On a Finite Element Formulation of Dynamical Torsion of Beams Including Warping Inertia and Shear Deformation Due to Nonuniform Warping

We start from the energetical expressions of dynamical torsion of beams in terms of angular and warping displacement and velocity. We derive the stiffness and two mass matrices including both secondary effects for torsion: the shear deformation due to nonuniform warping and the warping inertia. The suitability of these matrices for evaluation modified torsional frequencies is investigated in the case of thick, as well as thin-walled, cross section beams by comparison with analytical and experimental results.