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At least 1,441 records · Page 80
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NASA NTRS1987

Dynamic and thermal response finite element models of multi-body space structural configurations

Presented is structural dynamics modeling of two multibody space structural configurations. The first configuration is a generic space station model of a cylindrical habitation module, two solar array panels, radiator panel, and central connecting tube. The second is a 15-m hoop-column antenna. Discussed is the special joint elimination sequence used for these large finite element models, so that eigenvalues could be extracted. The generic space station model aided test configuration design and analysis/test data correlation. The model consisted of six finite element models, one of each substructure and one of all substructures as a system. Static analysis and tests at the substructure level fine-tuned the finite element models. The 15-m hoop-column antenna is a truss column and structural ring interconnected with tension stabilizing cables. To the cables, pretensioned mesh membrane elements were attached to form four parabolic shaped antennae, one per quadrant. Imposing thermal preloads in the cables and mesh elements produced pretension in the finite element model. Thermal preload variation in the 96 control cables was adjusted to maintain antenna shape within the required tolerance and to give pointing accuracy.

Edighoffer, Harold H.↗
NASA NTRS1987

A combined stochastic feedforward and feedback control design methodology with application to autoland design

A combined stochastic feedforward and feedback control design methodology was developed. The objective of the feedforward control law is to track the commanded trajectory, whereas the feedback control law tries to maintain the plant state near the desired trajectory in the presence of disturbances and uncertainties about the plant. The feedforward control law design is formulated as a stochastic optimization problem and is embedded into the stochastic output feedback problem where the plant contains unstable and uncontrollable modes. An algorithm to compute the optimal feedforward is developed. In this approach, the use of error integral feedback, dynamic compensation, control rate command structures are an integral part of the methodology. An incremental implementation is recommended. Results on the eigenvalues of the implemented versus designed control laws are presented. The stochastic feedforward/feedback control methodology is used to design a digital automatic landing system for the ATOPS Research Vehicle, a Boeing 737-100 aircraft. The system control modes include localizer and glideslope capture and track, and flare to touchdown. Results of a detailed nonlinear simulation of the digital control laws, actuator systems, and aircraft aerodynamics are presented.

Halyo, Nesim↗
NASA NTRS1987

A new method of imposing boundary conditions for hyperbolic equations

A new method to impose boundary conditions for pseudospectral approximations to hyperbolic equations is suggested. This method involves the collocation of the equation at the boundary nodes as well as satisfying boundary conditions. Stability and convergence results are proven for the Chebyshev approximation of linear scalar hyperbolic equations. The eigenvalues of this method applied to parabolic equations are shown to be real and negative.

Funaro, D.↗
NASA NTRS1987

Exact state reconstruction in deterministic digital control systems

A state reconstructor for deterministic digital systems is presented which is ideal in the following sense: if the plant parameters are known exactly, the output of the state reconstructor will exactly equal the true state of the plant, not just approximate it. Furthermore, this ideal state reconstructor adds no additional states or eigenvalues to the system. Nor does it affect the plant equation for the system in any way; it affects only the measurement equation. While there are countless ways of choosing the ideal state reconstructor parameters, two distinct methods are described here. An example is presented which illustrates the procedures to completely design the ideal state reconstructor using both methods.

Polites, Michael E.↗
NASA NTRS1987

The growth of Goertler vortices in compressible boundary layers

The linear instability of Goertler vortices in compressible boundary layers is considered. Using asymptotic methods in the high wavenumber regime, it is shown that a growth rate estimate can be found by solving a sequence of linear equations. The growth rate obtained in this way takes non-parallel effects into account and can be found much more easily than by ordinary differential equation eigenvalue calculations associated with parallel flow theories.

Hall, Philip↗
NASA NTRS1987

Computational procedures for evaluating the sensitivity derivatives of vibration frequencies and Eigenmodes of framed structures

Computational procedures are presented for evaluating the sensitivity derivatives of the vibration frequencies and eigenmodes of framed structures. Both a displacement and a mixed formulation are used. The two key elements of the computational procedure are: (a) Use of dynamic reduction techniques to substantially reduce the number of degrees of freedom; and (b) Application of iterative techniques to improve the accuracy of the derivatives of the eigenmodes. The two reduction techniques considered are the static condensation and a generalized dynamic reduction technique. Error norms are introduced to assess the accuracy of the eigenvalue and eigenvector derivatives obtained by the reduction techniques. The effectiveness of the methods presented is demonstrated by three numerical examples.

