Refined free vibration analysis of one-dimensional structures with compact and bridge-like cross-sections

The free vibration analysis of beam structures with compact and bridge-like sections is presented in this paper. Refined beam models are used. Their derivation is embedded in the Carrera Unified Formulation (CUF) framework, which allows us to obtain any-order theories with no need for ‘ad hoc’ formulations. Up to fifth-order models are used; classical (Euler–Bernoulli and Timoshenko) beam theories are considered as particular cases of the linear expansion. The finite element (FE) formulation is used in order to analyze arbitrary geometries and boundary conditions. Comparisons with analytical and solid 3D models from commercial code analyses are given. Natural frequencies and modal shapes are investigated. The results have revealed excellent accuracy in the bending frequency computation. Higher-order theories have shown enhanced capabilities to predict more complex phenomena such as torsional frequencies, bending/torsional coupling due to non-symmetrical cross-section and ‘shell-like’ modal shapes characterized by significant cross-section distortions. Moreover, the proposed formulation has shown it is capable in reducing the computational cost significantly.

► The Carrera Unified Formulation deals with any-order beam theories with no need for ‘ad hoc’ formulations.
► Symmetric, asymmetric and thin-walled sections have been investigated.
► Higher-order theories are able to predict bending/torsional coupling.
► Modal shapes characterized by significant cross-section distortions have been detected.
► Higher-order theories are able to predict torsional modes.