17 Evaluation of Stop Bands in Periodic and Semi-Periodic Structures by Experimental and Numerical Approaches 175 Fig. 17.5 Instrumented beams suspended in the laboratory and schemes of the experimental set-up 0 500 1000 1500 2000 2500 3000 3500 4000 0 1 2 3 4 5 Frequency (Hz) |λ| Fig. 17.6 Periodic beam with change in the cross-section. Dispersion curves whose dominant frequencies fall within the stop-bands. Figure 17.7b shows the transmission loss coefficient obtained using the Euler-Bernoulli and the Timoshenko theories when 9 cells were considered. Figure 17.7b shows that the Euler-Bernoulli theory predicts the beam behaviour quite accurately in the frequency range considered. It can be noticed that both the theories predict approximately the same position and length of the stop-bands but, as expected, the frequency occurrence of the stopbands for the Timoshenko model is lower then the Euler-Bernoulli one. Figure 17.8 shows a comparison between the results predicted using the two methods. It can be seen that both the methods predict almost the same stop-bands, although stop-bands can be identified more clearly looking at the dispersion curves obtained for the infinite periodic beam. Experimental results are showed in Figs. 17.9 and 17.10. Figure 17.9 shows the amplitude of the frequency-responsefunction for the non periodic beam and the periodic beam respectively, when the beams were excited by a series of single impacts using a miniature impact hammer. Figure 17.9c shows the acceleration-power-spectra of the periodic beam when a
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