A closed-form approximate solution for coupled vibrations of composite thin-walled beams with mid-plane symmetry

Abstract

The purpose of this paper is to develop and present an approximate analysis procedure to estimate the natural frequencies and mode shapes of thin-walled beams with arbitrary open cross-section, made of laminates with mid-plane symmetry. Theory of thin-walled composite beams is based on assumptions consistent with the Vlasov's beam theory and classical lamination theory. The equations of motion for coupled bending-torsional vibrations are derived from the principle of virtual displacements. In the case of simply supported thin-walled beam the frequency equation, given in determinant form, is expanded in an explicit analytical form, which gives the natural frequencies of free harmonic vibrations. For verification, the analytical study by other researchers and the FEM analysis using ANSYS are compared with the current results.