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At least 379 records · Page 21

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NASA NTRS1988

Dynamic analysis of the joint dominated beam

A method for determining the vibrational modes of the joint dominated beam is presented with reference to space erectable structures. Mathematical models with and without joint imperfection are developed. Joint imperfection is represented by a simple flexibility, k, in the axial direction of the chord members only. An interactive computer program is used to obtain eigenvalue characteristics and mode shapes of the system. Results are presented on frequencies of the given truss beam with and without joint imperfections for three-panel and 10-panel models. Also presented are results of parametric studies of the beam truss models of three and 10 panels with k = 0.05, 0.10, 0.50, and 1.0 x 10 to the -7th.

Abu-Saba, Elias G.↗

NASA NTRS1991

Adaptive control of Space Station during nominal operations with CMGs

An adaptive control approach is investigated for the Space Station. The main components of the adaptive controller are the parameter identification scheme, the control gain calculation, and the control law. The control law is the Space Station baseline control law. The control gain calculation is based on linear quadratic regulator theory with eigenvalue placement in a vertical strip. The parameter identification scheme is a real-time recursive extended Kalman filter which estimates the inertias and also provides an estimate of the unmodeled disturbances due to the aerodynamic torques and to the nonlinear effects. An analysis of the inertia estimation problem suggests that it is possible to compute accurate estimates of the Space Station inertias during nominal CMG (control moment gyro) operations. The closed-loop adaptive control law is shown to be capable of stabilizing the Space Station after large inertia changes. Results are presented for the pitch axis.

Bishop, R. H.↗

NASA NTRS1998

Development of a Probabilistic Dynamic Synthesis Method for the Analysis of Nondeterministic Structures

Accounting for the statistical geometric and material variability of structures in analysis has been a topic of considerable research for the last 30 years. The determination of quantifiable measures of statistical probability of a desired response variable, such as natural frequency, maximum displacement, or stress, to replace experience-based "safety factors" has been a primary goal of these studies. There are, however, several problems associated with their satisfactory application to realistic structures, such as bladed disks in turbomachinery. These include the accurate definition of the input random variables (rv's), the large size of the finite element models frequently used to simulate these structures, which makes even a single deterministic analysis expensive, and accurate generation of the cumulative distribution function (CDF) necessary to obtain the probability of the desired response variables. The research presented here applies a methodology called probabilistic dynamic synthesis (PDS) to solve these problems. The PDS method uses dynamic characteristics of substructures measured from modal test as the input rv's, rather than "primitive" rv's such as material or geometric uncertainties. These dynamic characteristics, which are the free-free eigenvalues, eigenvectors, and residual flexibility (RF), are readily measured and for many substructures, a reasonable sample set of these measurements can be obtained. The statistics for these rv's accurately account for the entire random character of the substructure. Using the RF method of component mode synthesis, these dynamic characteristics are used to generate reduced-size sample models of the substructures, which are then coupled to form system models. These sample models are used to obtain the CDF of the response variable by either applying Monte Carlo simulation or by generating data points for use in the response surface reliability method, which can perform the probabilistic analysis with an order of magnitude less computational effort. Both free- and forced-response analyses have been performed, and the results indicate that, while there is considerable room for improvement, the method produces usable and more representative solutions for the design of realistic structures with a substantial savings in computer time.

Brown, A. M.↗

NASA NTRS1992

Viscous and inviscid instabilities of a trailing vortex

The linear stability of the trailing line vortex model of Batchelor (1964) is studied using a spectral collocation and matrix eigenvalue method. The entire unstable region in the swirl/axial wavenumber parameter space is mapped out for various azimuthal wavenumbers for both the inviscid and viscous stability problem. The results of the study provide a direct numerical validation of the large-azimuthal-wavenumber asymptotic analysis of Leibovich and Stewartson (1983). It is shown that accurate results are obtained up to azimuthal wavenumbers of 10,000 and greater, and the agreement with the asymptotic theory is excellent.

