SEARCH · Search NASA
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
In the case of nonmultiple eigenvalues, each of the three real eigenvalue extraction methods available in NASTRAN will, for a given type of normalization, give essentially the same eigenvectors, but this is not so in the case of multiple eigenvalues. This discrepancy is explained and illustrated by considering the example of a NASTRAN demonstration problem that has both multiple and nonmultiple eigenvalues.
Monte Carlo method for estimating eigenvalues of elliptical partial differential equations
A novel and general procedure for obtaining eigenvalues and eigenvectors for multiple frequency ranges in a single NASTRAN execution is presented. The scheme is applicable to normal modes analyzes employing the FEER and Inverse Power methods of eigenvalue extraction. The procedure is illustrated by examples.
A new eigensolution routine, FEER (Fast Eigensolution Extraction Routine), used in conjunction with NASTRAN at Israel Aircraft Industries is described. The FEER program is based on an automatic matrix reduction scheme whereby the lower modes of structures with many degrees of freedom can be accurately extracted from a tridiagonal eigenvalue problem whose size is of the same order of magnitude as the number of required modes. The process is effected without arbitrary lumping of masses at selected node points or selection of nodes to be retained in the analysis set. The results of computational efficiency studies are presented, showing major arithmetic operation counts and actual computer run times of FEER as compared to other methods of eigenvalue extraction, including those available in the NASTRAN READ module. It is concluded that the tridiagonal reduction method used in FEER would serve as a valuable addition to NASTRAN for highly increased efficiency in obtaining structural vibration modes.
A method is presented for calculating the shape sensitivity of a wing aeroelastic response with respect to changes in geometric shape. Yates' modified strip method is used in conjunction with Giles' equivalent plate analysis to predict the flutter speed, frequency, and reduced frequency of the wing. Three methods are used to calculate the sensitivity of the eigenvalue. The first method is purely a finite difference calculation of the eigenvalue derivative directly from the solution of the flutter problem corresponding to the two different values of the shape parameters. The second method uses an analytic expression for the eigenvalue sensitivities of a general complex matrix, where the derivatives of the aerodynamic, mass, and stiffness matrices are computed using a finite difference approximation. The third method also uses an analytic expression for the eigenvalue sensitivities, but the aerodynamic matrix is computed analytically. All three methods are found to be in good agreement with each other. The sensitivities of the eigenvalues were used to predict the flutter speed, frequency, and reduced frequency. These approximations were found to be in good agreement with those obtained using a complete reanalysis.
A method is presented for calculating the shape sensitivity of a wing aeroelastic response with respect to changes in geometric shape. Yates' modified strip method is used in conjunction with Giles' equivalent plate analysis to predict the flutter speed, frequency, and reduced frequency of the wing. Three methods are used to calculate the sensitivity of the eigenvalue. The first method is purely a finite difference calculation of the eigenvalue derivative directly from the solution of the flutter problem corresponding to the two different values of the shape parameters. The second method uses an analytic expression for the eigenvalue sensitivities of a general complex matrix, where the derivatives of the aerodynamic, mass, and stiffness matrices are computed using a finite difference approximation. The third method also uses an analytic expression for the eigenvalue sensitivities, but the aerodynamic matrix is computed analytically. All three methods are found to be in good agreement with each other.
Computer methods for calculating eigenvalue and eigenvectors of real symmetric matrices arising in problems of molecular quantum mechanics
Generalized Rayleigh quotients for calculating eigenvalues and eigenvectors of large matrices
Special modeling techniques were developed to simulate an accurate mathematical model of the transporter/canister/payload system during ground transport of the Inertial Upper Stage/Tracking and Data Relay Satellite (IUS/TDRS) payload. The three finite element models - the transporter, the canister, and the IUS/TDRS payload - were merged into one model and used along with the NASTRAN normal mode analysis. Deficiencies were found in the NASTRAN program that make a total analysis using modal transient response impractical. It was also discovered that inaccuracies may exist for NASTRAN rigid body modes on large models when Given's method for eigenvalue extraction is employed. The deficiencies as well as recommendations for improving the NASTRAN program are discussed.
The present conference on the mechanics of composites discusses microstructure's influence on particulate and short fiber composites' thermoelastic and transport properties, the elastoplastic deformation of composites, constitutive equations for viscoplastic composites, the plasticity and fatigue of metal matrix composites, laminate damping mechanisms, the micromechanical modeling of Kevlar/epoxy composites' time-dependent failure, the variational characterization of waves in composites, and computational methods for eigenvalue problems in composite design. Also discussed are the elastic response of laminates, elastic coupling nonlinear effects in unsymmetrical laminates, elasticity solutions for laminate problems having stress singularities, the mechanics of bimodular composite structures, the optimization of laminated plates and shells, NDE for laminates, the role of matrix cracking in the continuum constitutive behavior of a damaged composite ply, and the energy release rates of various microcracks in short fiber composites.
The problem of optimal placement of active members which are used for vibration control in adaptive truss structures is investigated. The control scheme is based on the method of eigenvalue assignment as a means of shaping the transient response of the controlled adaptive structures, and the minimization of required control action is considered as the optimization criterion. To this end, a performance index which measures the control strokes of active members is formulated in an efficient way. In order to reduce the computation burden, particularly for the case where the locations of active members have to be selected from a large set of available sites, several heuristic searching schemes are proposed for obtaining the near-optimal locations. The proposed schemes significantly reduce the computational complexity of placing multiple active members to the order of that when a single active member is placed.
