Comparison of linear beam theories

Labuschagne, A., van Rensburg, N. J., & Van der Merwe, A. J. (2009). Comparison of linear beam theories. Mathematical and Computer Modelling, 49(1), 20-30. DOI: http://dx.doi.org/10.1016/j.mcm.2008.06.006In 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