Coupled flexural-torsional vibration of beams in the presence of static axial loads and end moments

The problem of coupled flexural-torsional vibration of a deep rectangular beam in the presence of a static axial load and an end moment is studied. Closed form analytical solutions are obtained for simply supported boundary conditions. Numerical results are obtained for the coupled frequencies and mode shapes (in terms of the location of axes of rotation of the cross-section) for different values of the load and the geometry parameters. The results show that the predominantly flexural frequencies of coupled flexural-torsional vibration can be obtained as uncoupled flexural frequencies of an equivalent beam-column by defining an effective axial load, and that by defining an equivalent moment parameter the presentation of the results for the predominantly flexural mode can be made in a form independent of the slenderness of the beam in the depth direction.