Mayer, Ernst W.↗

NASA NTRS1990

Eigensensitivity analysis for space structures with applications in design optimization

An approximate structural eigenvalue/vector analysis technique which uses eigensensitivities in a truncated Taylor series expression is presented. It is shown that this technique can provide the computational efficiency urgently needed for large scale control-structure optimization problems. In addition, a unified formulation and solution approach for calculating eigenvalue and eigenvector derivatives of the real symmetric structural eigenvalue problem is presented.

Kenny, Sean P.↗

NASA NTRS1998

Effect of altered sensory conditions on multivariate descriptors of human postural sway

Multivariate descriptors of sway were used to test whether altered sensory conditions result not only in changes in amount of sway but also in postural coordination. Eigenvalues and directions of eigenvectors of the covariance of shnk and hip angles were used as a set of multivariate descriptors. These quantities were measured in 14 healthy adult subjects performing the Sensory Organization test, which disrupts visual and somatosensory information used for spatial orientation. Multivariate analysis of variance and discriminant analysis showed that resulting sway changes were at least bivariate in character, with visual and somatosensory conditions producing distinct changes in postural coordination. The most significant changes were found when somatosensory information was disrupted by sway-referencing of the support surface (P = 3.2 x 10(-10)). The resulting covariance measurements showed that subjects not only swayed more but also used increased hip motion analogous to the hip strategy. Disruption of vision, by either closing the eyes or sway-referencing the visual surround, also resulted in altered sway (P = 1.7 x 10(-10)), with proportionately more motion of the center of mass than with platform sway-referencing. As shown by discriminant analysis, an optimal univariate measure could explain at most 90% of the behavior due to altered sensory conditions. The remaining 10%, while smaller, are highly significant changes in posture control that depend on sensory conditions. The results imply that normal postural coordination of the trunk and legs requires both somatosensory and visual information and that each sensory modality makes a unique contribution to posture control. Descending postural commands are multivariate in nature, and the motion at each joint is affected uniquely by input from multiple sensors.

NASA Discipline Neuroscience↗

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 NTRS1991

Structural representation for analysis of a controlled structure

The purpose was to determine what reduced order structural representation is most appropriate for coupling with a control system. The goal was to choose a reduced order structural model which retains as closely as possible the characteristics of the closed loop model with a full order structural representation. By characteristics of the closed loop model, it is meant that the closed loop eigenvalues and the closed loop transfer functions from commands to loads and from commands to response. This process does not address the accuracy of the full order model (usually a finite element model) but only the loss of accuracy associated with reducing th model. For the purposes of this study, only collocated sensors and actuators are examined. The choice of a structural representation for noncollocated sensors and actuators is not so clear.

Blelloch, Paul A.↗

NASA NTRS1979

Flap-lag-torsion flutter analysis of a constant life rotor

The constant lift rotor (CLR) employs a control input of pitch moment to several airfoil sections which are free to pivot on a continuous spar, allowing them to change their pitch to obtain the desired lift. A flap-lag-torsion flutter analysis of a constant lift rotor blade in hover was developed. The blade model assumes rigid body flap and lead-lag motions at the root hinge and each strip undergoes an independent torsional motion. The results are presented in terms of root locus plots of complex eigenvalues as a function of thrust. The effects of several parameters (including structural damping, center of gravity and elastic axis offset from aerodynamic center, compressibility pitch-lag and pitch-flap coupling) on the blade dynamics are examined. With a suitable combination of lag damper and pitch-flap coupling, it is possible to design a constant lift rotor blade free from flutter instability.

Chopra, I.↗

NASA NTRS1993

Acceleration of convergence and spectrum transformation of implicit finite difference operators associated with Navier-Stokes equations

Implicit difference operator spectra are presently computed by applying eigensystem analysis techniques to finite-difference formulations of 2D Euler and Navier-Stokes equations, and attention is given to these iterative methods' convergence and stability characteristics by taking into account the effects of grid geometry, time-step, numerical viscosity, and boundary conditions. On the basis of the eigenvalue distributions for various flow configurations, the feasibility of applying such convergence-acceleration techniques as eigenvalue annihilation and relaxation is discussed. Spectrum-shifting is applied to NASA-Ames' ARC2D flow code, achieving a 20-33 percent efficiency.

