Vibrations of composite thin-walled beams with arbitrary curvature – a unified approach

This paper presents a unified theory for the vibrational analysis of thin-walled composite beams (TWCB) with arbitrary planar axial curvature, variable cross section, and general composite material layup, allowing for the accurate modelling of a large class of composite beams with an accuracy normally achievable only through shell-type finite-element (FE) models, but at a fraction of the numerical cost. The kinematic description is based on the Frenet-Serret frame field, providing a transparent path for transforming the equations of motion from rectilinear to curved TWCB while fully accounting for curvature gradient terms, thereby allowing for the treatment of highly curved geometries. Additional innovations include the use of a novel formulation increasing the accuracy for cases with significant axial-bending-torsional structural coupling, as well as a computationally efficient Isogeometric Analysis (IGA) formulation. The new method has been applied to modal and transient analysis of several test cases where conventional TWCB models are found to yield limited accuracy. The results obtained are almost indistinguishable from those obtained with a full-sized shell-based FE model, at a computational cost which is about two orders-of-magnitude smaller.