Parallel numerical continuation of periodic responses of local nonlinear systems

The aim of this paper is to develop an efficient and robust parallel numerical continuation method for periodic solutions of local nonlinear systems. In this method, a component mode synthesis method is first employed to reduce the nonlinear system with local nonlinearity; the parallel principle is implemented in the correction part of the classic pseudo-arc length continuation, and the step control strategy is dependent on historical and current information from multiple cores. In addition, a numerical continuation (NC) jumping phenomenon may occur alongside the periodic solution tracking process; a geometrical indicator algorithm based on the frequency–amplitude curve is utilized to prevent NC jumping and enhance the robustness of the tracking behavior. By applying the methodology to a nonlinear energy sink and a rod-fastened rolling bearing rotor system, it is shown that numerical continuation can be employed to calculate periodic solutions efficiently and robustly.