Energy-Based Optimal Ranking of the Interior Modes for Reduced-Order Models under Periodic Excitation

This paper introduces a novel method for ranking and selecting the interior modes to be retained in the Craig-Bampton model reduction, in the case of linear vibrating systems under periodic excitation. The aim of the method is to provide an effective ranking of such modes and hence an optimal sequence according to which the interior modes should be progressively included to achieve a desired accuracy of the reduced-order model at the frequencies of interest, while keeping model dimensions to a minimum. An energy-based ranking (EBR) method is proposed, which exploits analytical coefficients to evaluate the contribution of each interior mode to the forced response of the full-order system. The application of the method to two representative systems is discussed: an ultrasonic horn and a vibratory feeder. The results show that the EBR method provides a very effective ranking of the most important interior modes and that it outperforms other state-of-the-art benchmark techniques.