Controlling Nonlinear Dynamics of Systems Liable to Unstable Interactive Buckling

A method for controlling the global nonlinear dynamics of mechanical systems is applied to an archetypal model of a guyed tower. This structure has coincident or nearly coincident buckling modes, and may fail at load levels well below the theoretical buckling load due to complex nonlinear phenomena that decrease the safety and the dynamic integrity of the structure; this often occurs as a consequence of imperfections and of the erosion of the basins of attraction of the safe pre-buckling solutions. So, it is of paramount practical importance to increase the safety of these structures in a dynamic environment. This can be achieved by increasing the integrity of the basin of attraction of the safe solutions, that in the present investigation is attained by a control method that consists in the optimal elimination of homoclinic intersections by properly adding superharmonic terms to a given harmonic excitation. By means of the solution of an appropriate optimization problem, it is possible to select the amplitudes and the phases of the added superharmonics in such a way that the manifolds distance is as large as possible. The results show that this methodology increases the integrity of the basins of attraction of the system and, consequently, the practical safety of the structure.