Complex Analysis of Flutter and Buckling of Beams Under Rotational and Transverse Spring Constraints

The flutter and buckling analysis of a beam, subjected to a follower force, is studied theoretically. The beam is constrained by a pair of transverse and rotational springs at one end and fixed at the other end. The effects of the transverse and rotational spring stiffnesses are studied to obtain the transition condition differentiating two distinct types of instability that co-existed in the beam. The critical follower force is derived for both flutter and buckling of the beam. In addition, the variations of the parametric curves for the critical follower force are analyzed, and the abrupt drop or rise points in the curve are taken as the indicators of the transition between different types of instability. The research discussed in this paper may be used as a benchmark for the flutter and buckling analysis of beams. Moreover, this work may provide an accurate model in dealing with the flutter and buckling analysis and design of general beams.