Fetterman, Timothy L.↗
NASA NTRS1987

An analysis of the vertical structure equation for arbitrary thermal profiles

The vertical structure equation is a singular Sturm-Liouville problem whose eigenfunctions describe the vertical dependence of the normal modes of the primitive equations linearized about a given thermal profile. The eigenvalues give the equivalent depths of the modes. The spectrum of the vertical structure equation and the appropriateness of various upper boundary conditions, both for arbitrary thermal profiles were studied. The results depend critically upon whether or not the thermal profile is such that the basic state atmosphere is bounded. In the case of a bounded atmosphere it is shown that the spectrum is always totally discrete, regardless of details of the thermal profile. For the barotropic equivalent depth, which corresponds to the lowest eigen value, upper and lower bounds which depend only on the surface temperature and the atmosphere height were obtained. All eigenfunctions are bounded, but always have unbounded first derivatives. It was proved that the commonly invoked upper boundary condition that vertical velocity must vanish as pressure tends to zero, as well as a number of alternative conditions, is well posed. It was concluded that the vertical structure equation always has a totally discrete spectrum under the assumptions implicit in the primitive equations.

Cohn, Stephen E.↗
NASA NTRS1987

Polynomial approximation of functions of matrices and its application to the solution of a general system of linear equations

During the process of solving a mathematical model numerically, there is often a need to operate on a vector v by an operator which can be expressed as f(A) while A is NxN matrix (ex: exp(A), sin(A), A sup -1). Except for very simple matrices, it is impractical to construct the matrix f(A) explicitly. Usually an approximation to it is used. In the present research, an algorithm is developed which uses a polynomial approximation to f(A). It is reduced to a problem of approximating f(z) by a polynomial in z while z belongs to the domain D in the complex plane which includes all the eigenvalues of A. This problem of approximation is approached by interpolating the function f(z) in a certain set of points which is known to have some maximal properties. The approximation thus achieved is almost best. Implementing the algorithm to some practical problem is described. Since a solution to a linear system Ax = b is x= A sup -1 b, an iterative solution to it can be regarded as a polynomial approximation to f(A) = A sup -1. Implementing the algorithm in this case is also described.

Tal-Ezer, Hillel↗
NASA NTRS1986

Properties of r-modes in the sun

Global oscillations of the sun (r-modes) with very long periods of about 1 month are reviewed and studied. Such modes would be trapped in an acoustic cavity formed either by most of the convective envelope or by most of the radiative interior. A turning point frequency giving cavity boundaries is defined and the run of eigenvalues for angular harmonics l less than or equal to 3 are plotted for a conventional solar convection zone. The r-modes show equipartition of oscillatory energy among shells which each contain one antinode in the radial dimension. Toroidal motion is dominant to at least the 14th radial harmonic mode. Viscosity from convective turbulence is strong and would damp any mode in just a few solar rotations if it were the only significant nonadiabatic effect. 'Radial fine splitting' which lifts the degeneracy in n is very small (20 nHz or less) for all n less than or equal to 14 trapped in the envelope. But if splitting could be detected, there would be a valuable new constraint on solar convection theories.

Wolff, C. L.↗
NASA NTRS1986

Synthesis of control laws for optimally designed large space structures

In this study, the vibration control of large space structures using the linear quadratic regulator technique is investigated. Emphasis is made on the control of both optimally designed structures and also the original (uniform) structures using the cantilever beam as an example. The open loop and closed loop eigenvalues are compared and the transient responses are obtained to determine the effectiveness of the control system design.

Satyanarayana, K.↗
NASA NTRS1986

A combined integrating- and differentiating-matrix formulation for boundary-value problems on rectangular domains

Integrating and differentiating matrices allow the numerical integration and differential of functions whose values are known at points of a discrete grid. Previous derivations of these matrices were restricted to one dimensional grids or to rectangular grids with uniform spacing in at least one direction. Integrating and differentiating matrices were developed for grids with nonuniform spacing in both directions. The use of these matrices as operators to reformulate boundary value problems on rectangular domains as matrix problems for a finite dimensional solution vector is considered. The method requires nonuniform grids which include near boundary points. An eigenvalue problem for the transverse vibrations of a simply supported rectangular plate is solved to illustrate the method.

Lakin, W. D.↗
NASA NTRS1987

A new PNS code for chemical nonequilibrium flows

A new parabolized Navier-Stokes (PNS) code has been developed to compute the hypersonic laminar flow of a multicomponent, chemically reacting mixture of thermally perfect gases over two-dimensional and axisymmetric bodies. The new PNS code solves the gas dynamic and species conservation equations in a coupled manner using a noniterative, implicit, space-marching finite-difference method. The conditions for well-posedness of the space-marching method have been derived from an eigenvalue analysis of the governing equations. The code has been used to compute hypersonic laminar flow of chemically reacting air over wedges and cones. The results of these computations are in good agreement with the results of reacting boundary-layer calculations.

