Spatial free vibration of shear deformable circular curved beams with non-symmetric thin-walled sections

For spatial free vibration of shear deformable circular curved beams with non-symmetric thin-walled cross-sections, an improved vibration theory is proposed. The elastic strain and kinetic energies are first derived by considering constant curvature effects and shear deformation effects due to shear forces and restrained warping torsion. Next equilibrium equations and force–deformation relations are obtained using a stationary condition of total potential energy. And then the closed-form solution for out-of-plane vibration of curved beam is newly derived. In addition F. E. procedures are developed by using isoparametric curved beam element with arbitrary thin-walled sections. In order to illustrate the accuracy and the practical usefulness of this study, closed-form and numerical solutions for spatial free vibration are compared with results by available references and ABAQUSʹs shell element. Particularly not only shear deformation and thickness–curvature effects on vibration behaviors of curved beams but also mode transition and crossover phenomena with change in curvatures and the length of beams are parametrically investigated.