SEARCH · Engineering Papers

Results for “eigenvalues”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 775 records · Page 43

All sources NASA NTRS DOE OSTI

NASA NTRS1982

Gain selection method and model for coupled propulsion and airframe systems

A longitudinal model is formulated for an advanced fighter from three subsystem models: the inlet, the engine, and the airframe. Notable interaction is found in the coupled system. A procedure, based on eigenvalue sensitivities, is presented which indicates the importance of the feedback gains to the optimal solution. This allows ineffectual gains to be eliminated; thus, hardware and expense may be saved in the realization of the physical controller.

Murphy, P. C.↗

NASA NTRS1982

An investigation of impurity centers in semiconductors of variable composition. Part 1: General theory and some applications

A theory of deep point defects imbedded in otherwise perfect semiconductor crystals is developed with the aid of pseudopotentials. The dominant short-range forces engendered by the impurity are sufficiently weakened in all cases where the cancellation theorem of the pseudopotential formalism is operative. Thus, effective-mass-like equations exhibiting local effective potentials derived from nonlocal pseudopotentials are shown to be valid for a large class of defects. A two-band secular determinant for the energy eigenvalues of deep defects is also derived from the set of integral equations which corresponds to the set of differential equations of the effective-mass type. Subsequently, the theory in its simplest form, is applied to the system Al(x)Ga(1-x)As:Se. It is shown that the one-electron donor level of Se within the forbidden gap of Al(x)Ga(1-x)As as a function of the AlAs mole fraction x reaches its maximum of about 300 meV (as measured from the conduction band edge) at the cross-over from the direct to the indirect band-gap at x = 0.44 in agreement with experiments.

Vonroos, O. H.↗

NASA NTRS1982

Influence of parameter changes to stability behavior of rotors

The occurrence of unstable vibrations in rotating machinery requires corrective measures for improvement of the stability behavior. A simple approximate method is represented to find out the influence of parameter changes to the stability behavior. The method is based on an expansion of the eigenvalues in terms of system parameters. Influence coefficients show the effect of structural modifications. The method first of all was applied to simple nonconservative rotor models. It was approved for an unsymmetric rotor of a test rig.

Fritzen, C. P.↗

NASA NTRS1982

Numerical computation of exponential matrices using the Cayley-Hamilton theorem

A method for computing exponential matrices, which often arise naturally in the solution of systems of linear differential equations, is developed. An exponential matrix is generated as a linear combination of a finite number (equal to the matrix order) of matrices, the coefficients of which are scalar infinite sums. The method can be generalized to apply to any formal power series of matrices. Attention is focused upon the exponential function, and the matrix exponent is assumed tri-diagonal in form. In such cases, the terms in the coefficient infinite sums can be extracted, as recursion relations, from the characteristic polynomial of the matrix exponent. Two numerical examples are presented in some detail: (1) the three dimensional infinitesimal rotation rate matrix, which is skew symmetric, and (2) an N-dimensional tri-diagonal and symmetric finite difference matrix which arises in the numerical solution of the heat conduction partial differential equation. In the second example, the known eigenvalues and eigenvectors of the finite difference matrix permit an analytical solution for the exponential matrix, through the theory of diagonalization and similarity transformations, which is used for independent verification. The convergence properties of the scalar infinite summations are investigated for finite difference matrices of various orders up to ten, and it is found that the number of terms required for convergence increases slowly with the order of the matrix.

Walden, H.↗

NASA NTRS1982

Population control of self-replicating systems

The literature concerning fibonacci sequence and the mathematics of self replication are reviewed. One option allows each primary to generate n-replicas, one in each sequential time frame after its own generation with no restrictions on the number of ancestors per replica. The state vector of the replicas in an efficient manner is determined. Option-B has a fixed number of replicas per primary and no restrictions on the number of ancestors for a replica. Any element fij represents the number of elements of type-j in time frame k+1 generated from type-i in time frame k. Option-D is a diagonal matrix whose eigenvalues are precisely those of f.

Mccord, R. L.↗

NASA NTRS1983

Efficient linear and nonlinear heat conduction with a quadrilateral element

A method is presented for performing efficient and stable finite element calculations of heat conduction with quadrilaterals using one-point quadrature. The stability in space is obtained by using a stabilization matrix which is orthogonal to all linear fields and its magnitude is determined by a stabilization parameter. It is shown that the accuracy is almost independent of the value of the stabilization parameter over a wide range of values; in fact, the values 3, 2, and 1 for the normalized stabilization parameter lead to the 5-point, 9-point finite difference, and fully integrated finite element operators, respectively, for rectangular meshes and have identical rates of convergence in the L2 norm. Eigenvalues of the element matrices, which are needed for stability limits, are also given. Numerical applications are used to show that the method yields accurate solutions with large increases in efficiency, particularly in nonlinear problems.

