A generalization of the Timoshenko beam model for coupled vibration analysis of thin-walled beams

A generalization of the Timoshenko beam model is presented which accounts for the influence of the shear strains, due to non-uniform bending and torsion, on the flexural-torsional vibrations of thin-walled cores with open or closed cross-section. The axial displacement field incorporates the torsion secondary warping as well as the warping terms depending on the shear resultants. It is shown that exact solutions for the interior domain problem can be obtained under proper load conditions. Moreover, a discrete model for the free-vibration analysis is derived by adopting a linear interpolation of the unknown functions and a reduced integration in order to avoid locking phenomena. Various applications are developed, including the case of the coupled vibrations of a shear-core-steel-frame building.