Efficient Model Order Reduction of Structural Dynamic Systems with Local Nonlinearities under Periodic Motion

In many nonlinear structural systems, compared with the local regions with induced nonlinear effects, the main portions of the structures are linear. An exact condensation technique based on the harmonic balance method (HBM) in conjunction with the modal expansion technique is employed to convert the motion equations of such a system to a set of nonlinear algebraic equations that are considerably small and adequately accurate to determine periodic responses. To demonstrate the capability of the suggested method, few case studies consisting of discrete systems with weak and essential nonlinearities are studied, and the results are compared to other methodologies results.