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Computation of upper and lower bounds to the frequencies of clamped cylindrical shells
Author(s) -
Nau Richard W.
Publication year - 1976
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290040603
Subject(s) - eigenvalues and eigenvectors , rayleigh–ritz method , computation , upper and lower bounds , extension (predicate logic) , vibration , mathematics , limit (mathematics) , matrix (chemical analysis) , mathematical analysis , structural engineering , algorithm , engineering , computer science , physics , boundary value problem , acoustics , materials science , quantum mechanics , programming language , composite material
Methods for obtaining bounds on natural frequencies are demonstrated for the free vibration of thin, clamped cylindrical shells. The upper bounds are obtained by a Rayleigh‐Ritz procedure. The lower bound method used is an extension of one previously applied to simpler structures; the extension is needed to adjust to limit points in a spectrum. For both bounds the problems reduce to matrix eigenvalue problems. Numerical techniques are employed to keep the order of these reduced problems small.