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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 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

A new method for determining acoustic-liner admittance in a rectangular duct with grazing flow from experimental data

A method is developed for determining acoustic liner admittance in a rectangular duct with grazing flow. The axial propagation constant, cross mode order, and mean flow profile is measured. These measured data are then input into an analytical program which determines the unknown admittance value. The analytical program is based upon a finite element discretization of the acoustic field and a reposing of the unknown admittance value as a linear eigenvalue problem on the admittance value. Gaussian elimination is employed to solve this eigenvalue problem. The method used is extendable to grazing flows with boundary layers in both transverse directions of an impedance tube (or duct). Predicted admittance values are compared both with exact values that can be obtained for uniform mean flow profiles and with those from a Runge Kutta integration technique for cases involving a one dimensional boundary layer.

Watson, W. R.↗
NASA NTRS1982

COSAL: A black-box compressible stability analysis code for transition prediction in three-dimensional boundary layers

A fast computer code COSAL for transition prediction in three dimensional boundary layers using compressible stability analysis is described. The compressible stability eigenvalue problem is solved using a finite difference method, and the code is a black box in the sense that no guess of the eigenvalue is required from the user. Several optimization procedures were incorporated into COSAL to calculate integrated growth rates (N factor) for transition correlation for swept and tapered laminar flow control wings using the well known e to the Nth power method. A user's guide to the program is provided.

Malik, M. R.↗
NASA NTRS1984

Enthalpy damping for the steady Euler equations

For inviscid steady flow problems where the enthalpy is constant at steady state, it was previously proposed to use the difference between the local enthalpy and the steady state enthalpy as a driving term to accelerate convergence of iterative schemes. This idea is analyzed, both on the level of the partial differential equation and on the level of a particular finite difference scheme. It is shown that for the two-dimensional unsteady Euler equations, a hyperbolic system with eigenvalues on the imaginary axis, there is no enthalpy damping strategy which moves all the eigenvalues into the open left half plane. For the numerical scheme, however, the analysis shows and examples verify that enthalpy damping is potentially effective in accelerating convergence to steady state.

Jespersen, D. C.↗
NASA NTRS1983

On the identification of continuous vibrating systems modelled by hyperbolic partial differential equations

This paper deals with the identification of spatially varying parameters in systems of finite spatial extent which can be described by second order hyperbolic differential equations. Two questions have been addressed. The first deals with 'partial identification' and inquires into the possibility of retrieving all the eigenvalues of the system from response data obtained at one location x-asterisk epsilon (0, 1). The second deals with the identification of the distributed coefficients rho(x), a(x) and b(x). Sufficient conditions for unique identification of all the eigenvalues of the system are obtained, and conditions under which the coefficients can be uniquely identified using suitable response data obtained at one point in the spatial domain are determined. Application of the results and their usefulness is demonstrated in the identification of the properties of tall building structural systems subjected to dynamic load environments.

Udwadia, F. E.↗
NASA NTRS1982

A general algorithm for solving the algebraic Riccati equation

The generalized eigenvalue problem provides a suitable framework for reliable solutions of many system theoretic, control, and estimation problems. A general algorithm for solving the matrix algebraic Riccati equation (ARE) which utilizes a pencil structure is described here. This algorithm avoids unnecessary inversion of cost or transition matrices, making it a numerically sound way to solve for the gains and/or ARE with singular quadratic costs, for cases satisfying detectability and stabilizability conditions. Examples are solution with discrete dead-beat control, noiseless measurements in Kalman filters and time-delays in discrete-time systems, which cause difficulties in the Hamiltonian standard eigenvalue problem formulation. The ARE algorithm implementatiton and numerical examples are shown.

Walker, R. A.↗
NASA NTRS1984

Perturbation analysis of optimal integral controls

The application of linear optimal control to the design of systems with integral control action on specified outputs is considered. Using integral terms in a quadratic performance index, an asymptotic analysis is used to determine the effect of variable quadratic weights on the eigenvalues and eigenvectors of the closed loop system. It is shown that for small integral terms the placement of integrator poles and gain calculation can be effectively decoupled from placement of the primary system eigenvalues. This technique is applied to the design of integral controls for a STOL aircraft outer loop guidance system.

