Nonlinear Normal Modes of Highly Flexible Beam Structures Modelled Under the \(SE(2)\) Lie Group Framework

We compute the periodic responses of geometrically nonlinear beam structures modelled using the Special Euclidean \(SE(2)\) Lie group formulation using shooting and pseudo-arclength continuation. Nonlinear normal modes (NNMs) are calculated for a cantilever beam and are compared to those obtained using a reference displacement-based finite element (FE) model with von Kàrmàn strains. Some specificities of the shooting algorithm which are unique to the underlying Lie group framework are discussed.