Comparison of linear beam theories

In this paper we consider three models for a cantilever beam based on three different linear theories: Euler-Bernoulli, Timoshenko and two-dimensional elasticity. Using the natural frequencies and modes as a yardstick, we conclude that the Timoshenko theory is close to the two-dimensional theory for modes of practical importance, but that the applicability of the Euler-Bernoulli theory is limited.

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