Similarity Law of Flow-Induced Vibration Considering the Velocity Doppler Effect

The Doppler effect resulting from the discrepancy in flow speed between flight conditions and ground testing conditions is a primary factor contributing to the inconsistency between structural and aerodynamic frequencies. To mitigate the impact of the Doppler effect in ground-based measurements, this study derives a similarity law for flow-induced vibration that accounts for the variation in flow speed. The findings of this research highlight that the key to formulating the similarity law lies in linearizing the natural frequencies of scaled models. To achieve this, a frequency division method is introduced, considering the differences in modal types, such as plate modes, curvature-dominated modes, and intermediate modes. In contrast to the frequency division method, the modal equivalence method offers a more unified expression of the similarity law, which is more practical for engineering applications. This work effectively addresses the Doppler effect in the derivation of similarity laws, providing a theoretical foundation for the accurate measurement of full-scale aircraft vibrations using scaled models.