Dynamic stability of thin-walled composite beams under periodic transverse excitation

The dynamic stability of thin-walled composite beams subjected to transverse external force has been investigated in this paper. The analysis is based on a seven-degree-of-freedom shear-deformable beam theory. A geometrically nonlinear theory is formulated in the context of large displacements and rotations. The regions of instability for simple and combination resonant frequencies are determined by applying Hsu's procedure to the Mathieu equation. This methodology is used for analyzing regions of dynamic instability of simply supported, cantilever and fixed-end beams considering open and closed cross-sections. The numerical results show the influence of the interaction between the forced vibration and the parametrically excited vibrations on the unstable regions size. Besides, the effect of geometrically nonlinear approximations is also analyzed. The analysis is supplemented by investigating the effects of the variation of load height parameter, beam length and fiber orientation angle.