Advanced models for free vibration analysis of laminated beams with compact and thin-walled open/closed sections

In this paper, refined one-dimensional beam theories are implemented for the free vibration analysis of laminated beams with compact and thin-walled cross-sections. The proposed models are based on the Carrera Unified Formulation, which was formerly introduced for the analysis of plates and shells and recently extended to beam structures by the first author and his co-workers. Carrera Unified Formulation is a hierarchical modelling technique leading to very accurate and computationally efficient finite element theories. According to the latest developments in the framework of Carrera Unified Formulation, refined beam models are implemented using either Taylor-like or Lagrange-like polynomials in order to expand the unknown kinematic variables on the cross-section of the beam. Equivalent single layer models result from the former approach. On the other hand, if Lagrange polynomials are used, layer-wise models are produced. In this work, a classical one-dimensional finite element formulation along the beam length is used to develop numerical applications. A number of laminated beam structures are analyzed and particular attention is given to laminated box beams with open and closed cross-sections. The frequencies and the mode shapes obtained with the present refined beam elements are compared with solid/shell finite element solutions from the commercial code MSC/Nastran and, when possible, with those found in the literature. The modal assurance criterion is used for model-to-model comparisons so as to demonstrate the enhanced capabilities of the proposed formulation in investigating the free vibration characteristics of both compact and thin-walled box laminated beams.