Fig. 4


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Time histories and Fourier transform. Out-of-plane time transient displacement and its Fourier transform for the broad-band excitation for both the ordinary (A, black line) and hierarchical (B, blue line) structures. The signals are acquired immediately after the end of the periodic structure. The Fourier transforms of the signals allow to show the difference of the two responses in terms of frequency content, showing the ability of the hierarchical unit cell to provide large attenuation in the [2.2 − 2.7] Hz frequency range and above 5.1 Hz, in good agreement with the dispersion diagrams reported in Figure 3B and E. BGs calculated in Figure 3B and E are superimposed onto each frequency response, to visually highlight how the frequency responses matches the dispersion diagrams.

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