Geometrically Nonlinear Vibration Analysis of Thin-Walled Composite Beams

Abstract

In this study, accounting for large displacements a geometrically nonlinear theory, which is valid for laminated thin-walled composite beams of open and closed cross sections, is developed. The beam model incorporates a number of non-classical effects such as material anisotropy, transverse shear deformation and warping restraint. Moreover, the directionality property of thin-walled composite beams produces a wide range of elastic couplings. In this respect, symmetric lay-up configuration i.e. Circumferentially Asymmetric Stiffness (CAS) is adapted to this model to generate coupled motion of flapwise bending-torsion-flapwise transverse shear. Initially, free vibration analyses are carried out for the linear model of the shearable and the non-shearable thin-walled composite beams. Similar to the linear model, the displacement-based nonlinear equations are derived by the variational formulation, considering the geometric non-linearity in the von Karman sense. Finally, the static and the dynamic analyses for the nonlinear beam model are carried out addressing the effects of transverse shear, fiber-orientation and sweep angle on the nonlinear frequencies and the static response of the beam.