Parametric vibration of thin-walled composite beams with shear deformation

The dynamic stability of thin-walled composite beams, considering shear deformation, subjected to axial external force, has been investigated in this paper. The analysis is based on a small strain and moderate rotation theory, which is formulated through the adoption of a second-order displacement field. The Galerkin's method is used in order to discretize the governing equation and the Bolotin's method is applied to determine the regions of dynamic instability of a simply supported beam. The regions of instability are evaluated, and are expressed in non-dimensional terms. The influence of the longitudinal vibration on the unstable regions has been investigated. The numerical results show that this effect has large influence when the forcing frequency approaches to the natural longitudinal frequency, obtaining parametric instability regions substantially wider. Besides, the effect of shear flexibility is also analyzed for different laminate stacking sequence, considering open and closed cross-section beams.