21 Similitude Analysis of the Frequency Response Function for Scaled Structures 215 0 200 400 600 0 200 400 600 800 0 0 50 -50 40 20 0 -20 -40 0 -20 -40 -60 -80 500 1000 1500 2000 2500 3000 3500 4000 4500 Small beam Medium beam Large beam 1000 Frequency (Hz) Frequency (Hz) Frequency (Hz) dB (m/s2/Newton) dB (m/s2/Newton) dB (m/s2/Newton) 1200 1400 1600 1800 2000 Fig. 21.7 Comparison of the unscaled frequency response functions of the small (top),medium(middle) and large (bottom) beams 50 40 30 20 10 0 -10 -20 -30 -40 0 500 1000 1500 2000 2500 3000 3500 4000 4500 Small beam Medium beam (scaled) Large beam (scaled) Frequency (Hz) dB (m/s2/Newton) Fig. 21.8 Comparison of the FRF of the small beam with the scaled FRFs of the medium and large beams suggests the similarity of the dynamic response for the different scales of the I-beams. However, the degree of correlation decreases for the higher modes. According to Eq. (21.2) and the length to height ratios of the beams, both flexural and shear stiffnesses are important in describing the natural frequencies of the beams. The effect of the flexural stiffness is dominant for the first two modes and the shear stiffness becomes dominant for the higher modes. The excellent correlation of the FRFs for the first two modes suggests that scaling has a negligible impact on the flexural stiffness of the beams. However, the decreased level of correlation for the higher modes indicates that scaling has a more significant impact on the shear stiffness of the beams. For fifth flexural bending mode where the shear stiffness is dominant, the resonance peaks shifts toward the higher frequencies for the smaller scales. This observation indicates that the shear stiffness of the designed beams decrease
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