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Results for “eigenvalue problem”

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 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Insights on the Effects of Magnetic Forces on the Efficiency of Vibration Energy Harvesting Absorbers in Controlling Dynamical Systems

This study investigates the effects of magnetic constraints on a piezoelectric energy harvesting absorber while simultaneously controlling a primary structure and harnessing energy. An accurate forcing representation of the magnetic force is investigated and developed. A reduced-order model is derived using the Euler–Lagrange principle, and the impact of the magnetic force is evaluated on the absorber’s static position and coupled natural frequency of the energy harvesting absorber and the coupled primary absorber system. The results show that attractive magnet configurations cannot improve the system substantially before pull-in occurs. A rigorous eigenvalue problem analysis is performed on the absorber’s substrate thickness and tip mass to effectively design an energy harvesting absorber for multiple initial gap sizes for the repulsive configurations. Then, the effects of the forcing amplitude on the primary structure absorber are studied and characterized by determining an effective design of the system for a simultaneous reduction in the primary structure’s motion and improvement in the harvester’s efficiency.

42 ENGINEERING↗
DOE OSTI2025

Filtered Rayleigh-Ritz is all you need

Recent work has shown that the (block) Lanczos algorithm can be used to extract approximate energy spectra and matrix elements from (matrices of) correlation functions in quantum field theory, and identified exact coincidences between Lanczos analysis methods and others. In this work, we note another coincidence: the Lanczos algorithm is equivalent to the well-known Rayleigh-Ritz method applied to Krylov subspaces. Rayleigh-Ritz provides optimal eigenvalue approximations within subspaces; we find that spurious-state filtering allows these optimality guarantees to be retained in the presence of statistical noise. We explore the relation between Lanczos and Prony's method, their block generalizations, generalized pencil of functions (GPOF), and methods based on the generalized eigenvalue problem (GEVP), and find they all fall into a larger "Prony-Ritz equivalence class", identified as all methods which solve a finite-dimensional spectrum exactly given sufficient correlation function (matrix) data. This equivalence allows simpler and more numerically stable implementations of (block) Lanczos analyses.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1971

The equilibrium and stability of the gaseous component of the galaxy, 3

The stability of a self-gravitating, nonrotating, isothermal gas layer threaded by a one-dimensional equipartition magnetic field, immersed in a rigid isothermal layer of stars, is considered with respect to waves with motions in and perpendicular to the X plane, where X is the equilibrium magnetic and gravitational field vectors. When motions are perpendicular to the X plane, the magnetic field hinders gravitational instability, increasing the minimum length necessary to produce instability by the factor (1 + alpha) to the 1/2 power, where alpha is the ratio of magnetic pressure to gas pressure. When motions are in the plane, no such simple analytical solution is found. However, the resulting system of equations reduces to a single fourth order differential equation in the perturbed gas potential that defines an eigenvalue problem for the marginally unstable state when the four appropriate boundary conditions are considered.

Kellman, S. A.↗
NASA NTRS1971

Dynamic response of nonuniform structures to classes of pressure fields

A semi-analytical method is developed for the calculation of the response of nonuniform structures to deterministic and random excitation. The method is based on parametric representations of the impulse response and input functions. With these representations, a class of structures of specified geometry and a class of pressure fields of practical concern can be considered simultaneously in a single analytical calculation of structural response. In engineering applications, the parameters in the impulse response function can be fixed once the numerical solution of the associated eigenvalue problem is available; the input function parameters can be specified given a particular input function or pressure field data. This methodology is applied to nonuniform beams and circular cylindrical shells for which parametric response solutions are derived. The computerized version of these solutions is also presented.

Cottis, M. G.↗
NASA NTRS1972

A NASTRAN correlation study for vibrations of a cross-stiffened ship's deck

To evaluate the effectiveness of NASTRAN for predicting the vibration modes of panels with bending-membrane coupling, a cross-stiffened ship deck was analyzed. In correlation with experimental data, one NASTRAN finite element representation gave results slightly more accurate than a previous analytical solution. Computational time was excessively long, due to the Guyan method of reducing the eigenvalue problem. It is recommended that a more efficient method of matrix reduction be implemented for the lumped mass formulation.

Thornton, E. A.↗
NASA NTRS1972

Sound propagation in duct shear layers.

Consideration of the propagation of sound in a two-dimensional inviscid shear layer for given initial sound pressure profiles. The eigenvalue problem resulting from an assumption of separable solutions in a form first obtained by Pridmore-Brown (1958) is solved numerically. It is shown that although the resulting eigenfunctions cannot be proven to be orthogonal or complete, they can be combined by a least total error squared method to give a good representation of the initial pressure profile. The acoustic pressure in the duct is then easily calculated. The results verify all the predictions made in an earlier perturbation calculation. Moreover, they show that the refraction effect gets saturated at high subsonic Mach numbers and at high frequencies. The proposed technique may be used, if necessary, with impedance boundary conditions at the duct walls.

