On triply coupled vibrations of thin-walled beams with arbitrary cross-section

The purpose of this paper is to analyze triply coupled vibrations of thin-walled beams with arbitrary open cross-section. Starting from the Vlasov's theory, the governing differential equations for coupled bending and torsional vibrations were performed using the principle of virtual displacements. In the case of a simply supported thin-walled beam, a closed-form solution for the natural frequencies of free harmonic vibrations was derived. The significance of neglecting cross-sectional warping and rotary inertia on the accuracy of results was analyzed. A recent paper on the same subject is discussed, with a critical review of it.