Free vibration analysis of thin to thick straight or curved beams by a solid-3D beam finite element method

Abstract

A solid-3D beam finite element method is presented for the vibration analysis of thin to thick beam-like structures. This method is efficient for a spatial beam and considers all mechanical effects: membrane, bending and torsion. The structure is discretized with solid elements and contains several elements throughout the cross-section. Displacement fields of first-order or higher-order beam theories are met by directly applying kinematic relations on the solid finite element model, throughout the cross-section. This leads to a set of linear equations applied at slave nodes. Only the master nodes are kept in the final model, resulting in a model size reduction. The effectiveness of this method is demonstrated through two numerical examples, including a straight and a curved beam. The modal shapes and natural frequencies obtained by the proposed method are compared with the complete solid model and classical beam model. The size of these solid-beam models is slightly larger than that of an approach with classical beam element.