The low-frequency bandgap characteristics of a new three-dimensional multihole phononic crystal

The development of sub-wavelength acoustic metamaterials such as local resonance phononic crystals is leading new research directions of elastic wavefront control as well as noise attenuation and vibration reduction. In this work, the low-frequency bandgap characteristics of a new three-dimensional local resonance phononic crystal model composed of lead sphere and multihole silicone rubber matrix are studied by finite element simulations. Compared with the reference model without matrix holes (Zhao et al. J. Sound Vib. 303:185, 2007), the first complete bandgap of the designed model possesses a lower starting frequency and a 133.68% relative bandwidth, that is the ratio of the bandwidth to the center frequency. The numerical results imply that the structure exists obvious transmission attenuation in the bandgap frequency range, and the effective mass density turns negative. It could be found that the excitation of torsional resonance mode as dominant mode for bandgap opening is attributed to the addition of the multiple holes, especially the cutting holes in the matrix, giving rise to the widening of bandgap. The effects of the component materials and the geometric parameters on the bandgap are further investigated.