Zhao H., Liu Y., Wen X., Wen J., Yu D.

As an analogy to electromagnetic wave attenuated by ¡°photonic band gap¡±, sound attenuation for certain frequency range can be achieved by phononic band gap, which comes from a strong periodic modulation in density and/or elastic coefficients. Recently, several articles try to bring the gap of phononic crystal with a reasonable size to low frequency range (around 500Hz) as a more useful sound shield. Conventionally, it is well known that the mass density law can predict the sound attenuation performances in this low frequency range. The improvement of the sound insulation in comparison with the mass law is verified experimentally [Kin Ming Ho et al. Appl. Phys. Lett. 83, 5566 (2003)]. Goffaux et al showed that the gap of bi-component phononic crystal offers better sound attenuation performances than that of the locally resonant, i.e., tri-component phononic crystal, where it is believed that the formation mechanism of the gap in bi-component phononic crystal is due to the periodic lattice, i.e., the Bragg reflection between the adjacent layers [C. Goffaux et al. Phys. Rev. B 70, 184302 (2004)]. In this paper, we present numerical investigations in the transmission of longitudinal wave across finite phononic crystal, composed of layered spheres in silicon rubber. It is show that the rigid body resonance plays an essential role in the formation of the absolute gap. The main mechanism of the rigid body resonance can be explained by a mass-spring model. And a severe sound attenuation can be induced by the rigid body resonance even in one-layer slab. By varying the size and geometry of the structural unit, we can tune the resonant frequency. Finally, a stacked four-layer slab, each layer containing different scatterer, is introduced as an effective broadband sound barrier. The improvement of the sound insulation in comparison with the periodic layered plate is also verified.