Saleem, M.↗

NASA NTRS2001

Instability Analysis of a Low-Density Gas Jet Injected into a High-Density Gas

The objective of this study was to determine the effects of buoyancy on the absolute instability of low-density gas jets injected into high-density gas mediums. Most of the existing analyses of low-density gas jets injected into a high-density ambient have been carried out neglecting effects of gravity. In order to investigate the influence of gravity on the near-injector development of the flow, a linear temporal stability analysis and a spatio-temporal stability analysis of a low-density round jet injected into a high-density ambient gas were performed. The flow was assumed to be isothermal and locally parallel; viscous and diffusive effects were ignored. The variables were represented as the sum of the mean value and a normal-mode small disturbance. An ordinary differential equation governing the amplitude of the pressure disturbance was derived. The velocity and density profiles in the shear layer, and the Froude number (signifying the effects of gravity) were the three important parameters in this equation. Together with the boundary conditions, an eigenvalue problem was formulated. Assuming that the velocity and density profiles in the shear layer to be represented by hyperbolic tangent functions, the eigenvalue problem was solved for various values of Froude number. The temporal growth rates and the phase velocity of the disturbances were obtained. It was found that the presence of variable density within the shear layer resulted in an increase in the temporal amplification rate of the disturbances and an increase in the range of unstable frequencies, accompanied by a reduction in the phase velocities of the disturbances. Also, the temporal growth rates of the disturbances were increased as the Froude number was reduced (i.e. gravitational effects increased), indicating the destabilizing role played by gravity. The spatio-temporal stability analysis was performed to determine the nature of the absolute instability of the jet. The roles of the density ratio, Froude number, Schmidt number, and the lateral shift between the density and velocity profiles on the jet s absolute instability were determined. Comparisons of the results with previous experimental studies show good agreement when the effects of these variables are combined together. Thus, the combination of these variables determines how absolutely unstable the jet will be. Experiments were carried out to observe the qualitative differences between a round low-density gas jet injected into a high-density gas (helium jet injected into air) and a round constant density jet (air jet injected into air). Flow visualizations and velocity measurements in the near-injector region of the helium jet show more mixing and spreading of the helium jet than the air jet. The vortex structures develop and contribute to the jet spreading causing the helium jet to oscillate.

Lawson, Anthony Layiwola↗

NASA NTRS1981

A hybrid state vector approach to aeroelastic analysis with application to composite lifting surfaces

A computational technique has been developed for performing preliminary design aeroelastic analyses of large aspect ratio lifting surfaces. This technique, applicable to both fixed and rotating wing configurations, is based upon a formulation of the structural equilibrium equations in terms of a hybrid state vector containing generalized force and displacement variables. An integrating matrix is employed to solve these equations for divergence and flutter eigenvalues and steady aeroelastic deformation. Results are presented for simple examples which verify the technique and demonstrate how it can be applied to analyze lifting surfaces, including those constructed from composite materials.

Lehman, L. L.↗

NASA NTRS1985

A cost-effective component modes analysis for Shuttle payloads using a combination of frequency domain and time domain approaches

A combination of the time and frequency domains which employs the latter only where the former is inefficient or uncertain is used in Space Shuttle payloads' component mode analyses. Attention is given to the time histories at the launch vehicle/spacecraft interface. The frequency domain allows interface acceleration to be determined without recourse to a new, merged system eigenvalue solution and subsequent 'system modal' responses. The approach has been employed in Galileo spacecraft loads analyses.

