Similitude Analysis of the Frequency Response Function for Scaled Structures

Full-scale testing of the large structures is time consuming and expensive. Scaled-down structures expedite and facilitate the testing process of the large structures. To design a scaled-down structure, a deliberate methodology should be used to ensure the similarity between the full-scale structure and its scaled-down model. Comparison of the frequency response functions of the full-scale structure and its scaled-down model can verify the similarity between two scales. In this study, three composite I-beams with different scales (i.e. small, medium and large) are designed and manufactured. The designed composite I-beams replicate the spar caps and the shear web of a utility-scale wind turbine blade. Frequency response functions of the three beams are measured using a hammer impact test. The scaling laws of the frequency response function are derived using similitude analysis. The derived scaling laws are used to map the frequency response functions of the large and medium beams to that of the small beam. The comparison between the FRF curve of the small beam and the mapped FRF curves of the large and medium beams indicates the similarity of the laminated beams with different scales and demonstrates the effect of the scaling on shear and flexural stiffnesses.