On coupled bending and torsional vibration of uniform beams

Abstract It is known that the Bernoulli-Euler theory of beam flexure may be combined with the Saint-Venant theory of torsion to describe the coupled antisymmetric free vibration of uniform beams having a plane of symmetry [1]. The principal modes may be expressed in terms of tabulated functions. This paper extends the theory to allow for warping of the beam cross-section, for this can make a large difference to results for thin-walled beams of open section.