Trubert, M.↗

NASA NTRS1976

Dynamic analysis of a class of mixed lumped-distributed parameter systems via numerical techniques

The modeling via transfer matrices of mixed lumped-distributed parameter systems with feedback control is discussed and novel methods of obtaining information on the controlled system's dynamic response via numerical methods is presented. These methods utilize numerical searches in the complex plane for the roots of the transcendental characteristic equation to determine the closed loop system eigenvalues. The fast Fourier transform (FFT) algorithm is utilized but in the inverse fashion (from frequency domain to time domain). The information obtained is identical to that contained in a model in modal coordinates, and can be used to construct such a model. An interactive computer program to do the required calculation is described, as well as its application to a manipulator arm design problem.

Book, W. J.↗

NASA NTRS1983

Finite element approximations in transient analysis

Alternative techniques for finite element models for transient analyses are explored, using as an example a pinned-pinned beam. Attention is given to the relationships between desired accuracy and the available computer resources. Stiffness, mass, damping, and loading components approximations are examined with note taken of optimization methods. Generation of regular grid results indicates a linear relationship between the number of elements or degrees of freedom and the number of eigenvalues for a given accuracy. Comparisons of the finite element models in terms of accuracy/element or accuracy/degree of freedom were found to be inaccurate for determining model efficiency. Higher accuracies were available from lumped mass and damping models than assumptions of consistent loading, which was preferred to statically equivalent loading.

Melosh, R. J.↗

NASA NTRS1975

Sustained small oscillations in nonlinear control systems

Some results of bifurcation theory were used to study the existence of small-amplitude periodic behavior in launch vehicle dynamics, assuming that nonlinearity exists as a cubic term in the rudder response. The analysis follows closely Sattinger's (1973) approach to the theory of periodic bifurcations. The conditions under which a bifurcating branch of orbitally stable periodic solutions will exist are determined. It is shown that in more complicated cases, the conditions under which the system matrix has a pair of simple purely imaginary eigenvalues can be determined with the aid of linear stability techniques.

George, J. H.↗

NASA NTRS1990

Eigenvalue computations with the QUAD4 consistent-mass matrix

The NASTRAN user has the option of using either a lumped-mass matrix or a consistent- (coupled-) mass matrix with the QUAD4 shell finite element. At the Sixteenth NASTRAN Users' Colloquium (1988), Melvyn Marcus and associates of the David Taylor Research Center summarized a study comparing the results of the QUAD4 element with results of other NASTRAN shell elements for a cylindrical-shell modal analysis. Results of this study, in which both the lumped-and consistent-mass matrix formulations were used, implied that the consistent-mass matrix yielded poor results. In an effort to further evaluate the consistent-mass matrix, a study was performed using both a cylindrical-shell geometry and a flat-plate geometry. Modal parameters were extracted for several modes for both geometries leading to some significant conclusions. First, there do not appear to be any fundamental errors associated with the consistent-mass matrix. However, its accuracy is quite different for the two different geometries studied. The consistent-mass matrix yields better results for the flat-plate geometry and the lumped-mass matrix seems to be the better choice for cylindrical-shell geometries.

Butler, Thomas A.↗

NASA NTRS1980

Stability of nonuniform rotor blades in hover using a mixed formulation

A mixed formulation for calculating static equilibrium and stability eigenvalues of nonuniform rotor blades in hover is presented. The static equilibrium equations are nonlinear and are solved by an accurate and efficient collocation method. The linearized perturbation equations are solved by a one step, second order integration scheme. The numerical results correlate very well with published results from a nearly identical stability analysis based on a displacement formulation. Slight differences in the results are traced to terms in the equations that relate moments to derivatives of rotations. With the present ordering scheme, in which terms of the order of squares of rotations are neglected with respect to unity, it is not possible to achieve completely equivalent models based on mixed and displacement formulations. The one step methods reveal that a second order Taylor expansion is necessary to achieve good convergence for nonuniform rotating blades. Numerical results for a hypothetical nonuniform blade, including the nonlinear static equilibrium solution, were obtained with no more effort or computer time than that required for a uniform blade.

Stephens, W. B.↗