Flexural-torsional vibration analysis of axially loaded thin-walled beam

The present paper considers the flexure-torsion coupled vibrations of axially loaded thin-walled beams with arbitrary open cross section, by means of an exact solution. The effects of axial force, warping stiffness and rotary inertia are included in the present formulations. In the case of simply supported thin-walled beam, a closed-form solution for the coupled natural frequencies of free harmonic vibrations was derived by using a general solution of the governing differential equations of motion based on Vlasov theory. The method is illustrated by its application to two test examples, to demonstrate the effects of bending-torsion coupling and axial force on the dynamic behavior of thin-walled beams. Compared with those available in the relevant literature, numerical results demonstrate the accuracy and effectiveness of the proposed method.