Computing Periodic Responses of Geometrically Nonlinear Structures Modelled Using Lie Group Formulations

This chapter presents a shooting algorithm to compute the periodic responses of geometrically nonlinear structures modelled using a Special Euclidean (SE) Lie group beam formulation. The formulation is combined with a pseudo-arc length continuation method and used to compute the nonlinear normal modes (NNMs) of various structures. Results are compared with a reference displacement-based FE model with von Kármán strains. It is shown that, in contrast to the Lie group model, the von Kármán model cannot adequately capture complex dynamics due to its simplified kinematic assumptions.