Simulation and stability analysis of periodic flexible multibody systems

The dynamic response of many flexible multibody systems of practical interest is periodic. The investigation of such problems involves two intertwined tasks: first, the determination of the periodic response of the system and second, the analysis of the stability of this periodic solution. Starting from Hamilton’s principle, a unified solution procedure for continuous and discontinuous Galerkin methods is developed for these two tasks. In the proposed finite element formulation, the unknowns consist of the displacement and rotation components at the nodes, which are interpolated via the dual spherical linear interpolation technique. Periodic solutions are obtained by solving the discrete nonlinear equations resulting from continuous and discontinuous Galerkin methods. The monodromy matrix required for stability analysis is constructed directly from the Jacobian matrix of the solution process. Numerical examples are presented to validate the proposed approaches.