Generalised Beam Theory to Analyse the Vibration Behaviour of Orthotropic Thin-Walled Members

This paper presents the formulation of a Generalised Beam Theory (GBT) developed to analyse the vibration behaviour of composite thin-walled members made of laminated plates and displaying arbitrary orthotropy. Initially, the equilibrium equations and corresponding boundary conditions are derived and their terms are physically interpreted, i.e., related to the member mechanical properties. Then, the derived equations are used to study the local and global vibration behaviour of lipped channel members displaying cross-ply orthotropy. The GBT results are validated through a comparison with numerical values obtained from finite element analyses, which employ thin-shell elements to discretise the member. Finally, a brief investigation is carried out in order to assess the variation of the fundamental frequency value and vibration mode nature with the member length.