Dynamic instability of damaged beams subjected to a nonconservative axial load

For non-conservative systems flutter and divergence instability can occur depending on the nature of loads, on the boundary conditions and on the structural integrity. In some cases the structural failure can start up as a consequence of damage evolution whose presence produces an alteration of the dynamic properties of the structure and its stability behaviour. In this paper the dynamic stability of multi-cracked Euler-Bernoulli beams subjected to conservative and non-conservative concentrated axial compressive loads is investigated. The exact dynamic stability problem of the beam-column in presence of an arbitrary number of concentrated crack under different boundary conditions are evaluated by means of the exact explicit solution derived by the authors in a recent study [1]. The solution is provided as functions of four integration constants only, irrespective of the number of the cracked cross-sections, to be determined by the standard boundary conditions. The enforcement of the boundary conditions leads to the exact evaluation of the vibration frequencies as well as the flutter and divergence buckling loads and the corresponding eigen-modes of the damaged beam-column subjected to both conservative and non-conservative forces. Several numerical applications are relative to a cantilever beam. The influence of positions, intensities and number of the cracks for different values of nonconservative degree of load are deeply investigated.