On the Interaction of Resonance And Bragg Scattering Effects for the Locally Resonant Phononic Crystal with Alternating Elastic and Fluid Matrices

Three-dimensional (3D) locally resonant phononic crystals (LRPCs) are studied with the aim of optimising the sub-wavelength band gaps of such composites. By analysing their effective acoustic properties, it has been found that the effective acoustic speed of the composite will drop to zero when local resonance arise, and will increase monotonically when Bragg scattering effects occur. Moreover, if the matrix is a low-shear-speed medium, local resonators can significantly reduce the effective acoustic speed of the composite and, therefore, lower the frequency where Bragg scattering effects occur. Hence, a specific LRPC with alternating elastic and fluid matrices is proposed, whose resonance and Bragg gaps are already close in frequency. The fluid matrix behaves as a wave filter, which prevents the shear waves from propagating in the composite. By using the layer-multiple-scattering theory, the coupling behaviour of local resonance and Bragg scattering band gaps has been investigated. Both gaps are enhanced when they move closer to each other. Finally, a gap-coupled case is obtained that displays a broad sub-wavelength band gap. Such proposal excels at the application of underwater acoustic materials since the arrangement of structure can be handily adjusted for tuning the frequency of coupled gap.