AbstractMethods 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 smal
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