The rotational frequency response function (RFRF) plays a crucial role in increasing the accuracy of the calculated results of the frequency-based substructuring method. However, RFRFs are often omitted due to the difficulties in the measurement process and limitations of the equipment. This paper presents a scheme of estimating the rotational FRF of an irregular plate structure using the FE model reduction and expansion method. The reduced FE model was introduced using the improved reduction system (IRS) and expanded to the experimental modal model (EMA model) using the system reduction and the expansion (SEREP) method. The FRF expanded method was then employed to derive the translational and rotational FRFs from the expanded EMA model. The accuracy of the expanded FRFs was evaluated with the EMA model of the irregular plate. It was found that the translational and rotational FRFs estimated from the proposed scheme were in good agreement with the EMA counterparts. Furthermore, the patterns of the estimated RFRFs were well correlated with the EMA RFRFs. This work shows that the proposed scheme may offer an attractive alternative way of accurately determining the RFRs of complex structures or structural components.
For frequency-based substructuring (FBS) to be accurate, translational and rotational data must be available at the connection points between substructures. However, obtaining rotational FRFs from experimental modal analyses is very difficult in practice. In this paper, an alternative method for estimating rotational FRFs is proposed using an approximated simplified finite element model (ASFE), modal updating, and mode expansion. The proposed approach was demonstrated on an assembled structure consisting of an irregular plate (test model) and a simple beam (FE model). The SEREP method was used to augment the translational and rotational FRFs to the updated ASFE mode shapes. The expanded rotational FRF of the test model was validated with the measured rotational FRF obtained from a piezoelectric direct rotational accelerometer. The results showed that the proposed approach for FBS correctly predicted the experimental FRF of the assembled structure with 90% accuracy. The FBS method is no longer dependent on the experimental rotational FRF, which is very difficult to measure with the methodology presented here.
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