Dynamic Stability Analysis of a Two Free-end Beam Subject to a Non-conservative Following Force

In this paper, dynamic stability of two free-end beam subject to a non-conservative following force has been investigated. In the first step, transverse vibration of beam structure in free-free mode with/without end force by modal analysis and FEM was analyzed and mode shapes and natural frequencies were obtained. Then, dynamic equations of the vibration with using the Galerkin method were solved. It can be seen that with increasing the axial force frequency of transverse the vibration of the beam decreased. Also, flutter phenomenon in the states of axial force much higher than buckling force is observed. Furthermore, in case of non-uniform beam, in free-free mode both flutter and divergence are occurred. It can be concluded that, due to low thrust weight ratio in nowadays flying objects, the effect of flutter on dynamic stability of structure itself is not significant. However, the effect of joint in beam significantly reduces the critical force of flutter.