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NASA NTRS1992

Hierarchical tapered bar elements undergoing axial deformation

A method is described to model the dynamics of tapered axial bars of various cross sections based on the well-known Craig/Bampton component mode synthesis technique. This element is formed in terms of the static constraint modes and interface restrained normal modes. This is in contrast with the finite elements as implemented in NASTRAN where the interface restrained normal modes are neglected. These normal modes are in terms of Bessel functions. Restoration of a few of these modes leads to higher accuracy with fewer generalized coordinates. The proposed models are hierarchical so that all lower order element matrices are embedded in higher order element matrices. The advantages of this formulation compared to standard NASTRAN truss element formulation are demonstrated through simple numerical examples.

Ganesan, N.↗

NASA NTRS1976

NASTRAN component-mode synthesis

Procedure for dynamic substructuring analysis technique is generally as follows: calculation of component modes; selection of component normal modes, calculation of component generalized matrices, assembly of system matrices, and computation of normal modes; and retrieval of component response.

Guyan, R. J.↗

NASA NTRS1977

On the use of attachment modes in substructure coupling for dynamic analysis

Substructure coupling or component-mode synthesis may be employed in the solution of dynamics problems for complex structures. Although numerous substructure-coupling methods have been devised, little attention has been devoted to methods employing attachment modes. In the present paper the various mode sets (normal modes, constraint modes, attachment modes) are defined. A generalized substructure-coupling procedure is described. Those substructure-coupling methods which employ attachment modes are described in detail. One of these methods is shown to lead to results (e.g., system natural frequencies) comparable to or better than those obtained by the Hurty (1965) method.

Craig, R. R., Jr.↗

NASA NTRS1987

A NASTRAN primer for the analysis of rotating flexible blades

This primer provides documentation for using MSC NASTRAN in analyzing rotating flexible blades. The analysis of these blades includes geometrically nonlinear (large displacement) analysis under centrifugal loading, and frequency and mode shape (normal modes) determination. The geometrically nonlinear analysis using NASTRAN Solution sequence 64 is discussed along with the determination of frequencies and mode shapes using Solution Sequence 63. A sample problem with the complete NASTRAN input data is included. Items unique to rotating blade analyses, such as setting angle and centrifugal softening effects are emphasized.

Lawrence, Charles↗

NASA NTRS1987

Comparison of Nd 1.06 and 1.33 micron operation in various hosts

Performances of Nd in various hosts including Nd:YAG, Nd:YLF, Nd:BEL, and Nd:Cr:GSGG were characterized and compared for operation on the nominal 1.06 micron and 1.33 micron transitions. Comparison included continuous mode operation, normal mode operation, Q-switched operation, and gain measurements. Continuous lasing of Nd:Cr:GSGG under lamp pumping is reported for what may be the first time. Characterization included operation with different mirror reflectivities to obtain the internal losses, measurement of the upper laser level lifetime, measurement of the beam quality of the lasers operating under nominally similar circumstances, and measurement of the wavelength. These measurements should provide a comparison of the various Nd hosts under similar circumstances for a wide variety of operational modes and at both wavelengths of interest.

Barnes, Norman P.↗

NASA NTRS1995

Control Electronics For Reaction Wheel

Bidirectional operation achieved with single-polarity main power supply. Control circuitry generates pulse-width-modulated 800-Hz waveforms to drive two-phase ac motor and reaction wheel. Operates partly in response to digital magnitude-and-direction torque command generated by external control subsystem and partly in response to tachometric feedback in form of two once-per-revolution sinusoids with amplitudes proportional to speed. Operation in either of two modes called "normal" and "safehold." In normal mode, drive pulses timed so that, on average over one or few cycles, motor applies commanded torque. In safehold mode, pulses timed to keep motor running at set speed in one direction.

Chamberlin, Keith↗

NASA NTRS1984

Line sources of instability waves in a Blasius boundary layer

Numerical solutions of the instability wave pattern behind a harmonic point source in a Blasius boundary layer are used to form line sources by superposition. For infinite-length spanwise line sources of constant amplitude and phase, the result is just the two-dimensional normal mode of the same frequency; for a sinusoidal amplitude or linear phase distribution, the result is an oblique normal mode of the same spanwise wavenumber. A finite-length spanwise source simulates a vibrating ribbon. In a study of the influence of the source length on the downstream amplitude, the effective field of view is found to have a half-angle of about 16 deg. If the source tips are within this field, the amplitude may be either greater than or less than the comparable normal-mode amplitude, depending on the distance from the source and the spanwise location. For an oblique line source, the downstream wave development at each spanwise location is found to be close to, but not identical with, that of an oblique normal mode which originates at the source with the initial wave angle of the source and satisfies the irrotationality condition on the wavenumber vector.

