Are There Cases in Which Classical Beam Theories Fail to Compute the Fundamental Frequency?

Beam structures are widely used in many engineering applications. Well-known examples are aircraft wings and helicopter rotor blades in aerospace engineering, and concrete beams in civil constructions. When dealing with this kind of slender structures, one-dimensional (1D) models are the primary engineers' choice. These models are based on the Euler–Bernoulli and Timoshenko theories. The former does not account for transverse shear effects on cross-section deformations. The latter provides a model which, at best, foresees a constant shear deformation distribution on the cross-section. As a result, they both consider the cross-section of the structure as rigid. This strong approximation has basically no effect when dealing with compact cross-sections. But when the cross-section has a more complicated geometry and has thin-walled portions, the approximation has a strong influence on the modelling capability of classical theories. In this work, those aspects are underlined with practical examples. Computationally heavier two-dimensional (2D) and three-dimensional (3D) models are used to model the same structures to build reference results, and they are compared with those obtained with classical 1D models. The attention is given to the modal characteristics and, in particular, to the first frequency. The capability of the classical models to catch the first frequency is here related to geometrical properties of the cross-section.