Liu, W. K.↗

NASA NTRS1983

Control of structures in space

Various topics related to the control of large space structures are discussed. Equations of motion for distributed systems, eigenvalue problems, modal equations, control implementation, and the Langley beam experiment are discussed.

Meirovitch, L.↗

NASA NTRS1983

Large amplitude MHD waves upstream of the Jovian bow shock

Observations of large amplitude magnetohydrodynamics (MHD) waves upstream of Jupiter's bow shock are analyzed. The waves are found to be right circularly polarized in the solar wind frame which suggests that they are propagating in the fast magnetosonic mode. A complete spectral and minimum variance eigenvalue analysis of the data was performed. The power spectrum of the magnetic fluctuations contains several peaks. The fluctuations at 2.3 mHz have a direction of minimum variance along the direction of the average magnetic field. The direction of minimum variance of these fluctuations lies at approximately 40 deg. to the magnetic field and is parallel to the radial direction. We argue that these fluctuations are waves excited by protons reflected off the Jovian bow shock. The inferred speed of the reflected protons is about two times the solar wind speed in the plasma rest frame. A linear instability analysis is presented which suggests an explanation for many of the observed features of the observations.

Goldstein, M. L.↗

NASA NTRS1981

LANDSAT-D MSS/TM tuned orbital jitter analysis model LDS900

The final LANDSAT-D orbital dynamic math model (LSD900), comprised of all test validated substructures, was used to evaluate the jitter response of the MSS/TM experiments. A dynamic forced response analysis was performed at both the MSS and TM locations on all structural modes considered (thru 200 Hz). The analysis determined the roll angular response of the MSS/TM experiments to improve excitation generated by component operation. Cross axis and cross experiment responses were also calculated. The excitations were analytically represented by seven and nine term Fourier series approximations, for the MSS and TM experiment respectively, which enabled linear harmonic solution techniques to be applied to response calculations. Single worst case jitter was estimated by variations of the eigenvalue spectrum of model LSD 900. The probability of any worst case mode occurrence was investigated.

Pollak, T. E.↗

NASA NTRS1983

Implicit upwind methods for the compressible Navier-Stokes equations

A class of implicit upwind differencing methods for the compressible Navier-Stokes equations is described and applied. The methods are based on the use of local eigenvalues or wave speeds to control spatial differencing of inviscid terms and are aimed at increasing the level of accuracy and stability achievable in computation. Techniques for accelerating the rate of convergence to a steady state solution are also used. Applications to inviscid and viscous transonic flows are discussed and compared with other methods and experimental measurements. It is shown that accurate and efficient transonic airfoil calculations can be made on the Cray-l computer in less than 2 min.

Coakley, T. J.↗

NASA NTRS1983

On the control canonical structure of a class of scalar input systems

A discrete finite dimensional system, nonharmonic Fourier series and controllability, reduction to canonical form, and spectral synthesis are considered. The extent to which the eigenvalue associated with a controllable pair of a certain type may be modified via continuous linear state feedback is demonstrated.

Teglas, R.↗

NASA NTRS1983

Design, implementation and flight testing of PIF autopilots for general aviation aircraft

The designs of Proportional-Integrated-Filter (PIF) auto-pilots for a General Aviation (NAVION) aircraft are presented. The PIF autopilot uses the sampled-data regulator and command generator tracking to determine roll select, pitch select, heading select, altitude select and localizer/glideslope capture and hold autopilot modes. The PIF control law uses typical General Aviation sensors for state feedback, command error integration for command tracking, digital complementary filtering and analog prefiltering for sensor noise suppression, a control filter for computation delay accommodation and the incremental form to eliminate trim values in implementation. Theoretical developments described in detail, were needed to combine the sampled-data regulator with command generator tracking for use as a digital flight control system. The digital PIF autopilots are evaluated using closed-loop eigenvalues and linear simulations. The implementation of the PIF autopilots in a digital flight computer using a high order language (FORTRAN) is briefly described. The successful flight test results for each PIF autopilot mode is presented.