Mack, L. M.↗

NASA NTRS2003

Inflow/Outflow Conditions for Unsteady Aerodynamics and Aeroacoustics in Nonuniform Flow

The effect of a nonuniform mean flow on the normal modes; the inflow/outflow nonreflecting boundary conditions; and the sound power are studied. The normal modes in an annular duct are computed using a spectral method in combination with a shooting method. The swirl causes force imbalance which couples the acoustic and vortical modes. The acoustic modes are distinguished from the vortical modes by their large pressure and small vorticity content. The mean swirl also produces a Doppler shift in frequency. This results in more counter-spinning modes cut-on at a given frequency than modes spinning with the swirl. Nonreflecting boundary conditions are formulated using the normal mode solutions. The inflow/outflow boundary conditions are implemented in a linearized Euler scheme and validated by computing the propagation of acoustic and vortical waves in a duct for a variety of swirling mean flows. Numerical results show that the evolution of the vortical disturbances is sensitive to the inflow conditions and the details of the wake excitations. All three components of the wake velocity must be considered to correctly compute the wake evolution and the blade upwash. For high frequencies, the acoustic-vortical mode coupling is weak and a conservation equation for the acoustic energy can be derived. Sound power calculations show significant mean flow swirl effects, but mode interference effects are small.

Atassi, Oliver V.↗

NASA NTRS1989

Development of flashlamp-pumped Q-switched Ho:Tm:Cr:YAG lasers for mid-infrared LIDAR application

A flashlamp-pumped 2.1 micron Ho:Tm:Cr:YAG laser was studied for both normal mode and Q-switched operations under a wide variety of experimental conditions in order to optimize performance. Laser output energy, slope efficiency, threshold and pulselength were determined as a function of operating temperature, output mirror reflectivity, input electrical energy and Q-switch opening time. The measured normal-mode laser thresholds of a Ho(3+) (0.45 atomic percent):Tm(3+) (2.5 atomic percent):Cr(3+) (0.8 atomic percent):YAG crystal ranged form 26 to 50 J between 120 and 200 K with slope efficiencies up to 0.36 percent with a 60 percent reflective output mirror. Under Q-switched operation the slope efficiency was 90 percent of the normal-mode result. Development of solid state lasers with Ho(3+), Tm(3+) and/or Er(3+) doped crystals has been pursued by NASA for eye-dafe mid-infrared LIDAR (light detection and ranging) application. As a part of the project, the authors have been working on evaluating Ho(3+):Tm(3+):Cr(3+):YAG crystals for normal-mode and Q-switched 2.1 micron laser operations in order to determine an optimum Tm(3+) concentration under flashlamp pumping conditions. Lasing properties of the Ho(3+) in the mid-infrared region have been studied by many research groups since the early 1960's. However, the technology of those lasers is still premature for lidar application. In order to overcome the inefficiency related to narrow absorption bands of the Ho(3+), Tm(3+) and Er(3+), the erbium has been replaced by chromium. The improvement in flashlamp-pumped Ho(3+) laser efficiency has been demonstrated recently by several research groups by utilizing the broad absorption spectrum of Cr(3+) which covers the flashlamp's emission spectrum. Efficient energy transfer to the Tm(3+) and then the Ho(3+) occurs subsequently. It is known that high Tm(3+) concentration and low Ho(3+) concentration are preferred to achieve a quantum efficiency approaching two and to avoid large reabsorption losses. However, determination of the optimum Tm(3+) concentration required to ensure efficient energy transfer from Cr(3+) to Tm(3+) and from Tm(3+) to Ho(3+) has not been made in the Ho:Tm:CR:YAG crystal. The results obtained so far are given.

Choi, Young S.↗

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 NTRS1989

Multibody dynamics: Modeling component flexibility with fixed, free, loaded, constraint, and residual modes

The assumed-modes method in multibody dynamics allows the elastic deformation of each component in the system to be approximated by a sum of products of spatial and temporal functions commonly known as modes and modal coordinates respectively. The choice of component modes used to model articulating and non-articulating flexible multibody systems is examined. Attention is directed toward three classical Component Mode Synthesis (CMS) methods whereby component normal modes are generated by treating the component interface (I/F) as either fixed, free, or loaded with mass and stiffness contributions from the remaining components. The fixed and free I/F normal modes are augmented by static shape functions termed constraint and residual modes respectively. A mode selection procedure is outlined whereby component modes are selected from the Craig-Bampton (fixed I/F plus constraint), MacNeal-Rubin (free I/F plus residual), or Benfield-Hruda (loaded I/F) mode sets in accordance with a modal ordering scheme derived from balance realization theory. The success of the approach is judged by comparing the actuator-to-sensor frequency response of the reduced order system with that of the full order system over the frequency range of interest. A finite element model of the Galileo spacecraft serves as an example in demonstrating the effectiveness of the proposed mode selection method.

Spanos, John T.↗

NASA NTRS1977

Development of an automated multi-stage modal synthesis system for NASTRAN

A mode synthesis development to be scheduled in the NASTRAN multi-level substructuring system for general dynamics applications is described. The method combines the better features of several state of the art mode synthesis techniques, yet is general enough to provide for any arbitrary combination of boundary degrees of freedom and normal mode boundary conditions. Normal modes or complex eigenvectors may be used in the definition of a structure component which may be combined with other components of any type. Combination structures fabricated from component modes may be processed as normal substructures, including further multi-stage mode synthesis reductions. Included are discussions of the user control of the system and advantages in actual application.

