported or clamped on all four edges. The panel can be subjected to linearly varying normal loads N(sub x) and N(sub y) in addition to a constant shear load N(sub xy). The applied loads can be divided into two parts: a preload component; and a variable (eigenvalue-dependent) component. The analysis is based on the modified Donnell's equations for shallow shells. The governing equations are solved by Galerkin's method.

Cruz, Juan R.↗