โ Scribed by Nathan Rubinstein; James T. Stadter
No coin nor oath required. For personal study only.
Two lower bound methods are applied to obtain bounds to frequencies of bending vibration of a rotating uniform beam simply supported at one end, free at the other. These methods, in conjunction with the well-known Rayleigh-Ritz procedure, can also be used to provide rigorous upper and lower bounds to a wide variety of vibration problems. The virtues qf the methoda are discussed and numerical results are given.
๐ SIMILAR VOLUMES
The upper bound of the fundamental bending frequency of a rotating uniform Timoshenko beam with general elastically restrained root is derived via Rayleigh's principle. Comparing the upper bound with the results in the existing literature and those obtained by the transfer matrix method reveals that
An elegant and accurate method for determining the number of clamped-clamped natural frequencies of a bending-torsion coupled beam which lie below a specified frequency is presented. The method facilitates an easy and straightforward application of the WittrickWilliams algorithm when finding natural