Energy-based interior mode selection for reduced-order models under harmonic excitation
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This paper introduces a novel ranking method for the selection of the interior modes to be retained in the Craig-Bampton reduction, suitable for vibrating systems under single-or multi-harmonic excitation. The goal is to keep model dimensions to a minimum while preserving system response accuracy. The ranking of the interior modes is carried out using a novel energy-based coefficient, which takes into account the frequency and the spatial distribution of the force exciting the system. The aforementioned coefficients provide a measure of the contribution of each interior mode to the forced dynamics of the full-order system in term of kinetic and potential elastic energy. The technique is general and applicable to any linear time-invariant and undamped vibrating system. The method validation is proposed by applying it to the model reduction of ultrasonic horn, usually employed in ultrasonic welding and modeled through solid finite elements. The numerical test shows that the method proposed here outperforms the other state-of-the-art techniques, by leading to a model with significantly smaller dimensions.