Herting, D. N.↗

NASA NTRS1996

Visualizing Infrared (IR) Spectroscopy with Computer Animation

IR Tutor, an interactive, animated infrared (IR) spectroscopy tutorial has been developed for Macintosh and IBM-compatible computers. Using unique color animation, complicated vibrational modes can be introduced to beginning students. Rules governing the appearance of IR absorption bands become obvious because the vibrational modes can be visualized. Each peak in the IR spectrum is highlighted, and the animation of the corresponding normal mode can be shown. Students can study each spectrum stepwise, or click on any individual peak to see its assignment. Important regions of each spectrum can be expanded and spectra can be overlaid for comparison. An introduction to the theory of IR spectroscopy is included, making the program a complete instructional package. Our own success in using this software for teaching and research in both academic and industrial environments will be described. IR Tutor consists of three sections: (1) The 'Introduction' is a review of basic principles of spectroscopy. (2) 'Theory' begins with the classical model of a simple diatomic molecule and is expanded to include larger molecules by introducing normal modes and group frequencies. (3) 'Interpretation' is the heart of the tutorial. Thirteen IR spectra are analyzed in detail, covering the most important functional groups. This section features color animation of each normal mode, full interactivity, overlay of related spectra, and expansion of important regions. This section can also be used as a reference.

Charles B. Abrams↗

NASA NTRS1993

Evaluation of MARC for the analysis of rotating composite blades

The suitability of the MARC code for the analysis of rotating composite blades was evaluated using a four-task process. A nonlinear displacement analysis and subsequent eigenvalue analysis were performed on a rotating spring mass system to ensure that displacement-dependent centrifugal forces were accounted for in the eigenvalue analysis. Normal modes analyses were conducted on isotropic plates with various degrees of twist to evaluate MARC's ability to handle blade twist. Normal modes analyses were conducted on flat composite plates to validate the newly developed coupled COBSTRAN-MARC methodology. Finally, normal modes analyses were conducted on four composite propfan blades that were designed, analyzed, and fabricated at NASA Lewis Research Center. Results were compared with experimental data. The research documented herein presents MARC as a viable tool for the analysis of rotating composite blades.

Bartos, Karen F.↗

NASA NTRS1984

A preliminary analysis of flight data from the AFTI/F-16 airplane

Flight test data from the AFTI/F-16 airplane are analyzed. Two flight control system modes (Independent Backup Unit and Standard Normal Mode) are considered. Estimated stability and control derivatives are compared with values from the wind tunnel and F-16A flight tests. Modeling difficulties are shown to arise due to the near-neutral static stability of the airplane and the number of coordinated control surface movements commanded in the Standard Normal Mode.

Batterson, J. G.↗

NASA NTRS1982

Dynamic modeling of structures from measured complex modes

A technique is presented to use a set of identified complex modes together with an analytical mathematical model of a structure under test to compute improved mass, stiffness and damping matrices. A set of identified normal modes, computed from the measured complex modes, is used in the mass orthogonality equation to compute an improved mass matrix. This eliminates possible errors that may result from using approximated complex modes as normal modes. The improved mass matrix, the measured complex modes and the higher analytical modes are then used to compute the improved stiffness and damping matrices. The number of degrees-of-freedom of the improved model is limited to equal the number of elements in the measured modal vectors. A simulated experiment shows considerable improvements, in the system's analytical dynamic model, over the frequency range of the given measured modal information.

Ibrahim, s. R.↗

NASA NTRS1985

Dynamic Modeling of Structures from Measured Complex Modes

Ibrahim, S. R.↗

NASA NTRS1992

CSM solutions of rotating blade dynamics using integrating matrices

The dynamic behavior of flexible rotating beams continues to receive considerable research attention as it constitutes a fundamental problem in applied mechanics. Further, beams comprise parts of many rotating structures of engineering significance. A topic of particular interest at the present time involves the development of techniques for obtaining the behavior in both space and time of a rotor acted upon by a simple airload loading. Most current work on problems of this type use solution techniques based on normal modes. It is certainly true that normal modes cannot be disregarded, as knowledge of natural blade frequencies is always important. However, the present work has considered a computational structural mechanics (CSM) approach to rotor blade dynamics problems in which the physical properties of the rotor blade provide input for a direct numerical solution of the relevant boundary-and-initial-value problem. Analysis of the dynamics of a given rotor system may require solution of the governing equations over a long time interval corresponding to many revolutions of the loaded flexible blade. For this reason, most of the common techniques in computational mechanics, which treat the space-time behavior concurrently, cannot be applied to the rotor dynamics problem without a large expenditure of computational resources. By contrast, the integrating matrix technique of computational mechanics has the ability to consistently incorporate boundary conditions and 'remove' dependence on a space variable. For problems involving both space and time, this feature of the integrating matrix approach thus can generate a 'splitting' which forms the basis of an efficient CSM method for numerical solution of rotor dynamics problems.

Lakin, William D.↗