Flutter and divergence instability of the multi-cracked cantilever beam-column

For conservative systems instability can occur only by divergence and the presence of damage can produce both a reduction of the buckling loads and modification of the corresponding mode shapes, depending on the positions and intensities of the damage distribution. For nonconservative systems instability is found to occur by divergence, flutter, or both, characterised by multiple stable and unstable ranges of the loads whose boundary can be altered by the damage distribution. This paper focuses on the stability behaviour of multi-cracked cantilever Euler beam-column subjected to conservative or nonconservative axial loads. The exact flutter and divergence critical loads are obtained by means of the exact closed form solution of the multi-cracked beam-column, derived by the authors in a previous paper. The extensive numerical applications, reported in the paper, aimed at evaluating the influence of several damage scenarios for different values of the degree of nonconservativeness. It is shown how the presence of damage can strongly modify the ranges of divergence and flutter critical loads of the corresponding undamaged cantilever column, which has been the subject of several papers starting from the Pflüger paradoxical results.