Dynamic analysis of thin-walled closed-section beams

The present paper considers the problem of dynamic behavior of thin-walled beams of arbitrary, closed cross-section, by means of an exact solution. Starting from Benscoter's theory, the differential equations of motion are derived by postulating the principle of the virtual work due to a variation of displacements. In the case of simply supported thin-walled beam, a closed-form solution for the coupled natural frequencies of free harmonic vibrations was derived. The method is illustrated by examples and results are compared with analytical results analyzed by Vlasov's theory as well as with FEM results.