Torsional warping eigenmodes including the effect of the secondary torsion moment on the deformations

• Influence of torsional warping of twisted beams on their eigenvibrations is investigated.
• Secondary Torsion Moment Deformations (STMDE) due to the angle of twist are considered.
• The investigation is based on the analogy of second-order bending beam theory.
• Non-uniform torsion theory of thin-walled cross-sections is used.
• The numerical investigation is focused on modal analysis of straight beams with consideration of warping.

In this paper the influence of torsional warping of cross-sections of twisted beams on their eigenvibrations is investigated, considering the secondary deformations due to the angle of twist. The investigation is based on the analogy of second-order bending beam theory, including the effect of the deformations due to the shear forces on the deformations, and the non-uniform torsion theory of thin-walled open and closed cross-sections, including the secondary torsion moment deformation effect. The solutions of the underlying differential equations are used for setting up the transfer matrix relations. The numerical investigation is focused on modal analysis of straight beams with and without consideration of warping of doubly symmetric open and closed cross-sections. The influence of the secondary torsion moment on the non-uniform torsional eigenfrequency is also studied and evaluated. The obtained results are compared with the ones calculated by standard solid and warping beam finite elements.