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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Centrifugal acceleration modes for incompressible fluid in the leakage annulus between a shrouded pump impeller and its housing

An algorithm is developed for calculating complex eigenvalues and eigenvectors associated with the fluid resonances and is used to analyze the perturbed flow in the leakage path between a shrouded-pump impeller and its housing. The eigenvalues obtained are consistent with the forced-response curves. First- and second-natural-frequency eigensolutions are presented for mode shapes corresponding to lateral excitations, and first-natural-frequency eigensolutions are presented for mode shapes corresponding to axial excitation.

Childs, D. W.↗
NASA NTRS1992

Efficient use of high performance computers for integrated controls and structures design

Simply transporting design codes from sequential-scalar computers to parallel-vector computers does not fully utilize the computational benefits offered by high performance computers. By performing integrated controls and structures design on an experimental truss platform with both sequential-scalar and parallel-vector design codes, conclusive results are presented to substantiate this claim. The efficiency of a Cholesky factorization scheme in conjunction with a variable-band row data structure is presented. In addition, the Lanczos eigensolution algorithm has been incorporated in the design code for both parallel and vector computations. Comparisons of computational efficiency between the initial design code and the parallel-vector design code are presented. It is shown that the Lanczos algorithm with the Cholesky factorization scheme is far superior to the sub-space iteration method of eigensolution when substantial numbers of eigenvectors are required for control design and/or performance optimization. Integrated design results show the need for continued efficiency studies in the area of element computations and matrix assembly.

Belvin, W. K.↗
NASA NTRS2012

On Dynamics of Spinning Structures

This paper provides details of developments pertaining to vibration analysis of gyroscopic systems, that involves a finite element structural discretization followed by the solution of the resulting matrix eigenvalue problem by a progressive, accelerated simultaneous iteration technique. Thus Coriolis, centrifugal and geometrical stiffness matrices are derived for shell and line elements, followed by the eigensolution details as well as solution of representative problems that demonstrates the efficacy of the currently developed numerical procedures and tools.

Rotating bodies↗
NASA NTRS1974

Dynamic analysis of multi-degree-of-freedom systems using phasing matrices

A mathematical technique is presented for improved analysis of a wide class of dynamic and aeroelastic systems characterized by several degrees-of-freedom. The technique enables greater utilization of the usual eigensolution obtained from the system dynamic equations by systematizing the identification of destabilizing and/or stiffening forces. Included, as illustrative examples of the use of the technique, are analyses of a helicopter rotor blade for bending-torsion divergence and flutter and for pitch-lag/flap instability.

Bielawa, R. L.↗
NASA NTRS1976

Eigenvalue extraction in NASTRAN by the tridiagonal reduction (FEER) method: Real eigenvalue analysis

The development of the tridiagonal reduction method and its implementation in NASTRAN are described for real eigenvalue analysis as typified by structural vibration and buckling problems. This method is an automatic matrix reduction scheme whereby the eigensolutions in the neighborhood of a specified point in the eigenspectrum can be accurately extracted from a tridiagonal eigenvalue problem whose order is much lower than that of the full problem. The process is effected without orbitrary lumping of masses or other physical quantities at selected node points and thus avoids one of the basic weaknesses of other techniques.

Newman, M.↗
NASA NTRS1976

Aeroelastic analysis for helicopter rotor blades with time-variable, non-linear structural twist and multiple structural redundancy: Mathematical derivation and program user's manual

The differential equations of motion for the lateral and torsional deformations of a nonlinearly twisted rotor blade in steady flight conditions together with those additional aeroelastic features germane to composite bearingless rotors are derived. The differential equations are formulated in terms of uncoupled (zero pitch and twist) vibratory modes with exact coupling effects due to finite, time variable blade pitch and, to second order, twist. Also presented are derivations of the fully coupled inertia and aerodynamic load distributions, automatic pitch change coupling effects, structural redundancy characteristics of the composite bearingless rotor flexbeam - torque tube system in bending and torsion, and a description of the linearized equations appropriate for eigensolution analyses. Three appendixes are included presenting material appropriate to the digital computer program implementation of the analysis, program G400.

