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                <term xml:lang="en">sonic crystals</term>
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                <term xml:lang="en">acoustic barrier</term>
                <term xml:lang="en">acoustic metamaterial</term>
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              <p>Broadband acoustic attenuation produced by a three dimensional (3D) locally resonant sonic crystal (LRSC), exploiting both the multiple coupled resonances and the Bragg band gaps, is numerically and experimentally reported in this work. The LRSC is made of square cross-section scatterers arranged on a square lattice and periodically incorporating both quarter-wavelength and Helmholtz resonators along their heights. Local resonators of different types are combined with the periodicity of the system generating multiple coupled resonances at low frequencies and opening Bragg band gaps respectively. This twofold coupling produces a strong broadband attenuation: a large insertion loss (IL), with an average value of 16.8 dB, covering three and a half octaves from 350 Hz to 5000 Hz with a LRSC of 30 cm width. This frequency band corresponds to one of the several railway noise sources (rolling noise, traction auxiliaries , etc.). A simplified 2D LRSC is finally analyzed numerically in a real train-track configuration, showing the efficiency of the proposed design to attenuate the railway rolling noise.</p>
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