Shankar, P. N.↗
NASA NTRS1973

Studies in tilt rotor VTOL aircraft aeroelasticity, volume 2

Two methods for natural mode vibration analysis are discussed. The first consists of a direct approach based on a finite element representation of the complete structure as an entity. The mass and stiffness matrices for the complete structure are assembled by properly combining the mass and stiffness matrices of the individual elements into which the structure has been divided. The second approach is that of component mode synthesis. This method is based on the concept of synthesizing the natural modes of the complete structure from modes of conveniently difined substructures, or components, into which the structure has been partitioned. In this way the expedient of reducing the system degrees of freedom, and thus the size of the eigenvalue problem, can be introduced by partial modal synthesis.

Kvaternik, R. G.↗
NASA NTRS1973

Free vibration analysis of spinning structural systems.

This article presents an efficient digital computer procedure, along with the complete listing of the associated computer program, which may be conveniently utilized for the accurate solution of a wide range of practical eigenvalue problems. Important applications of the present work are envisaged in the natural frequency analysis of spinning structures discretized by the finite element technique, and in the determination of transfer functions associated with the dynamic blocks of control systems of spacecraft utilizing gas jets or reaction wheels for attitude control, as well as of spin-stabilized and dual-spin-stabilized satellites. The validity of the Sturm sequence property is first established for the related matrix formulation involving Hermitian and real symmetric, positive-definite matrices, both being usually of highly banded configuration. A numerically stable algorithm based on the Sturm sequence method is then developed which fully exploits the banded form of the associated matrices.

Gupta, K. K.↗
NASA NTRS1973

Eigenvalue uncertainty in stressed structures.

A method is presented for calculating the statistics of the natural frequencies and mode shapes of vibration for a structure acted upon by an external static loading which results in the structure being stressed for eigenvalue analysis. The analytical tools presented apply to the probabilistic eigenvalue problem, and it is apparent that structural parameter uncertainty will significantly influence all aspects of the structure's response. The treatment of a sample problem serves the purpose of furthering understanding for the importance of considering structural parameters as random variables.

Hart, G. C.↗
NASA NTRS1973

Eigenproblem solution by a combined Sturm sequence and inverse iteration technique.

Description of an efficient and numerically stable algorithm, along with a complete listing of the associated computer program, developed for the accurate computation of specified roots and associated vectors of the eigenvalue problem Aq = lambda Bq with band symmetric A and B, B being also positive-definite. The desired roots are first isolated by the Sturm sequence procedure; then a special variant of the inverse iteration technique is applied for the individual determination of each root along with its vector. The algorithm fully exploits the banded form of relevant matrices, and the associated program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be most significantly economical in comparison to similar existing procedures. The program may be conveniently utilized for the efficient solution of practical engineering problems, involving free vibration and buckling analysis of structures. Results of such analyses are presented for representative structures.

Gupta, K. K.↗
NASA NTRS1974

Dynamic transformation method

Eigenvalue problem associated with modal-synthesis vibration analysis of complex structures requires simplifying assumptions for solution. Computer program, Dynamic-transformation Adapted to Modal-synthesis Using Stiffness-coupling, improves computational economy for vibration analysis of complex structures while still considering substructure modes.

Admire, J. R.↗
NASA NTRS1975

Ellipsometer measurements of epitaxial GaAs layers: A concept

Report discusses analysis involving Maxwell's equations formed in a 6-by-6 matrix. By applying boundary conditions at proper points in sample, equation for propagation of light through anisotropic medium is reduced to eigenvalue problem resulting in 4-by-4 matrix.

Desmet, D. J.↗
NASA NTRS1974

Ellipsometric measurements of epitaxial GaAs layers on a GaAs substrate

An extensive examination of ellipsometric equations for anisotropic surfaces and films is reported. It is shown that the reflection matrix can be calculated by writing Maxwell's equations in 6 x 6 matrix form and by applying appropriate boundary conditions at proper points in the development of the formalism, reducing the equation for the propagation of light to an eigenvalue problem using a 4 x 4 matrix.

Desmet, D. J.↗
NASA NTRS1975

Shuttle wing panel stability analysis

The use of the NASTRAN program in the shuttle wing stability analysis is described, and details of the actual structure, the finite element idealization, and the NASTRAN results are given. A comparison of the NASTRAN results with those obtained with another computer program and with hand generated results indicates good agreement. An alternate approach for solving eigenvalue problems is illustrated and shows a considerable savings in computer time. Some emphasis is placed on the relationship of the NASTRAN analysis in the design process bringing out more clearly the contribution of the results and showing the importance of the mode plots. A deficiency in the NASTRAN plate elements when used to model structures made up of intersecting plates is discussed.

Balderes, T.↗