Free vibration analysis of cross-ply laminated thin-walled beams with open cross sections: Exact solution

Abstract

The objective of the present paper is to analyze the free vibrations of thin-walled beams with arbitrary open cross section, made of cross-ply laminates with midplane symmetry, by means of an exact solution. The theory of thin-walled composite beams is based on assumptions consistent with Vlasov's beam theory and classical lamination theory. The governing differential equations for coupled bending-torsional vibrations were obtained using the principle of virtual displacements. To simplify the coupled system of differential equations, an ideal center of gravity and shear center were introduced. In the case of a simply supported thin-walled beam, the closed-form solution for the natural frequencies of free harmonic vibrations was derived. The frequency equation, given in determinantal form, is expanded in an explicit analytical form. To demonstrate the validity of this method, the natural frequencies of nonsymmetric thin-walled beams having coupled deformation modes are evaluated and compared with results available in the literature as well as with FEM results. © 2013 American Society of Civil Engineers.