21 Similitude Analysis of the Frequency Response Function for Scaled Structures 213 Table 21.1 Geometry and layup of the small, medium and large beams. Beamscale Dimensions (l b3 b1) m3 Layup of the flanges Layup of the shear web Small 0.58 0.05 0.03 [0]2 [˙45] Medium 1.17 0.10 0.06 [0]4 [˙45]2 Large 3.51 0.32 0.18 [0]12 [˙45]6 Fig. 21.3 Hammer impact test on the small (left),medium(middle) and large (right) beams 50 40 30 20 10 0 -10 -20 -30 -40 0 500 1000 1500 2000 Frequency (Hz) dB (m/s2/Newton) 2500 3000 3500 4000 4500 Small beam Fig. 21.4 Frequency response function of the small beam for the drive point to be an I-beam consisting of two identical laminated plates and a sandwich shear web having an overall dimension of 29.3m 2.446m 1.5 m with layup [0 ]100 and ply thickness of t D1.36 mm. The shear web is a sandwich panel with the foam thickness of 160 mm and two face sheets with layup [˙45]50 with an overall thickness of 17.5 mm. Because the blade is tapered throughout its length and the geometry of the structure changes significantly, the geometry of the full-scale component (i.e. the first 1/3 of the Sandia blade from its root) is assumed to have a uniform cross-section whose height along its length was averaged to simplify the analysis. All computations are implemented for the glass/epoxy materials with following material characteristics [24]: E1 D41.8 GPa, E2 DE3 D14 GPa, G12 DG13 D2.63 GPa, G23 D1.83 GPa, ¤12 D¤13 D0.28, ¤23 D0.47. The sizes of the designed beams were chosen based on the manufacturing capabilities and limitation of the test equipment. The scale of the small, medium and large beams were selected to be 1/50, 1/25 and 1/8.33 of the prototype respectively. The flanges of the small beam consisted of two unidirectional plies and the shear web foam was wrapped in a [˙45] glass fabric. Medium and large beams had 4 and 12 unidirectional plies in their flanges and their shear webs have the layup [˙45]2 and [˙45]6 respectively as summarized in Table 21.1. The beams were manufactured and their frequency response functions were measured using a hammer impact test in freefree boundary conditions as shown in Fig. 21.3. The FRF curves of the drive points of the all three beams were measured as shown in Figs. 21.4, 21.5, and 21.6. The comparison of the FRF curves for all three beams within their frequency range are shown in Fig. 21.7. The first five flexural bending modes were measured for all three beams. Only modes in the y-direction are considered in this work; however, the actual measurements shows these five major modes in the y-direction but there are
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