Prabhu, D. K.↗
NASA NTRS1986

Linear stability analysis of the Vlasov-Poisson equations in high density plasmas in the presence of crossed fields and density gradients

The equations for the single-particle orbits in a nonneutral high density plasma in the presence of inhomogeneous crossed fields are obtained. Using these orbits, the linearized Vlasov equation is solved as an expansion in the orbital radii in the presence of inhomogeneities and density gradients. A model distribution function is introduced whose cold-fluid limit is exactly the same as that used in many previous studies of the cold-fluid equations. This model function is used to reduce the linearized Vlasov-Poisson equations to a second-order ordinary differential equation for the linearized electrostatic potential whose eigenvalue is the perturbation frequency.

Kaup, D. J.↗
NASA NTRS1987

Chaotic nature of the spin-glass phase

The microscopic structure of the ordered phase of spin glasses is investigated theoretically in the framework of the T = 0 fixed-point model (McMillan, 1984; Fisher and Huse, 1986; and Bray and Moore, 1986). The sensitivity of the ground state to changes in the interaction strengths at T = 0 is explored, and it is found that for sufficiently large length scales the ground state is unstable against arbitrarily weak perturbations to the bonds. Explicit results are derived for d = 1, and the implications for d = 2 and d = 3 are considered in detail. It is concluded that there is no hidden order pattern for spin glasses at all T less than T(C), the ordered-phase spin correlations being chaotic functions of spin separation at fixed temperature or of temperature (for a given pair of spins) at scale lengths L greater than (T delta T) exp -1/zeta, where zeta = d(s)/2 - y, d(s) is the interfacial fractal dimension, and -y is the thermal eigenvalue at T = 0.

Bray, A. J.↗
NASA NTRS1987

Distributed feedback modes in a partially filled ring cavity

The threshold longitudinal modes of a structure composed of a ring cavity partially filled with a distributed feedback (DFB) medium have been studied. An eigenvalue equation and dispersion relation for the propagation constant, threshold gain, and mode location are derived and numerically solved for a number of cases. It is shown that the incommensurate nature of the unfilled ring cavity eigenfrequencies and DFB eigenfrequencies can lead to an enhancement of the frequency selectivity of the distributed feedback laser. The analysis is extended to consider finite linewidth and dispersion.

Rabinovich, William S.↗
NASA NTRS1986

Integrated control/structure design and robustness

When a flexible structure is to be controlled actively, optimum performance is obtained by integrated, or simultaneous, design of the structure and the controller, as opposed to the common practice of designing the structure independently of control consideration and then designing a controller for a fixed structure. The primary design objective from the structural point of view usually is to minimize weight, while the control design objectives depend on the application. An important requirement for a practical control system is robustness with respect to uncertain plant parameters. This paper discusses simultaneous control/structure design when the overall design objective combines the weight of the structure and the robustness of the closed-loop control system. For numerical optimization, robustness is represented by the sensitivity of the closed-loop eigenvalues with respect to uncertain parameters. An example illustrates the optimal design of a flexible structure along with a robust compensator.

Adamian, A.↗
NASA NTRS1987

Viscous damping of Alfven normal modes in non-uniform plasmas

The Alfven normal mode in a nonuniform, viscous plasma is investigated. Because the ideal hydromagnetic equation is singular in a nonuniform magnetic field, viscosity is included in order to regularize the equation, analogous to the removal of the singular point by resistivity (Mok and Einaudi, 1985). The eigenvalue equation is then solved numerically for a particular magnetic configuration. The real part of the frequency of this viscous normal mode is found to be similar to the one in the resistive case, while the damping is shown to be comparable, and sometimes to exceed, the resistive effect under certain conditions in which the Lundquist number is sufficiently large. The damping rate is evaluated for various plasma conditions corresponding to different parts of the solar atmosphere. The effects of viscosity are found to dominate resistivity in the quiet sun corona and solar wind.

Mok, Y.↗
NASA NTRS1987

A versatile and low order hybrid stress element for general shell geometry

A hybrid stress general shell element is developed based on the Hellinger-Reissner principle modified for relaxed element compatibility conditions. The element is based on a consistent first order thin shell theory with Love Kirchhoff hypotheses. It is of quadrilateral shape with only four corner nodes and five degrees of freedom per node. The geometry of the element is approximated through a bi-cubic polynomial surface patch. Numerical examples consist of torsion-loaded slit cylinder and pinched cylinder with open ends and rigid diaphragmed ends. Also, the representation of the rigid body motion is studied by series of parametric eigenvalue analysis of the stiffness matrix.

Kang, David S.↗