Slater, G. L.↗
NASA NTRS1985

Finite Element Prediction of Loss Factors for Structures with Frequency-dependent Damping Treatments

A finite element procedure is described for calculating the loss factors for elastic structures to which frequency-dependent viscoelastic damping treatments were applied. The frequency dependence of the viscoelastic damping material is treated by approximating its shear modulus with a second-order polynomial so that the stiffnesses associated with the constant, linear, and quadratic terms can be combined, respectively, with the stiffness, damping, and mass matrices assembled for the rest of the structure. A single complex eigenvalue analysis is then performed in which the eigenvalues are purely imaginary. The loss factor is computed by the modal strain energy (MSE) approach. In the the MSE approach, the loss factor of a composite structure vibrating in one of its natural modes may be visualized as a weighted average of the loss factors of the component parts, with the relative stored energies as weighting constants. The finite element procedure, which can treat very general geometries, is illustrated for the case of a vibrating constrained-layer damped plate.

Everstine, G. C.↗
NASA NTRS1984

Computation of eigenpairs of Ax = lambda Bx for vibrations of spinning deformable bodies

It is shown that, when linear theory is used, the general eigenvalue problem related with the free vibrations of spinning deformable bodies is of the type AX = lambda Bx, where A is Hermitian, and B is real positive definite. Since the order n of the matrices may be large, and A and B are banded or block banded, due to the economics of the numerical solution, one is interested in obtaining only those eigenvalues which fall within the frequency band of interest of the problem. The paper extends the well known method of bisections and iteration of R to the n power to n dimensional complex spaces, i.e., to C to the n power, so that it can be applied to the present problem.

Utku, S.↗
NASA NTRS1985

Accelerating an iterative process by explicit annihilation

A slowly convergent stationary iterative process can be accelerated by explicitly annihilating (i.e., eliminating) the dominant eigenvector component of the error. The dominant eigenvalue or complex pair of eigenvalues can be estimated from the solution during the iteration. The corresponding eigenvector or complex pair of eigenvectors can then be annihilated by applying an explicit Richardson process over the basic iterative method. This can be done entirely in real arithmetic by analytically combining the complex conjugate annihilation steps. The technique is applied to an implicit algorithm for the calculation of two dimensional steady transonic flow over a circular cylinder using the equations of compressible inviscid gas dynamics. This demonstrates the use of explicit annihilation on a nonlinear problem.

Jespersen, D. C.↗
NASA NTRS1985

Enthalpy damping for the steady Euler equations

For inviscid steady flow problems where the enthalpy is constant at steady state, it was previously proposed to use the difference between the local enthalpy and the steady state enthalpy as a driving term to accelerate convergence of iterative schemes. This idea is analyzed, both on the level of the partial differential equation and on the level of a particular finite difference scheme. It is shown that for the two-dimensional unsteady Euler equations, a hyperbolic system with eigenvalues on the imaginary axis, there is no enthalpy damping strategy which moves all the eigenvalues into the open left half plane. For the numerical scheme, however, the analysis shows and examples verify that enthalpy damping is potentially effective in accelerating convergence to steady state.

Jespersen, D. C.↗
NASA NTRS1985

On the spectrum of some singular equations in magnetohydrodynamics

A class of singular differential equations that often occurs in problems in magnetohydrodynamics, plasma physics, and astrophysics is studied; first by means of the specific and fairly straightforward example of motions in a stratified magnetofluid, and secondly in terms of the nature of the eigenvalue spectrum for the more general class of problems. It is shown that in the absence of discontinuities in the basic profiles, the eigenvalue spectrum is real and continuous, and no discrete spectrum exists. Bounds are obtained on the location of the continuous spectrum.

Adam, J. A.↗
NASA NTRS1985

A method for determining acoustic-liner admittance in ducts with sheared flow in two-cross-sectional directions

A method is developed for determining the acoustic admittance of a test liner installed in the wall of a grazing flow impedance tube. The mean flow is permitted flow gradients in both cross-sectional directions of the tube. The unknown admittance value is obtained by solving an eigenvalue problem. This eigenvalue problem results from the application of the finite-element method to the partial differential equation and boundary conditions governing the acoustic field. The credibility of the method is established by comparing results with exact solutions obtained for a constant mean-flow profile and with previous results for cases involving shear in only one cross-sectional direction. Excellent comparisons are obtained in both cases. The analysis is used in conjunction with a limited amount of experimental data and shows that the flow must be accurately modeled in order to determine the acoustic-liner properties.