Broussard, J. R.↗

NASA NTRS1983

Development of a distributed-parameter mathematical model for simulation of cryogenic wind tunnels

A one-dimensional distributed-parameter dynamic model of a cryogenic wind tunnel was developed which accounts for internal and external heat transfer, viscous momentum losses, and slotted-test-section dynamics. Boundary conditions imposed by liquid-nitrogen injection, gas venting, and the tunnel fan were included. A time-dependent numerical solution to the resultant set of partial differential equations was obtained on a CDC CYBER 203 vector-processing digital computer at a usable computational rate. Preliminary computational studies were performed by using parameters of the Langley 0.3-Meter Transonic Cryogenic Tunnel. Studies were performed by using parameters from the National Transonic Facility (NTF). The NTF wind-tunnel model was used in the design of control loops for Mach number, total temperature, and total pressure and for determining interactions between the control loops. It was employed in the application of optimal linear-regulator theory and eigenvalue-placement techniques to develop Mach number control laws.

Tripp, J. S.↗

NASA NTRS1983

A design procedure for active control of beam vibrations

The transverse vibrations of beams is discussed and a methodology for the design of an active damping device is given. The Bernoulli-Euler equation is used to derive a transcendental transfer function, which relates a torque applied at one end of the beam to the rotational position and velocity at that point. The active damping device consists of a wire, a linear actuator and a short torque arm attached to one end of the beam. The action of the actuator varies a tension in the wire and creates a torque which opposes the rotation of the beam and thus damps vibration. A design procedure for such an active damper is given. This procedure shows the relationships and trade-offs between the actuator stroke, power required, stress levels in the wire and beam and the geometry of the beam and wire. It is shown that by consideration of the frequency response at the beam natural frequencies, the aforementioned relationships can be greatly simplified. Similarly, a simple way of estimating the effective damping ratios and eigenvalue locations of actively controlled beams is presented.

Dickerson, S. L.↗

NASA NTRS1982

Application of matrix singular value properties for evaluating gain and phase margins of multiloop systems

A stability margin evaluation method in terms of simultaneous gain and phase changes in all loops of a multiloop system is presented. A universal gain-phase margin evaluation diagram is constructed by generalizing an existing method using matrix singular value properties. Using this diagram and computing the minimum singular value of the system return difference matrix over the operating frequency range, regions of guaranteed stability margins can be obtained. Singular values are computed for a wing flutter suppression and a drone lateral attitude control problem. The numerical results indicate that this method predicts quite conservative stability margins. In the second example if the eigenvalue magnitude is used instead of the singular value, as a measure of nearness to singularity, more realistic stability margins are obtained. However, this relaxed measure generally cannot guarantee global stability.

Mukhopadhyay, V.↗

NASA NTRS1981

Multigrid solvers on parallel computers

Massively parallel computers, as considered in this investigation, are not yet available. However, a large-scale parallel computer cannot usefully be designed before the hypothetical algorithms which will employ it are studied. Most of the studies of parallel partial differential equations (PDE) solvers are based on solution techniques much slower (on sequential machines) than multigrid methods. Multigrid methods are highly parallelizable. Each of their processes can simultaneously be performed at all grid points. The present investigation is concerned with a preliminary exploration of the potential of multigrid, or, more generally, Multi-Level Adaptive Techniques (MLAT) on computers with many processors. Basic processes are considered, taking into account coarse-grid approximation, relaxation, coarse-grid corrections, full multigrid algorithms, nonlinear problems and eigenvalue problems, fine-to-coarse correction, and chains of problems. Details of parallel multigrid processing are also examined.

Brandt, A.↗

NASA NTRS1982

Angles of multivariable root loci

A generalized eigenvalue problem is demonstrated to be useful for computing the multivariable root locus, particularly when obtaining the arrival angles to finite transmission zeros. The multivariable root loci are found for a linear, time-invariant output feedback problem. The problem is then employed to compute a closed-loop eigenstructure. The method of computing angles on the root locus is demonstrated, and the method is extended to a multivariable optimal root locus.

Thompson, P. M.↗

NASA NTRS1982

Calculation of exact vibration modes for plane grillages by the dynamic stiffness method

A dynamic stiffness method is developed for the calculation of the exact modal parameters for plane grillages which consist of straight and uniform beams with coincident elastic and inertial axes. Elementary bending-torsion beam theory is utilized, and bending translation is restricted to one direction. The exact bending-torsion dynamic stiffness matrix is obtained for a straight and uniform beam element with coincident elastic and inertial axes. The element stiffness matrices are assembled using the standard procedure of the static stiffness method to form the dynamic stiffness matrix of the complete grillage. The exact natural frequencies, mode shapes, and generalized masses of the grillage are then calculated by solving a nonlinear eigenvalue problem based on the dynamic stiffness matrix. The exact modal solutions for an example grillage are calculated and compared with the approximate solutions obtained by using the finite element method.

Hallauer, W. L., Jr.↗