
Accession Number : AD0742818
Title : Energy Methods in SelfAdjoint Eigenvalue Problems. II. RitzGalerkin and Related Methods,
Corporate Author : POLYTECHNIC INST OF BROOKLYN N Y DEPT OF AEROSPACE ENGINEERING AND APPLIED MECHANICS
Personal Author(s) : Morduchow,Morris ; Pulos,John G.
Report Date : APR 1972
Pagination or Media Count : 68
Abstract : For linear selfadjoint systems with discrete eigenvalue spectra, the Galerkin, RayleighRitz and modified RayleighRitz methods are shown to yield upper bounds of the eigenvalues, and to converge, in all modes. Methods of obtaining lower bounds of the eigenvalues in all modes by means only of the above energy methods are established. The theory is illustrated by numerical examples, especially on vibrations of nonuniform beams. A simple general theorem and approximation is given for the effect of additional terms in the governing differential equations. These are then applied to vibrations of a beam on a nonuniform elastic foundation. (Author)
Descriptors : (*DIFFERENTIAL EQUATIONS, MATRICES(MATHEMATICS)), (*BEAMS(STRUCTURAL), *VIBRATION), INTEGRALS, SERIES(MATHEMATICS), APPROXIMATION(MATHEMATICS), NUMERICAL INTEGRATION, BUCKLING, NUMERICAL ANALYSIS
Subject Categories : Theoretical Mathematics
Mechanics
Distribution Statement : APPROVED FOR PUBLIC RELEASE