The dynamics of flexible spacecraft are not usually well known before launch. This makes it important to develop controllers for such systems that can never be destabilized by perturbations in the structural model. Virtual passive controllers, or active vibration absorbers, possess this guaranteed stability property; they mimic a fictitious flexible structure attached to the true physical one. This report analyzes the properties of such controllers, and shows that disturbance absorption behavior can be naturally described in terms of a set of virtual zeros that they introduce into the closed-loop dynamics of the system. Based on this analysis, techniques are then derived for selecting the active vibration absorber internal parameters, i.e., the gain matrices of such controllers, so as to achieve specified control objectives. Finally, the effects on closed-loop stability of small delays in the feedback loop are investigated. Such delays would typically be introduced by a digital implementation of an active vibration absorber. It is shown that these delays only affect the real parts of the eigenvalues of a lightly-damped structure. Furthermore, it is only the high-frequency modes that are destabilized by delays; low-frequency modes are actually made more heavily damped. Eigenvalue perturbation methods are used to obtain accurate predictions of the critical delay at which a given system will become unstable; these methods also determine which mode is critical.
Numerical solution of the MHD wave equations for stability of the cometary sheath determined by the balance between the inward Lorentz body force and the outward ion-neutral drag force is obtained by using a two-point boundary value method. The eigenvalues and the eigenfunctions are obtained numerically by treating the cometary inner sheath as a layer of finite thickness, bounded by the contact surface, i.e., the diamagnetic cavity boundary. The magnetic field structure discovered in the ionosphere of Comets Halley and Giacobini-Zinner is found to be unstable. The effects of finite plasma pressure, dissociative recombination, and mass loading due to photoionization are found to be stabilizing but are unable to quench the instability completely. It is also found that the higher the neutral production rate the lesser is the growth rate for the instability.
The MHD stability of the cometary inner sheath determined by the balance between the inward Lorentz body force and the outward ion-neutral drag force is investigated by numerically solving the wave equations which include resistivity, plasma motion and plasma pressure with the help of two-point boundary value method. The eigenvalues and the eigenfunctions are obtained numerically by treating the cometary inner sheath as a layer of finite thickness, bounded by the contact surface, that is, the diamagnetic cavity boundary. To gain insight into the problem, certain limiting cases of the wave equations are also discussed. The diamagnetic cavity boundary and the adjacent layer of about 100-km thickness of Comet Halley is found to be unstable. The effects of finite plasma pressure, dissociative recombination, mass loading due to photoionization, resistivity, and plasma motion are found to be stabilizing but are unable to quench the instability completely. Motion of the Halley ionopause has been confirmed by observations.
On a swept wing, contamination along the leading edge, Tollmien-Schlichting waves, stationary or traveling crossflow vortices, and/or Taylor-Gortler vortices can cause the catastrophic breakdown of laminar to turbulent flow, which leads to increased skin-friction drag for the aircraft. The discussion in this Note will be limited to disturbances which evolve along the attachment line (leading edge of swept wing). If the Reynolds number of the attachment-line boundary layer is greater than some critical value, then the complete wing is inevitably engulfed in turbulent flow. Essentially, there are two critical Reynolds number points that must be considered. The first is for small-amplitude disturbances, and the second is for bypass transition. The present study will use direct numerical simulations to validate a linear 2D-eigenvalue prediction method based on parabolized stability equations by Lin and Malik. This method is considered because it suggests that a number of symmetric and asymmetric modes exist and are stable or unstable on the attachment line depending on the Reynolds number. If validated, the approach would predict a number of modes which are linearly damped in the Reynolds number regime 100 to 245; however, these modes may grow nonlinearly and provide an explanation to this region.
Radio frequency interference (RFI) can corrupt passive remote sensing measurements taken with microwave radiometers. With the increasingly utilized spectrum and the push for larger bandwidth radiometers, the likelihood of RFI contamination has grown significantly. In this work, an eigenvalue-based algorithm is developed to detect the presence of RFI and provide estimates of RFI-free radiation levels. Simulated tests show that the proposed detector outperforms conventional kurtosis-based RFI detectors in the low-to-medium interference-to-noise-power-ratio (INR) regime under continuous wave (CW) and quadrature phase shift keying (QPSK) RFIs.
Radio frequency interference (RFI) can corrupt passive remote sensing measurements taken with microwave radiometers. With the increasingly utilized spectrum and the push for larger bandwidth radiometers, the likelihood of RFI contamination has grown significantly. In this work, an eigenvalue-based algorithm is developed to detect the presence of RFI and provide estimates of RFI-free radiation levels. Simulated tests show that the proposed detector outperforms conventional kurtosis-based RFI detectors in the low-to-medium interferece-to-noise-power-ratio (INR) regime under continuous wave (CW) and quadrature phase shift keying (QPSK) RFIs.
Development of a numerical method, using the multistep integration approach, in which the buckling and vibration analyses are formulated as a succession of linear eigenvalue problems. The method does not require an estimate of the eigenvector, and once an eigenvalue has been converged good estimates for other eigenvalues are automatically available. This is accomplished through the use of an in-core Householder scheme for solution of the eigenvalue problem. Furthermore, since the method uses an eigenvalue solution, the possibility of missing modes is eliminated.