Bielawa, R. L.↗
NASA NTRS1976

Analytical comparison of effects of solid-friction and viscous structural damping on panel flutter

A Galerkin modal analysis is presented that accounts for the effects of both solid friction and viscous structural damping on panel flutter, based on unsteady aerodynamic forces from supersonic potential flow. The eigensolutions are made by complex eigenvalue computer routines. Markedly different effects on the flutter boundary of the two types of structural damping are obtained. This result establishes that there is not, in general, an "equivalent viscous" damping for solid-friction damping. For the limiting case of the static-aerodynamic approximation, a substantially different flutter dynamic pressure is obtained for solid friction identically zero compared with solid friction approaching zero as a limit. Use of the quasi-static aerodynamic approximation eliminates that difference.

Cunningham, H. J.↗
NASA NTRS1977

Complex eigenvalue extraction in NASTRAN by the tridiagonal reduction (FEER) method

An extension of the Tridiagonal Reduction (FEER) method to complex eigenvalue analysis in NASTRAN is described. As in the case of real eigenvalue analysis, the eigensolutions closest to a selected point in the eigenspectrum are extracted from a reduced, symmetric, tridiagonal eigenmatrix whose order is much lower than that of the full size problem. The reduction process is effected automatically, and thus avoids the arbitrary lumping of masses and other physical quantities at selected grid points. The statement of the algebraic eigenvalue problem admits mass, damping and stiffness matrices which are unrestricted in character, i.e., they may be real, complex, symmetric or unsymmetric, singular or non-singular.

Newman, M.↗
NASA NTRS1978

Extension of the tridiagonal reduction (FEER) method for complex eigenvalue problems in NASTRAN

As in the case of real eigenvalue analysis, the eigensolutions closest to a selected point in the eigenspectrum were extracted from a reduced, symmetric, tridiagonal eigenmatrix whose order was much lower than that of the full size problem. The reduction process was effected automatically, and thus avoided the arbitrary lumping of masses and other physical quantities at selected grid points. The statement of the algebraic eigenvalue problem admitted mass, damping, and stiffness matrices which were unrestricted in character, i.e., they might be real, symmetric or nonsymmetric, singular or nonsingular.

Newman, M.↗
NASA NTRS1979

Sound radiation from hyperboloidal inlet ducts

This paper presents rigorous solutions for the problem of sound radiation from various inlet ducts including hyperboloidal (or hyperbolic) inlet ducts and circular ducts with wide flange. The numerical results include the complex conversion (or reflection) coefficients and the radiation directivity for the various incident wave modes - spinning modes as well as axisymmetric modes. The analysis utilizes hyperboloidal wave functions which are defined here as a class of eigensolutions of the wave equation for oblate spheroidal coordinates, and is valid for the whole frequency range including frequencies above and below the cutoff frequencies of duct modes involved.

Cho, Y. C.↗
NASA NTRS1978

Steady state spurious errors in shock-capturing numerical schemes

The behavior of the steady state spurious error modes of the MacCormack scheme and the upwind scheme of Warming and Beam was obtained from a linearized difference equation for the steady state error. It was shown that the spurious errors can exist either as an eigensolution of the homogeneous part of this difference equation or because of excitation from large discretization errors near oblique shocks. It was found that the upwind scheme does not permit spurious oscillations on the upstream side of shocks. Examples are given for the inviscid Burgers' equation and for one and two dimensional gasdynamic flows.

Karlsen, L. K.↗
NASA NTRS1980

A method of order reduction for structural dynamics

This paper presents a new method of order reduction based on recent work of a similar nature applicable to system dynamics and control. This method provides a practical computational procedure for producing a condensed model which exactly preserves the slowest n1 modes (where n1 is the number of 'slow' eigenvalues) of the total n modes of the original model for almost any set of n1 degrees of freedom retained in the condensed model. The method can also be used to compute the eigensolutions corresponding to the n1 slowest modes of the original structural dynamics problem. The accuracy of the condensed model and the speed/accuracy performance of the eigensolver are compared with standard methods for a 90 DOF cantilevered plate.

