Instability regions of a prestressed compound column subjected to a follower force

The influence of prestressing and bending rigidity distribution between rods of a non-linear column on its natural vibrations and stability is studied. The perturbation method is used for solving the problem. Regions of divergence and flutter instabilities for a column have been determined on the basis of courses of eigencurves as a function of bending rigidity ratio and prestress rate. Discontinuities of the critical force have been observed for certain values of the investigated parameters leading to instability of the column, even for small values of the external load. Although each prestress reduces the critical force, it can be applied to passive vibration control.