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Results for “Rayleigh-Ritz method”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Analytical and experimental studies of natural vibrations modes of ring-stiffened truncated-cone shells with variable theoretical ring fixity

Experimental and analytical investigations of the vibratory behavior of ring-stiffened truncated-cone shells are described. Vibration tests were conducted on 60 deg conical shells having up to four ring stiffeners and for free-free and clamped-free edge constraints and 9 deg conical shells, for two thicknesses, each with two angle rings and for free-free, free-clamped, and clamped-clamped edge constraints. The analytical method is based on linear thin shell theory, employing the Rayleigh-Ritz method. Discrete rings are represented as composed of one or more segments, each of which is a short truncated-cone shell of uniform thickness. Equations of constraint are used to join a ring and shell along a circumferential line connection. Excellent agreement was obtained for comparisons of experimental and calculated frequencies.

Naumann, E. C.↗
NASA NTRS1973

Variational calculations for resonance oscillations of inhomogeneous plasmas

The electrostatic resonance properties of an inhomogeneous plasma column are reported by application of the Rayleigh-Ritz method. A description of the rf equation of motion and pressure term that expresses the system of equations in Euler-Lagrange form is presented. The Rayleigh-Ritz procedure is applied to the corresponding Lagrangian to obtain approximate resonance frequencies and eigenfunctions. An appropriate set of trial coordinate functions is defined, which leads to frequency and eigenfunction estimates.

Peng, Y. K. M.↗
NASA NTRS1946

The Lagrangian multiplier method of finding upper and lower limits to critical stresses of clamped plates

The theory of Lagrangian multipliers is applied to the problem of finding both upper and lower limits to the true compressive buckling stress of a clamped rectangular plate. The upper and lower limits thus bracket the true stress, which cannot be exactly found by the differential-equation approach. The procedure for obtaining the upper limit, which is believed to be new, presents certain advantages over the classical Rayleigh-Ritz method of finding upper limits. The theory of the lower-limit procedure has been given by Trefftz, but, in the present application, the method differs from that of Trefftz in a way that makes it inherently more quickly convergent. It is expected that in other buckling problems and in some vibration problems the Lagrangian multiplier method of finding upper and lower limits may be advantageously applied to the calculation of buckling stresses and natural frequencies.

Budiansky, Bernard↗
NASA NTRS1973

Computer based analyses of the response of box type structures to random pressures.

Analysis of the vibration of the internal structure of a relatively simple flight vehicle structural model consisting of a multicellular box in which two parallel outer face plates (skins) are connected together by several internal plates (ribs) which are parallel to each other and normal to the face plates. Such a box is representative of a wing or stabilizer structure. Three representations of the structure were considered in the computation. The simplest model which can account for the coupling between the face plates and the ribs is a two-dimensional assembly of beams. A more realistic, yet still simple, three-dimensional model has been developed using the Rayleigh-Ritz method. The third computational method employed was the NASTRAN finite-element displacement method. The computational results are compared with experimental data.

Clarkson, B. L.↗
NASA NTRS1973

Sinusoidal response of composite-material plates with material damping.

A general forced-vibration analysis is presented for laminated anisotropic rectangular plates including material damping. The theory used is the laminated version of the Mindlin plate theory and includes thickness-shear flexibility and rotatory and coupling inertia. A solution is obtained by the Rayleigh-Ritz method, extended to include the energy dissipated and the work done by the excitation. The analysis is applied to prediction of the resonant frequencies and associated nodal patterns and damping ratios of the first five modes for a series of rectangular plates with free edges. The plates considered consist of unidirectional boron-fiber/epoxy composite material with respective fiber orientations of 0, 10, 30, 45, 60, and 90 deg.

Siu, C. C.↗
NASA NTRS1979

Variational description of the positive column with two-stem ionization

The ionization balance in diffusion dominated discharges which depends on both one and two step ionization processes is considered. The Spenke diffusion equation (D sq delta n + neutrino n + sq kn =0) describing such conditions is solved by the Rayleigh-Ritz variational method. Simple analytic approximations to the density profile, and the similarity relation between neutrino,k,D and the discharge dimensions, are derived for planar and cylindrical geometry, and compared with exact computations for certain limiting cases.

Crawford, F. W.↗
NASA NTRS1951

Analytical determination of coupled bending-torsion vibrations of cantilever beams by means of station functions

A method based on the concept of station functions is presented for calculating the modes and the frequencies of nonuniform cantilever beams vibrating in torsion, bending, and coupled bending-torsion motion. The method combines some of the advantages of the Rayleigh-Ritz and Stodola methods, in that a continuous loading function for the beam is used, with the advantages of the influence-coefficient method, in that the continuous loading function is obtained in terms of the displacements of a finite number of stations along the beam.

Mendelson, Alexander↗
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 NTRS1974

Compressible seal flow analysis using the finite element method with Galerkin solution technique

High pressure gas sealing involves not only balancing the viscous force with the pressure gradient force but also accounting for fluid inertia--especially for choked flow. The conventional finite element method which uses a Rayleigh-Ritz solution technique is not convenient for nonlinear problems. For these problems, a finite element method with a Galerkin solution technique (FEMGST) was formulated. One example, a three-dimensional axisymmetric flow formulation has nonlinearities due to compressibility, area expansion, and convective inertia. Solutions agree with classical results in the limiting cases. The development of the choked flow velocity profile is shown.

Zuk, J.↗
NASA NTRS1973

A theoretical analysis of the free vibrations of ring- and/or stringer-stiffened elliptical cylinders with arbitrary end conditions. Volume 1: Analytical derivation and applications

The derivation and application of a Rayleigh-Ritz modal vibration analysis are presented for ring and/or stringer stiffened noncircular cylindrical shells with arbitrary end conditions. Comparisons with previous results from experimental and analytical studies showed this method of analysis to be accurate for a variety of end conditions. Results indicate a greater effect of rings on natural frequencies than of stringers.

Boyd, D. E.↗