Anderson, L. R.↗
NASA NTRS1980

Rigorous solutions for sound radiation from circular ducts with hyperbolic horns or infinite plane baffle

A rigorous treatment is presented of sound radiation from circular ducts with either a hyperbolic horn or an infinite plane baffle. In the analysis hyperboloidal wave functions are used, which are defined here, for the first time, as a class of eigensolutions of the wave equation for oblate spheroidal co-ordinates. The numerical results include the complex conversion (or reflection) coefficients and the radiation directivity for various incident wave modes, spinning modes as well as axisymmetric modes. The solutions are valid for the whole frequency range including frequencies above and below the cut-off frequencies of the duct modes involved.

Cho, Y. C.↗
NASA NTRS1980

Instability of non-zonal baroclinic flows

Linear instabilities have been found for tropospheric flows consisting of a mean zonal component and a tilted, forced, stationary wave. The eigensolutions of maximum growth rate provide an adequate explanation of the location and structure of regions of maximum bandpass transient activity (storm tracks). The study also highlights the importance of adequate resolution in models involving first-order coupling mechanisms, such as a standing wave. It identifies the curvature of the mean state as a possibly significant factor in determining the 'baroclinicity' of a region.

Niehaus, M. C. W.↗
NASA NTRS1982

Improvement of a large dynamic analytical model using ground vibration test data

A method has been developed which uses measured normal modes and natural frequencies to improve an analytical mass and stiffness matrix model of a structure. The method directly identifies, without iteration, a set of minimum changes in the analytical matrices which force the eigensolutions to agree with the test measurements. An application is presented in which the analytical model had 508 degrees of freedom and 19 modes were measured at 101 locations on the structure. The resulting changes in the model are judged to be small compared to expectations of errors in the analysis. Thus the improved model is accepted as a reasonable model of the structure with improved dynamic response characteristics. In addition, it is shown that the procedure may be a useful tool in identifying apparent measured modes which are not true normal modes of the structures.

Berman, A.↗
NASA NTRS1982

A nonlocal theory of an electrostatic sinusoidal density drift instability

The stability of space plasmas in which the macroscopic variables vary in the direction x perpendicular to the magnetic field is usually studied by means of the local approximation, in which the fluctuating potential is assumed to be independent of x. To remove this approximation, a nonlocal problem is studied in which the background density, and hence the fluctuating potentials, are periodic in x. From the linear Vlasov/Poisson equations, a set of coupled, linear, homogeneous, algebraic equations relating the Fourier amplitudes of the eigensolution is derived. The equations are solved numerically and a hierarchy of exact eigenmodes characterized by different growth rates and spatial structures is found. At points where the density gradient is locally zero, the mode amplitude is generally several orders of magnitude lower than the peak amplitude. The dependence of these solutions on the parameters which define the background density perturbation is studied and a correspondence between these nonlocal results and those obtained with the local approximation is demonstrated.

Thomsen, M. F.↗
NASA NTRS1983

Close-mode identification performance of the ITD algorithm

Results of Monte Carlo numerical simulations conducted to study the close-mode performance of the Ibrahim Time-Domain (ITD) modal identification algorithm are presented. The ITD technique is a matrix eigensolution method for obtaining structural modal parameters directly from free-response test data without using the FFT. Thus, the well-known resolution and leakage limitations of the FFT procedure, that are particularly significant with short records, are avoided. As an example, one of several experimental data analyses where close modes have been accurately identified using very short records is shown. Although the identification scatter is found to increase as the square of reductions in frequency separation at small separations, the ability to differentiate modes spaced at fractions of the FFT resolution is substantiated.

Pappa, R. S.↗
NASA NTRS1983

Normal mode study of the earth's rigid body motions

In this paper it is shown that the earth's rigid body (rb) motions can be represented by an analytical set of eigensolutions to the equation of motion for elastic-gravitational free oscillations. Thus each degree of freedom in the rb motion is associated with a rb normal mode. Cases of both nonrotating and rotating earth models are studied, and it is shown that the rb modes do incorporate neatly into the earth's system of normal modes of free oscillation. The excitation formula for the rb modes are also obtained, based on normal mode theory. Physical implications of the results are summarized and the fundamental differences between rb modes and seismic modes are emphasized. In particular, it is ascertained that the Chandler wobble, being one of the rb modes belonging to the rotating earth, can be studied using the established theory of normal modes.

Chao, B. F.↗