Free vibration and spatial stability of non-symmetric thin-walled curved beams with variable curvatures

An improved formulation for free vibration and spatial stability of non-symmetric thin-walled curved beams is presented based on the displacement field considering variable curvature effects and the second-order terms of finite-semitangential rotations. By introducing Vlasov’s assumptions and integrating over the non-symmetric cross-section, the total potential energy is consistently derived from the principle of virtual work for a continuum. In this formulation, all displacement parameters and the warping function are defined at the centroid axis and also thickness-curvature effects and Wagner effect are accurately taken into account. For F.E. analysis, a thin-walled curved beam element is developed using the third-order Hermitian polynomials. In order to illustrate the accuracy and the practical usefulness of the present method, numerical solutions by this study are presented with the results analyzed by ABAQUS’ shell elements. Particularly, the effect of arch rise to span length ratio is investigated on vibrational and buckling behaviour of non-symmetric curved beams.