214 M.E. Asl et al. 0 -50 200 400 600 800 1000 1200 1400 1600 1800 2000 40 30 20 10 0 -10 -20 -30 -40 dB (m/s2/Newton) Frequency (Hz) Medium beam Fig. 21.5 Frequency response function of the medium beam for the drive point 0 -50 -60 -70 -80 -90 100 200 300 400 500 600 700 0 -10 -20 -30 -40 dB (m/s2/Newton) Frequency (Hz) Large beam Fig. 21.6 Frequency response function of the large beam for the drive point also some off axis motion in the x-direction (perpendicular to the y-direction that are not of interest in this study). Because the designed I-beams satisfy the conditions for the complete similarity described by Eq. (21.3), both of the response scaling laws Eq. (21.4a) and Eq. (21.4b) can be used to scale the FRF curves. The FRF of the medium and large beams are scaled to that of the small beam using the derived response scaling law Eq. (21.4a) for comparison of the FRF curves of the designed beams. The stiffness, density and geometry ratios (i.e. œEI, œ¡, œA and œl) were calculated based on Eqs. (21.1c) and (21.1d) and the dimensions of the beams assuming that the modes of the large and medium beams are mapped to their corresponding modes of the small beams (i.e. œn D1). The frequency scale factor œ¨ for the medium and large beams were calculated based on Eq. (21.4b) and were applied to FRF curves of the medium and large beams. The FRF of the small beam and the scaled FRFs of the medium and large beams are shown in Fig. 21.8. According to Fig. 21.8, there is a very good correlation among the FRFs of the three beams for the first five flexural bending modes which
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