Abstract
The effect of rotational and translational support flexibility on the fundamental frequency of both an almost-clamped-clamped beam and a flexibly supported cantilever beam is considered. In each case the effect of a rotationally flexible support becomes more pronounced for decreasing values of the length-to-depth ratio. It is shown that the effect of end-fixity on the fundamental frequency can be of a magnitude equal to or greater than that due to the effect of shear deformation or rotatory inertia. Results using Bernoulli-Euler beam theory and Timoshenko beam theory are compared. Expressions are formulated that give the fundamental frequency as a function of the support flexibility, length to depth ratio and fundamental frequency for a rigid support.
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