Multimodal galloping of dense spectra-structures

Nonlinear interaction phenomena among galloping modes of slender structures having several frequencies contained in one or more bands are analyzed. Due to nonlinear modal coupling associated with aerodynamic forces, all the modes of a band are in internal resonance. By referring to a nearly-periodic system consisting of weakly coupled beams and using the multiple scale perturbation method, a system of nonlinear differential equations in the amplitudes and phases of the interactive modes is obtained. Numerical results relative to a two-beam system are presented. In particular, the conditions under which steady-state solutions can occur are determined and their stability is investigated, while the occurrence of periodic motions involving exchanges of energy among the interactive modes is also remarked upon. Attention is given to the influence of small imperfections causing asymmetry of the structure.