Watson, W. R.↗
NASA NTRS1985

Instability analysis procedure for 3-level multi-bearing rotor-foundation systems

A procedure for the instability analysis of a three-level multispan rotor systems is described. This procedure is based on a distributed mass elastic representation of the rotor system in several eight-coefficient bearings. Each bearing is supported from an elastic foundation on damped, elastic pedestals. The foundation is represented as a general distributed mass elastic structure on discrete supports, which may have different stiffness and damping properties in the horizontal and vertical directions. This system model is suited to studies of instability threshold conditions for multirotor turbomachines on either massive or flexible foundations. The instability conditions is found by obtaining the eigenvalues of the system determinant, which is obtained by the transfer matrix method from the three-level system model. The stability determinant is solved for the lowest rotational speed at which the system damping becomes zero in the complex eigenvalue, and for the whirl frequency corresponding to the natural frequency of the unstable mode. An efficient algorithm for achieving this is described. Application of this procedure to a rigid rotor in two damped-elastic bearings and flexible supports is described. A second example discusses a flexible rotor with four damped-elastic bearings. The third case compares the stability of a six-bearing 300 Mw turbine generator unit, using two different bearing types. These applications validate the computer program and various aspects of the analysis.

Zhou, S.↗
NASA NTRS1986

Inclusion of elastically connected members in exact buckling and frequency calculations

A standard stiffness matrix procedure which permits any combination of rigid, elastic, pinned or sliding connections of the degrees of freedom at the ends of a member to the nodes of its parent structure is described, in order to show how easily it can be extended to allow an existing algorithm to be used to ensure that no eigenvalues of the parent structure can be missed even when 'exact' member theory is used. The eigenvalues are the natural frequencies of undamped free vibration analyses or the critical load factors of buckling problems. The method preserves the exactness of the member theory and an efficient method for computer application is indicated. The theory also permits any combination of rigid, elastic, pinned or sliding connections between the freedoms of a substructure and those of its parent structure.

Williams, F. W.↗
NASA NTRS1985

The influence of sampling rate on the dynamics and control of aeronautical systems

It is shown in the design of aeronautical control systems that sampling rate variations give rise to migrations of the discrete eigenvalues for both the plant and the controllers. In general, these migrations tend to degrade simulation fidelity and the overall performance of Ultrareliable Fault Tolerant Control Systems (UFTCS). These systems consist of a redundant asynchronous network of microprocessors which use sensor information to generate the servo commands that drive actuators, thrust linkages, etc. A change in the sampling period of a single microprocessor will, in addition to causing an eigenvalue shift, alter the magnitude of the servo command issued by the controller. The influence of these changes and the effect of initial conditions and skew are considered.

Howard, J. C.↗
NASA NTRS1986

Parameter sensitivity in the dynamics of rotor-bearing systems

When designing a rotor system it is frequently desirable to have at hand a set of design sensitivity coefficients which quantitatively predict a change in specific system characteristics to changes in design parameters. This paper presents eigenvalue sensitivity coefficients for the damped natural frequencies of whirl of general linear rotor system modelled by finite element discretization. In addition, a simple and direct method for calculation of the damped critical speeds is presented, which utilizes the eigenvalue sensitivity with respect to the spin speed. It is shown that the combination of design parameter and spin speed whirl frequency sensitivity coefficients may be used to also evaluate the damped critical speed sensitivity coefficients.

Rajan, M.↗
NASA NTRS1986

Design of a multivariable flutter control/gust load alleviation system

This paper discusses the use of eigenspace techniques for the design of an active flutter control/gust load alleviation system for a hypothetical research drone. One leading edge and two trailing edge aerodynamic surfaces are available for control. Full state control laws are designed for two combinations of control surfaces by selecting feedback gains which place closed loop eigenvalues and shape closed loop eigenvectors so as to stabilize wing flutter and reduce gust loads at the wing root while yielding acceptable robustness and satisfying constraints on rms control surface activity. These controllers are realized by state estimators designed using an eigenvalue placement/eigenvector shaping technique which results in recovery of the loop transfer characteristics of the full state feedback systems. The resulting feedback compensators are shown to perform almost as well as the full state designs. They also exhibit acceptable performance in situations in which the failure of an actuator is simulated.

Liebst, B. S.↗
NASA NTRS1987

Survey of methods for calculating sensitivity of general eigenproblems

A survey of methods for sensitivity analysis of the algebraic eigenvalue problem for non-Hermitian matrices is presented. In addition, a modification of one method based on a better normalizing condition is proposed. Methods are classified as Direct or Adjoint and are evaluated for efficiency. Operation counts are presented in terms of matrix size, number of design variables and number of eigenvalues and eigenvectors of interest. The effect of the sparsity of the matrix and its derivatives is also considered, and typical solution times are given. General guidelines are established for the selection of the most efficient method.

Murthy, Durbha V.↗